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Essays in development and experimental economics

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Essays in development and experimental economics

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Content Essays in Development
and Experimental Economics
by
Ashish Sachdeva
A Dissertation presented to the
Faculty of The USC Graduate School
University of Southern California
In partial fullment of the
Requirements for the degree
Doctor of Philosophy, Economics
May 2016
Copyright 2016 Ashish Sachdeva
Contents
Acknowledgments iv
List of Figures vi
List of Tables vii
Abstract viii
1 Introduction 1
1.1 Pathways to Preventive Health . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Choice and Reasoning in Sequential and Simultaneous Games . . . . . . . . 2
2 Pathways to Preventive Health, Evidence from India's Rural Roads Pro-
gram 5
2.1 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 The Program: Pradhan Mantri Gram Sadak Yojana (PMGSY) . . . . . . . 9
2.3 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3.1 Online Management and Monitoring System (OMMS) . . . . . . . . 11
2.3.2 DLHS Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.4 Empirical Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.5 Estimation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.5.1 Usage of Preventive health care . . . . . . . . . . . . . . . . . . . . . 17
2.5.2 Supply . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.5.3 Information and Awareness . . . . . . . . . . . . . . . . . . . . . . . 18
2.5.4 Social Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.6 Discussion and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.7 Tables and Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3 The Path to Equilibrium in Sequential and Simultaneous games 34
3.1 Theory and Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.1.1 The Game . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.1.2 Non-choice data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.1.3 Design and procedures . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.2 Aggregate analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.2.1 Equilibrium play . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.2.2 Alternative theories: empirical best response and social preferences . 43
3.2.3 Occurrence of lookups . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.2.4 Transitions of lookups . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.2.5 Regression analysis: predicting choice from lookups . . . . . . . . . 49
ii
3.2.6 Summary of aggregate analysis . . . . . . . . . . . . . . . . . . . . . 50
3.3 Cluster analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.3.1 Lookup transitions: correct sequence and wandering . . . . . . . . . 51
3.3.2 Cluster based on lookup transitions . . . . . . . . . . . . . . . . . . 52
3.3.3 Clusters and level k . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.3.4 Summary of cluster analysis . . . . . . . . . . . . . . . . . . . . . . . 57
3.4 Individual analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.4.1 Econometric model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.4.2 Estimation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.4.3 Summary of individual analysis . . . . . . . . . . . . . . . . . . . . . 61
3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4 Conclusion 69
4.1 Pathways to Preventive Health . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.2 Choice and Reasoning in Sequential and Simultaneous Games . . . . . . . . 69
References 71
Pathways to Preventive Health . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
Choice and Reasoning in Sequential and Simultaneous Games . . . . . . . . . . . 74
iii
Acknowledgments
To my deity, Radha Rani. There can be no me without your unlimited love
and blessings.
The time spent at USC's Economics department is extremely important to me. It en-
hanced my skills and knowledge in many ways. This dissertation would not have been
possible without the constant support and encouragement of my advisors, faculty and sta
at USC, and my family and friends.
I thank my advisors Juan Carillo and John Strauss. John's constant support and encour-
agement was instrumental in making me the researcher that I am today. I have learnt
a lot about Development economics and research in general through him. He stood by
me; painstakingly going over my project for hours at end. His unwavering faith in my
professional abilities have helped me improve my craft. Juan taught me the methods
of experimental economics. He helped me understand minute details of a project in the
most scientic manner. I appreciate the progress and learning gained from the weekly lab
meetings and discussion with Juan in his oce. I thank him for many hours he has spent
with me talking about research, our project, job market, and many other things, both
professional and personal.
I am also tremendously grateful to Prof. Isabelle Brocas for her constant support, com-
ments, professional and personal advice over the last six years. I thank Anant Nyshadham
for his guidance and support. He has spent many hours discussing my ideas and papers,
he was a big help during the job market. He has been a friend and mentor who has always
encouraged me to become a better researcher and an academician.
I also thank Jerey Nugent, Tridib Banerjee, and Emma Aguila for their comments and
for being supportive of my research agenda.
This journey would have been incomplete without the wonderful set of friends at USC.
I am grateful to Aleks, Niree, Rakesh, Kelsey, Jorge, Mallory, Tushar, Riddhi, Nazmul,
Karrar, Bilal, Ida, Petra, Bahar, Diego, and Yilmaz for their friendship and support.
I thank Young Miller and Morgan Ponder for ensuring that I did not have to deal with
administrative hurdles. I am also grateful for the various fellowships and funding provided
by USC's Dornsife College of Letters and Science, Department of Economics, and the
Graduate School.
All of this would not have been possible without the love and support of my parents: Ravi
Kiran and Rani Sachdeva, my uncle: Surjeet Lal Sachdeva, sister: Priyanka, brother:
Sameer, niece: Aadya, sister in law: Shenny, friends: Rajat and Sumit, my in-laws: Vijay,
Prabha, Mohit, and Khushboo and my extended family and friends.
Finally and most importantly; I owe a lifelong gratitude to my childhood friend and wife
Ruchika who has stood by me through thick and thin over the years. She left her family
iv
and a good job in India and moved with me to the U.S for my dream of getting a PhD.
She has been a constant support in every challenge life has presented us over the course
of this program. I cannot thank her enough for her love.
v
List of Figures
1 Data Creation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2 Probability of a Sanctioned road with respect to village population . . . . . 28
3 Distribution of Villages with Population . . . . . . . . . . . . . . . . . . . . 29
4 Auxiliary Nurse Midwife(ANM) . . . . . . . . . . . . . . . . . . . . . . . . . 30
5 Information Health Worker . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
6 Self Help Group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
7 Village Health Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
8 Sample screenshots of the game with close cells (left) and open cells (right) 41
9 Cluster based on correct sequence (percent correct) and wandering (pre-
correct) for simultaneous (left) and sequential (right) treatments. . . . . . . 54
10 Screenshot of the game: Display 1 . . . . . . . . . . . . . . . . . . . . . . . 65
11 Screenshot of the game: Display 2 . . . . . . . . . . . . . . . . . . . . . . . 66
vi
List of Tables
1 Mean Dierence of Matched and Unmatched Villages . . . . . . . . . . . . . 22
2 Village Level, First Stage regression: Treatment on Cutos . . . . . . . . . 23
3 Preventive Care . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4 Health Povider in the Villages . . . . . . . . . . . . . . . . . . . . . . . . . . 25
5 Information and Awareness . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
6 Social Interaction in a village . . . . . . . . . . . . . . . . . . . . . . . . . . 27
7 Four-player, type-H game (shaded cell is Nash equilibrium). . . . . . . . . . 37
8 Four-player, type-L game (shaded cell is Nash equilibrium). . . . . . . . . . 38
9 Minimum steps of dominance D
s
and cognitive level L
k
necessary to play
Nash. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
10 Probability of Nash (darker shade re
ects higher level k needed for Nash
play). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
11 Equilibrium choice in early (rst 12) and late (last 12) matches for roles 0
and 1 (dierence between early and late signicant at the 10% (*), 5% (**)
and 1% (***) level) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
12 Equilibrium choice based on lookup occurrence (MIN) . . . . . . . . . . . . 45
13 Lookup behavior of subjects who play and do not play Nash. . . . . . . . . 46
14 Percentage of action, payo and non-adjacent transitions for Nash players . 47
15 Percentage of action, payo and non-adjacent transitions for Nash players
conditional on reaching the payo matrix of role 3 . . . . . . . . . . . . . . 48
16 Probit regression of Nash behavior as a function of lookups . . . . . . . . . 49
17 Equilibrium choice based on correct sequence (COR) . . . . . . . . . . . . . 52
18 Summary statistics by cluster. . . . . . . . . . . . . . . . . . . . . . . . . . . 53
19 Statistics by cluster in early (rst 12) and late (last 12) matches. . . . . . . 55
20 Probability of Nash choice by cluster (darker shade re
ects substantial drop
in Nash rates). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
21 Matrix of types correlation (shaded cells for correlations >:90) . . . . . . . 58
22 Estimated type probabilities in simultaneous and sequential treatments . . 59
23 Individual classication in types (N/C = not classied) . . . . . . . . . . . 60
24 Individual classication in types by cluster . . . . . . . . . . . . . . . . . . . 61
25 Payo-Variants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
26 Support table to nd MIN (values are not payos in the game but instead
the cell codes given to facilitate the explanation of MIN) . . . . . . . . . . . 68
vii
Abstract
This dissertation is a two-part essays on development economics and experimental eco-
nomics. In the rst essay "Pathways to Preventive Health, Evidence from India's Rural
Roads Program"

we estimate the impact of a massive nationwide road construction pro-
gram on the usage, provision, and awareness of preventive health care. Under this program,
the government mandates to connect all villages with a population of at least 500 within
the reach of the nearest link road via an all-weather road. Using the population of the
village, we match the household survey data (DLHS-3) with the program placement data
at the village (treatment) level. We use a Fuzzy Regression Discontinuity (FRD) technique
to overcome the problem of endogenous program placement. Our results suggest that the
provision of roads increases the use of preventive health care by women and households.
We further show that this increase in health care usage comes not only from increase in
income or reduction in travel cost but also from: a) increase in the awareness amongst
households and individual, b) improvement in health care supply, and c) increase in social
interaction within and between villages. Our results show additional benets of providing
roads and provides important insights for increasing preventive health care use in devel-
oping countries.
In the second essay "The Path to Equilibrium in Sequential and Simultaneous Games"
y
we study in the laboratory three-player and four-player, two-action, dominance solv-
able games of complete information. We consider sequential and simultaneous versions of
games that have the same equilibrium actions. Our objective is to test whether players
play dierently in the sequential games than in the simultaneous games and in case we see
a dierence in their behavior between these two games, with the help of mousetracking
technique we want to know whether the players also analyze the two games dierently. We
nd slightly more equilibrium choices in sequential than in simultaneous, and an overall
good t of level k theory. Two attentional variables are highly predictive of equilibrium be-
havior in both versions: looking at the payos necessary to compute the Nash equilibrium
and looking at payos in the order predicted by sequential elimination of the strategies.
Finally, the sequence of lookups reveals dierent decision making processes between se-
quential and simultaneous games, even among subjects who play the equilibrium strategy.
Subjects have a harder time nding the player with a dominant strategy in simultaneous
than in sequential. However conditional on nding such player, the unraveling logic of
iterated elimination of dominated strategies is performed (equally) fast and ecient in
both games.

this is co-authored with Rakesh Banerjee
y
this is co-authored with Isabelle Brocas and Juan Carrillo
viii
1 Introduction
This dissertation is a two-part essays on development economics and experimental eco-
nomics. In the rst essay, I study the eect of provision of roads on preventive health care
usage. In the second essay, I use an economic experiment to understand the dierence in
behavior and decision making process between sequential and simultaneous games.
1.1 Pathways to Preventive Health
Around the world, on one hand we see that despite the benets, there is very low preven-
tive health care usage in low-income countries. It is a problem that is hard to understand
and in
uence. On the other hand it is well established that provision of roads lead to
increase in income, consumption, school enrollment, presence of markets etc. In this pa-
per, we combine the two. We want to know if provision of roads can in
uence preventive
health care usage. and in case we see a positive impact on health care usage, we want to
understand the plausible mechanisms through which the increase might happen.
For this we study the program, Prime Minister Gram Sadak Yojna (PMGSY). Under this
program, the government of India mandates to connect all villages with a population of
at least 500 via an all-weather road. This is a massive and an ongoing project, till today
close to 250,000 miles of roads have been constructed under this program. Under this
program roads are provided according to a population cuto criterion. Villages with a
population of more than 1,000 are rst to be provided with a road, followed by villages
with a population of 500 or more. We use this rule based implementation of the program
and apply fuzzy regression discontinuity design to overcome the problem of endogenous
treatment and estimate the unbiased causal impact of road provision on preventive health
care usage, provision and awareness.
We estimate the impacts separately for the two cutos of 500 and 1,000. Most other pa-
pers in Economics, when dealing with similar situation assumes that the eect is the same
for two (or more) cutos and estimate just one average treatment eect. In this paper,
we estimate the eects separately at the two cutos. In fact our results suggest that the
estimated eects are not the same for these two cutos.
For our analysis we use the third wave of District Level Household Survey (DLHS). The
focus of this dataset is providing information on reproductive and child health care. DLHS
is publically available dataset, but it does not let us identify villages in our sample. We use
the village population provided in DLHS-3 to match DLHS dataset with the census. We
then use the census village codes to match this data set with the OMMS (roads provision)
data set. We are able to match around 75% of villages using this method. To the best to
our knowledge, ours is the rst paper to match and use DLHS dataset at the village level.
This is important for analysis, as the treatment is provided at the village level.
Our results suggest that provision of roads lead to an increase in preventive health care
usage. Women in the treatment villages are more likely to seek prenatal care. They are
1
more likely to use modern contraceptive methods like condoms, pills, and sterilization.
They are less likely to use traditional contraceptive methods, like rhythm and withdrawal.
We also nd that Households are more likely to treat water, and are more likely to be
enrolled in a health scheme.
We further explore some of the plausible mechanisms that may lead to this increase in the
health care usage. Earlier literature have shown that provision of roads lead to decrease
in travel cost and an increase in income. Studies on health have shown that these two
factors increases the health care usage, although the elasticity is estimated to be low. In
this paper we explore three additional mechanisms through which roads might increase
health care usage. Although these mechanisms might operate through the channel of low-
ering of travel cost, they deserve their own mention and analysis. These mechanisms are
awareness, health care supply and social interaction.
We show that households in these villages are more likely to be aware of government run
health care programs, like AIDS prevention, prevention of sex selection, TB prevention
program and personal hygiene. We also nd provision of roads improves health care supply
in the villages. The likelihood that the village health guide, Health information worker,
women and child worker and auxiliary midwife being present in the village is higher in the
treatment villages. We also nd that it is more likely that a health camp is organized in
the treatment villages. The village head is more likely to report an improvement in the
primary health center. The third mechanism we explore is of social interaction. Social
interaction has a potential to increase preventive health care usage, for example, a women
is more likely to use a modern contraceptive method if she knows that her neighbor is us-
ing the same method. We nd that social interaction increases in the treatment villages.
Provision of roads increases the likelihood of having a youth club, a women's assembly,
inter-village assembly, self-help group, and a committee for the sick.
Our results provide important insights for increasing preventive health care use in devel-
oping countries. We extend the roads literature to show additional benets of providing
physical connectivity to the villages. We also show that roads not only create physical
pathways but also improves the informational connectivity between regions.
1.2 Choice and Reasoning in Sequential and Simultaneous Games
The order of moves is key in game theory. Despite its importance, our empirical knowl-
edge of the eect of pure sequencing on choice and reasoning is still incomplete. In our
paper we try to ll this gap. We ask the following questions: Are choices dierent between
sequential and simultaneous games? Are decision processes dierent between equilibrium
and non-equilibrium players? Most importantly, are decision processes conditional on
equilibrium choices dierent between sequential and simultaneous games?
To answer these questions, we conduct a lab experiment where subjects play games of
2
complete information. The game is dominance solvable with a unique Nash equilibrium.
We consider two treatments, sequential and simultaneous. The simultaneous and sequen-
tial versions of the game has the same equilibrium actions and require the same reasoning
to reach to that equilibrium actions. We design the game such that in the sequential treat-
ment observing the choice(s) of players who move before you does not provide a direct
help in nding the equilibrium. We keep the same formal representation for the sequential
and simultaneous versions. This is done to abstract away from any framing eect that
might come from the strategic form vs extensive form representation.
In our experiment we also collect non choice data using mouse-tracking technique. Dur-
ing the experiment, payos are hidden behind blank cells. The payos can be revealed
by moving a mouse into the payo cell and clicking-and-holding a mouse button. The
mousetracking software records the occurrence, timing, duration, and sequence of clicks.
We use this data to understand the decision making process of the players.
We nd the subjects almost always played the Nash equilibrium when they have a domi-
nant strategy. When the decision requires a higher level of strategic thinking compliance
to equilibrium decreases.
Next, we try to nd the answer to our rst question: Is there any dierence in choice
between sequential and simultaneous games. We expect the choice to be dierent between
these two games due to two reasons; observation and Anticipation. In the sequential game
subjects observe the choice made by players who move before them. Even though in our
game, this does not directly help the players in nding the Nash equilibrium but this still
reduces the set of feasible outcomes and therefore the complexity of the game. The second
is the anticipation or the cue provided by the sequential order of the game. The rst
player might realize that her action will be observed by last player, this might make it
easier for her to unravel the logic of backward induction. We nd that equilibrium choice
is higher in sequential than in simultaneous, but not widely so. Dierences are signicant
only for the second mover in four-player games. We nd that combination of observation
and anticipation leads to more equilibrium choices in sequential games. Either factor alone
does not warrant a better decision.
Next we look at whether decision processes in dierent between equilibrium and non equi-
librium players. we nd that the decision processes are vastly dierent between these
two players. Subjects who play Nash spend signicantly less time on their own payo.
They are more likely to look at the payos of the player with the dominant strategy. Two
additional attentional variables are predictive of equilibrium behavior. The rst is MIN
(minimum information necessary), captures whether the subject has opened all the payo
cells that are essential to compute her equilibrium action, The second is COR (correct
sequence), captures whether at some point in the decision process the subject has looked
at payos in the order predicted by sequential elimination of strategies. We show that
for subjects who satisfy MIN are 1.5 to 3.5 times more likely to play Nash strategy, and
those who satisfy COR are 2 to 4 times more likely to play Nash strategy. We verify
3
these results using the regression analysis. Interestingly the dummy variable for Sequence
treatment is insignicant in our regression analysis. It suggests that most dierences in
choices between the sequential and simultaneous treatments can be accounted with the
two attentional variables discussed above.
Next we look at our third question, which is, conditioning only on players who play the
equilibrium strategy, whether there is any dierence in the decision making process be-
tween SEQ and SIM games. For this we analyze transitions of lookups, which is a move
from looking at a payo of particular player to looking at payo of a dierent player. We
specically look at backward transitions, transitions from the dominant strategy player
to your own payos and forward transitions, transitions from your payo to the domi-
nant strategy player. We nd although the choices are similar between sequential and
simultaneous treatments, the reasoning is not. The ratio between backward and forward
transitions is around 3:1 in the sequential treatment (75%-25%) and 1.5:1 in the simulta-
neous treatment (60%-40%).
In simultaneous games subjects take signicantly longer time to reach the payo matrix of
the player with a dominant strategy. However, once this matrix is reached, the subsequent
lookup transitions are remarkably similar in both treatments and follow the sequence of
elimination of dominated strategies. This result suggests that even if behavior in both
treatments is similar when the setting is suciently simple, the reasoning process is not:
unveiling the logic of iterated elimination proves harder in simultaneous than in sequential.
Hence, as the game gets more complex, one would expect to observe a bigger dierences
in choices as well.
In this paper, In adition to the above mentioned results, we also show that players in our
experiments who do not play Nash don't do it because they are playing an empirical nash
or they have some kind of social preference but instead this behavior is because of limited
cognition. For our game, level k explains the behavior better than steps of dominance.
Overall, we believe that choice and non-choice data are complementary measures and that
experimental research in that direction will improve our understanding of (the limits to)
human cognition.
4
2 Pathways to Preventive Health, Evidence from India's
Rural Roads Program
3
Low usage of preventive health care is a major challenge in low-income countries today.
This appears surprising as the benet of preventing many of these diseases seems much
higher than their cost. High cost, nancial constraints, lack of information and awareness,
and poor supply are some of the reasons cited to explain the low usage of preventive health
care in low-income countries (See Dupas 2011 for review).
Along with the low usage of preventive health care, we also observe that, much of the
rural areas in these countries remain unconnected to the city or link road. For instance, in
the year 2000, 40 percent of villages in India lacked an all-weather road. Access to roads
can increase preventive health care usage through multiple channels. One of the channels
through which roads can increase health care usage is through reduction in transportation
cost and travel time. Studies have shown that high transportation costs and long travel
time inhibit access to health care (Wong et al. 1987, Gertler et al. 1987, Mwabu et al 1993,
Dow 1999, Adhvaryu & Nyshadham 2012, 2014). Provision of roads can also potentially
improve health care supply, increase household income, increase awareness, and improve
social interaction in the village. All of these factors together can additionally increase
usage of preventive health care.
In this paper, we study the impact of a massive road-building program undertaken
by the government of India on the usage, availability, and awareness of preventive health
care. The government of India launched Pradhan Mantri Gram Sadak Yojana (PMGSY)
in 2000. Under this program, the government of India mandates to bring all villages with
a population of at least 500
4
within reach to the nearest link road via an all-weather road.
The program prioritized the road provision based on population cutos, rst providing
access to an all-weather road to villages
5
with a population of 1; 000 or more, followed by
villages with a population of 500 or more. We exploit this rule-based implementation of the
program to estimate the unbiased causal eects of the program. Using village population,
we match the roads data with the District Level Household and Facility Survey (DLHS-3)
6
at the village level. To the best of our knowledge, this is the rst paper that matches
this data set at the village level. This is a tedious yet important task as the treatment
is provided at the village level. Doing this allows us to better estimate the unbiased
causal impacts of the PMGSY program. We use a Fuzzy Regression Discontinuity Design
(FRDD) to estimate the causal eect of the road-building program.
Our ndings suggest that connecting villages with an all-weather road increases pre-
3
This chapter is co-authored with Rakesh Banerjee
4
250 in case of hilly areas
5
Program implementation was actually based on population of habitations in the village. We classify
the village as treated if at least one habitation gets a new road
6
DLHS 3 is a district level survey conducted in 2007 by the IIPS, Mumbai with the focus of providing
information on use of reproductive and child health care
5
ventive health care usage by the residents of the village. This is an important result for
health policy in low-income countries. In the treatment villages, we nd that women are
more likely to seek antenatal care, to have delivery being conducted by a trained health
personnel and are more likely to use modern contraceptive methods. We also nd that
households are more likely to treat water and are more likely to be covered by health
insurance. We further discuss some of the potential mechanisms through which provision
of roads can lead to this increase in preventive health care usage. Roads can poten-
tially reduce travel cost and time, increase income of households, improve information and
awareness, improve supply of health care services, and improve social interactions within
and outside the village. Even though we cannot separate out the eect that each of these
mechanisms have on preventive health care usage, our results suggest that both the de-
mand and supply side factors are at work. We observe that the households in the treated
villages are more likely to be aware of the various government-run health care programs.
Provision of roads increases the likelihood of various health care workers being present in
the village, health camps being organized, and improvement in the health center. In the
treatment villages, there is an increase in social interaction; these villages are more likely
to have a women's assembly, welfare committee for sick, self-help group and a youth club.
Moreover, in these villages, it is more likely that the village assembly takes decisions on
health related issues. We show that the increase in preventive health care usage comes not
only from increase in income or reduction in travel cost but also from increased awareness,
improvement in health care supply and increase in social interactions. To the best of our
knowledge, this is the rst paper to show this result.
The remainder of this paper proceeds as follows. Section 2.1 summarizes the most
relevant literature on preventive health care and rural roads. Section 2.2 provides descrip-
tion of India's PMGSY road construction program. Section 2.3 explains the data used.
Section 2.4 describes our empirical strategy, Section 2.5 presents the results and Section
2.6 concludes. Tables and gures are provided in Section 2.7.
2.1 Literature Review
Low usage of preventive health care is a major challenge in low-income countries today.
Households in low-income countries spend a signicant portion of their income on remedial
health care. Banerjee et al. (2009), in a study in Hyderabad, India nd that households
spend around 10% of their total expenditure on health care. Dupas & Robinson (2009)
nd similar evidence for rural households in western Kenya. In the United States, out-
of-pocket health expenditure is typically considered unaordable if it is more than 5% of
family income (Shen & McFeeters 2006, Cunningham 2009). In addition, the demand for
remedial health care is price inelastic (Akin et al 1986, Gertler et al. 1987, Akin et al. 1998,
Dow 1999, Sahn et al. 2003, Cohen et al 2011). However, these same households spend
little on preventive health care (Miller et al. 2007, Stockman et al. 2007, Banerjee et al.
6
2010). In addition, demand for these preventive services like prenatal care and chlorination
of water reduces signicantly when travel time to the health care center increases or when
price of service rises above zero (Wong et al 1987, Kremer & Miguel 2007, Cohen & Dupas
2010, Ashraf et al 2010). These ndings appear surprising, as the benet of preventing
many of these diseases seems much higher than their cost (Clasen et al. 2007).
There are several reasons for low usage of preventive health care in low-income coun-
tries. First, travel costs to the health center may be high. Many of the poor areas of
developing countries are not well-connected. Studies have shown that the reduction in
distance, travel time, and travel cost increases the use of formal health care (Acton 1975,
Akin et al 1986, Wong et all 1987, Gertler et all 1987, Gertler & van der Gaag 1990,
Mwabu et al 1993, Dow 1999, Adhvaryu & Nyshadham 2012, 2014). For instance, Wong
et al (1987) show that, among several other factors, accessibility to the health facility af-
fects the amount and quality of prenatal care used. Access to roads can reduce the travel
time and cost to health care. Moreover, access to an all-weather road can reduce the extra
cost of accessing health care during heavy rainfall.
Second, high cost of services combined with low levels of income inhibits health care
usage. Many of the preventive health behaviors require substantial amounts of investment
upfront. Akin et al (1986) show that cost of service signicantly (though inelastically)
depresses use of prenatal care. Several studies show a positive impact of increase in
income on health care usage, though the elasticity is again small. (Newhouse 1977, Parkin
et al. 1987, Hitiris & Posnett 1992, Manning & Marquis 1996, Nyman 1999, Getzen 2000).
Provision of roads has been shown to increase household income and consumption,
reduce poverty, and improve the credit markets in the aected region (Binswanger et al.
1993, Levy 1996, Jacoby 2000, BIDS 2004; Fan et.al 2000, Bakht et al. 2009, Aggarwal
2014). Lokshin & Yemtsov (2005) nds that investment in roads leads to growth in rural
enterprises. Aggarwal (2014)
7
, analyzing PMGSY, India, nds that provision of roads
leads to increase in agricultural investment and an improvement in household income and
consumption.
Third, a poor supply of services reduces usage of preventive health care. There are
important linkages between demand and supply for preventive health care. Poor supply,
either in form of poor services, high absenteeism amongst health care providers, unavail-
ability or poor quality of supplies & equipment, and poor conditions of the health care
facility, discourages usage of preventive health care. Improvements in health care supply
could increase the usage of preventive health care. Wong et al. (1987) nd that quality
of care has a signicant impact on the choice of prenatal care. Banerjee et al. (2010),
for a study in Udaipur, India, nd that the public facilities that are supposed to provide
free immunization have very high absenteeism amongst health care workers and that their
absence does not follow a pattern. This unreliability in services provided by the health
7
Due to data limitations, she is unable to identify the treatment villages and instead uses proportion
of eligible villages in a district that gets a road as her treatment variable.
7
center may deter the households from seeking the services in the rst place. They also
show that holding well-advertised immunization camps with consistent hours of operation
signicantly increases the rates of immunization. Since roads reduce the cost of trans-
portation, it becomes easier for the health care providers to travel to and from the village
and this may reduce their absenteeism. Improvement in roads makes it cheaper to provide
mobile health care services and awareness to these villages. On the margin, roads make
it cheaper to bring in equipment and supplies to the health center. All of these combined
may improve the quality of health care services oered and in turn potentially increase
the usage of health care.
Fourth, households in low-income countries lack information on preventive techniques,
returns to investment, and risks or costs of illness. Success of a health care program will
depend not only on its quality but also on the awareness amongst the users about the
costs and benets of that program. Studies have shown that information about preventive
techniques can aect the behavior of a household (Wilson & Chandler 1993, Cairncross
et al. 2005, Rhee et al. 2005) and people respond to information about health care
(Madajewicz et al. 2007, Jalan & Somanathan 2008, Dupas 2011, Cohen et al. 2011).
Madajewicz et al. (2007) show that informing the households about the unsafe amount
of arsenic in their well's water increased the likelihood that they switched to a safer well.
Similarly, Jalan & Somanathan (2008) show that informing the households about the
fecal bacteria in their drinking water increased the likelihood that they change their water-
purication or water-storage behavior. Evidence presented in these studies seem to suggest
that households in low-income countries often lack basic information on the health returns
to specic behaviors or products. Roads can improve the usage of preventive health care by
an individual or a community not only through the provision of better and improved health
care services but also through improvement in information and awareness. Individuals,
households and community members may become more informed about better health
practices and about the availability of dierent government health programs. In the case
of rural areas of the developing world, where access to the internet is limited and even when
it exists, is of a poor quality, roads play an important role in information transmission.
People in these areas still rely on the physical transmission of information through posters,
pamphlets, loud speakers etc. The provision of roads makes it cheaper and easier for
households to travel outside their villages. Roads also make it easier for government
health awareness programs to reach these villages. This increase in physical movements
may increase awareness amongst these households and, therefore, can potentially increase
usage of health care.
Fifth, levels of social interaction and learning could aect the uptake of preventive
health care. Households (villages) might not only learn from their own experimentations,
but also from that of others (Adelman et. al 2009). Provision of roads (and lowering
of travel costs) makes it easier to have inter-village assembly meetings and to organize
women's assembly, self-help group, and youth groups. These lead to more social interac-
8
tion, learning, and awareness which may further lead to increase in health care usage.
In the existing literature on roads provision, the causal impact of the investments is not
well known as the program placement is often driven by endogenous economic, social, and
political factors (see Binswanger et al. 1993, Jalan & Ravallion 1998). Khemani (2004),
Rogger (2013), and Rasul & Rogger (2013) show evidence of a relationship between polit-
ical competition or bureaucracy and public goods provision. Identication in the earlier
papers is largely based on either the historical routes or on the amount by which the
distance between the region and the road (or rail) diers from the direct straight-line dis-
tance. It has been shown that infrastructure creates long-term path dependency (Bleakley
& Lin, 2012; Berger & En
o, 2013; Jedwab et al. 2013) and, therefore, the validity of
such variables as instruments is questionable. There are few papers that attempt to ad-
dress the endogenous program placement issue by estimating the causal impact using a
dierence in dierence method. These studies show that provision of roads lead to an
increase in income, consumption, student enrollment, reduction in poverty, improvement
in availability of markets (Jacoby 2000, Lokshin & Yemtsov 2005, Mu and Van de Walle
2007, Bakht et al. 2009, Aggarwal 2014). Using a dierence-in-dierence method with
propensity score matching, Lokshin & Yemtsov (2005) nd that investment in roads leads
to growth in rural enterprises. Mu and Van de Walle (2007) use the same method to as-
sess the impact of rural road habitation on market and institutional development in rural
Vietnam, they nd signicant impacts on the development of markets and commercial-
ization. Bakht et al. (2009) estimate a dierenced equation using household xed eects
to examine the impact of rural road project in Bangladesh, they nd that provision of
roads lead to higher agricultural production, lower input and transportation costs, higher
secondary school enrollment, and reduction in poverty. Aggarwal (2014) uses a dierence-
in-dierence strategy to study the impact of PMGSY, India. The author nds positive
impact on investment, income, consumption, and student enrolment. These papers focus
on dierent outcomes than those we study in this paper. In this paper, we use a fuzzy
regression discontinuity technique to analyze the impact of provision of roads on usage,
provision, and awareness of preventive health care. In the following section we discuss the
road provision program in more detail.
2.2 The Program: Pradhan Mantri Gram Sadak Yojana (PMGSY)
Pradhan Mantri Gram Sadak Yojana (PMGSY) was launched on December 25, 2000. Un-
der this program, the government of India mandates to bring all unconnected habitations
8
with a population of at least 500
9
within reach to the nearest link road via an all-weather
8
PMGSY Scheme and Guidelines denes an unconnected habitation as one with population of desig-
nated size located at a distance of at least 500 meters or more (1:5 Km of path distance in case of hills)
from an all-weather Road or a connected habitation
9
250 in case of hilly areas
9
road.
10
The program prioritized the road provision based on population cutos, rst
providing access to an all-weather road to unconnected habitations with a population of
1; 000 or more followed by unconnected habitations with a population of 500 or more.
11
.
The program stipulates that priority should be given to larger unconnected villages and
to roads that incidentally serve other habitations. Under this rule, sometimes a village
with a population in the lower population category might get a road before a village in a
higher category does. For example, a smaller village that falls on the path of a road built
to connect some larger village might get a road before other larger villages. This program
is federally funded but the implementation is left to the states.
In the year 2000, states were asked to prepare a plan of Core Network of roads for
the implementation of the program. The purpose of this Core Network was to identify
the set of roads that are required to provide access to all eligible habitations to a set of
basic health and economic facilities. Only the roads that were part of the Core Network
could be constructed under this program. The core network plan is rst prepared at
the block level
12
, then presented to intermediate panchayat
13
for approval and to the
concerned Members of Parliament (MPs) and Members of Legislative Assembly (MLA)
14
for suggestions. Once an intermediate panchayat approves the plan, it is placed before
the district panchayat
15
for approval. Once approved at the district level, the plan is sent
to state and national level agencies for implementation. As part of this scheme between
2000 and 2014, 138,710 roads were sanctioned of which 102,828 roads, covering 391,991
kms beneting 172,052 habitations, have been completed.
16
2.3 Data
Data creation is one of the key contributions of this paper. For our analysis, we match
the program placement data (OMMS) and the household survey data (DLHS-3) at the
treatment (village) level. Aggarwal (2014), studies the impact of the same program on
income, consumption and enrollment. Due to data limitations, she had to create the
treatment variable at the district level, she uses the proportion of unconnected villages
receiving a road in a district as her measure of treatment. In this paper, we are able to
identify the treatment at the village level. To best of our knowledge, this is the rst paper
to do so for the DLHS data set. Figure 1 below shows our matching procedure.
10
PMGSY Scheme and Guidelines denes an all-weather road is one which is navigable in all seasons
of the year. This implies that the road-bed is drained eectively (by adequate cross-drainage structures
such as culverts, minor bridges and causeways), this does not necessarily imply that it should be paved or
surfaced or black-topped.
11
250 or more in case of hill states, desert areas, and tribal areas
12
An administrative division less than or equal to a subdistrict
13
Rural local self government
14
These are the elected representative to the national assembly and the elected representative to the
State level assembly
15
The district level local self government
16
www.omms.nic.in
10
Figure 1: Data Creation
2.3.1 Online Management and Monitoring System (OMMS)
To promote transparency, the government of India has mandated that the ministry in
charge of any large-scale public program shall make all program-related data publicly
11
available. The data on PMGSY is available online through OMMS. This dataset contains
information on the baseline connectivity status of the habitation, population (used for
eligibility), date of road sanction, and date of road completion (if completed). In this
paper, we use the sanction date of a road to dene our treatment.
17
2.3.2 DLHS Data
We use DLHS-3 for information on household, village, and individual usage and access
to health care. DLHS-3 is a district level survey conducted between December 2007 and
December 2008 by the IIPS, Mumbai, with the focus on providing information on use of
reproductive and child health care. DLHS 3 conducts separate interviews at the village,
household, individual \ever married" woman (15-49 years of age), and individual \un-
married" woman (15-24 years of age). The household interview focuses on information
about household assets, use of health care, mortality, and general information and aware-
ness about various health programs. The interview of an ever-married woman focuses
on her pregnancy history, use of antenatal and post-natal care, immunization of children,
contraception use, fertility preferences, and general reproductive health. A member from
the village
18
is also interviewed and a host of information about the village is collected.
In particular, information is collected on the availability of various health and educa-
tion facilities, accessibility of the village, availability of various types of health providers,
implementation of various government programs, and general functioning of the local self-
government. We use this rich set of information available to analyze the impact of the
road provision on utilization, awareness and provision of preventive health care.
DLHS-3 covered 22; 825 villages in 601 districts from 34 states and union territories
of India
19
. The survey does not identify villages and, hence, cannot be matched directly
to the program placement data. For each village, DLHS-3 provides information on the
census 2001 village population. We use this village population to match the DLHS-3
data set with the census 2001 data. We are able to uniquely match 19; 850 of the 22; 825
(87%) villages interviewed in DLHS-3
20
. Matching the two data sets provides us with
information on census village codes and villages names for all of the DLHS sample. We
then use the village directory of the 2001 Census data to match the DLHS data with the
habitations (or villages) of the OMMS data. OMMS data does not always consistently
provide the census village code, rendering the matching process dicult. We rst match
17
Completion date is when the contract for road construction was completed and when the nal payments
were made to the contractor. This date could be later than the actual road completion date. Sanctioned
date is closer to date of beginning of the construction and since many of these roads are not long, the
sanctioned date is closer to the actual completion of the road. This is similar to Aggarwal (2014)
18
in the following order of availability; the head of the local self government, any other member of the
local self government, teacher, the community health worker
19
http://www.rchiips.org/
20
matching is done at the sub district level. To prevent matching a wrong village, we dropped all villages
that have the same population within a sub district.
12
the habitations that have a correct village code. For the villages that cannot be matched
using village code, we use the village name as the matching variable. The matching was
done at the sub-district level, taking care to remove duplicate names. Using this procedure
we are able to match 16; 158 of the 19; 850 (81.4%) villages. For these 16; 158 villages we
now have the program placement as well as the household survey information.
To check for selection in matching, we compare the mean dierence between matched
and unmatched villages and the results are presented in Table 1. Although we nd signi-
cant dierence in means for many variables, the magnitude of these dierences are usually
small.
OMMS data set (program placement) is at the habitation level which provides in-
formation on whether the previously unconnected habitation got a road under PMGSY.
However, DLHS data set does not identify the habitations for the surveyed individual (or
household or village). Given this, we had three options to create our treatment variable.
First, we could have used proportion of originally unconnected habitations in a village that
got connected. Second was to dene a village being treated if any additional habitation
in the village got connected. This could have created an error in our analysis since we
might have ended up placing an individual (or household) in the treatment group whereas
she might have lived in a habitation that was already connected in year 2000. We use
the third and the cleanest option; we remove all the villages where even one habitation
was connected in year 2000. This leaves us with 5,331 villages. These are villages where
none of the habitations were originally connected. We then classify a village as treated if
at least one habitation in the village gets connected before Dec 2007 (before the survey
period).
2.4 Empirical Strategy
To analyze the causal impact of any program, the best a researcher could hope for is to
have a randomized control trial. In such a case, one could estimate the impact of the
program using a simple OLS
Y
iv
= +T
v
+
iv
whereY
iv
is outcome of individuali living at villagev andT
v
is whether villagev has been
treated or not. Road construction is very investment intensive; this makes a privately run
randomized control trial for road provision unlikely. Government usually has other motives
in providing the road, rendering the exogenous program placement unlikely. Therefore, in
general, we face a problem of endogenous program placement. In such cases, the coecient
would provide a biased estimate of treatment eect as there would be unobservables
which would determine both the treatment and outcome, making T
v
and
iv
correlated.
For example, more politically in
uential or informed communities could lobby better to
get access to roads and these communities might, in general, have higher health care use,
13
thus biasing upwards. On the other hand, government could choose poorer communities
for road building and these communities may otherwise have lower healthcare use, thus
biasing downwards. To get an unbiased casual estimate of impacts of road provision,
one either needs to assign roads randomly to villages or instrument assignment of roads
using some exogenous variation.
In this paper, we use a regression discontinuity (RD) design to estimate causal impacts
of the road construction under PMGSY. The program stipulates an order of priority, where
villages with at least one habitation with a population of 1; 000 or more are to be con-
nected rst, and then villages with at least one habitation with a population of 500 or
more are to be connected
21
. This rule provides us the discontinuity to estimate the impact
of provision of roads. As of the date of the DLHS survey, there are many villages with
populations exceeding 1,000 that are yet to be provided a road. Moreover, contrary to the
population-based priority rule, some habitations that belong to the low population tier
have been provided roads. This could happen because of many reasons, for example, due
to political motivations, or if these smaller villages lie on the direct route connecting a
larger village to the link road. Considering the large scale of the government-run project,
we know that deviations from complete compliance are likely. This can also be seen in our
data, we observe that the probability of receiving the treatment does not change from 0 to
1 as we cross the population threshold. Instead we see a smaller jump in the probability
and, therefore, use a fuzzy RD design.
We, rst, need to show that there is a jump in probability of assignment of roads at pop-
ulation cuto of 500 and 1; 000. i.e. at c equal to 500 and 1; 000
lim
x#c
Pr(T
i
= 1jX
i
=x)6= lim
x"c
Pr(T
i
= 1jX
i
=x)
Here T
i
is the treatment indicator, X
i
is the village population and c is the cuto
(either 500 or 1,000). This discontinuous jump in probability can be seen in Table 2 and
in Figure 2. Table 2 shows the regression results from regressing treatment (provision of
road) on polynomial of village population, village level control variables
22
and two binary
variables: a dummy variable each for whether the village population is greater than or
equal to 500 and 1,000. We can see from Table 2 that the likelihood of a village getting
a road increases by 22.5% at the cuto of 500 and by 15.4% at cuto of 1,000. Similar
result can be seen in Figure 2. Figure 2 shows a smoothed non-parametric t of treatment
on population. We can see that there is a discontinuous jump in the tted values at the
two cutos. Evidence from Table 2 and Figure 2 supports the use of fuzzy RD for our
estimation.
21
from here on we would interchangeably use village population and the maximum of habitation popu-
lations
22
Regression controls for district xed eects, total number of households in the village, whether vil-
lage has drain, electricity, ICDS center, Sub-Center (health center), Primary Health Center, Government
Dispensary, distance to the nearest town, district head quarter and railway station.
14
In case of fuzzy RD, the average treatment eect is equal to

FRD
=
lim
x"c
E[YjX=x]lim
x#c
E[YjX=x]
lim
x"c
E[TjX=x]lim
x#c
E[TjX=x]
where Y is the outcome variable of interest, X is the running variable, T is the treatment
indicator and c is the cuto. We use the two-stage least squares method to estimate the
causal impact of provision of roads. In a typical setting we would have the following rst
and second stage
First Stage equation: T
i
=
1
+
o
D
i
+f
1
(x
i
) +H
i
+
i
Second Stage equation: Y
i
= +
o
T
i
+f
2
(x
i
) +H
i
+
i
Here, Y is the outcome variable, T is the treatment indicator, D is a dummy to indicate
whether an individual is above or below the cuto, f
1
and f
2
are polynomial functions of
the running variable and H are the other control variables. For our analysis, we slightly
modify the equations to incorporate two cutos. We instrument the treatment status of a
village with binary variables of whether the village has any habitation with a population
exceeding 500 or 1; 000. We estimate the treatment eect using the following specication.
First Stage:
T
ivd
=
0
+
1
X
vd
+
2
X
2
vd
+
3
X
3
vd
+
4
D
1
+
5
D
2
+
d
+H
ivd
+
ivd
To estimate the treatment eect at the two cutos, we estimate the modied second stage.
Second stage (A) is used to estimate the treatment eect at cuto 2 (1,000) and Second
stage (B) is used to estimate the treatment eect at cuto 1 (500)
Second stage (A):
Y
ivd
=
0
+
1
X
vd
+
2
X
2
vd
+
3
X
3
vd
+
4
T
ivd
+
5
D
1
+
d
+H
ivd
+
ivd

4
is the treatment eect at the population cuto of 1,000
Second stage (B):
Y
ivd
=
0
+
1
X
vd
+
2
X
2
vd
+
3
X
3
vd
+
4
T
ivd
+
5
D
2
+
d
+H
ivd
+
ivd
15

4
is the treatment eect at the population cuto of 500
Where T
ivd
is treatment status
23
of an individual (or household or village)
24
i living
in village v located in district d, X
vd
is Population of village
25
v located in district d,
D
1
=I(Population>= 500), D
2
=I(Population>= 1000). Since the plans were drawn
at the district levels, we include the district xed eects (
d
) to control for unobserved
factors at the district level. H
ivd
are other control variables. Village equations control
for total number of households in the village, distance to the nearest town, district head
quarter, and railway station, whether village has a drain, ICDS center, sub-center (health
center), primary health center, and government dispensary. Household equations controls
for the village level control variables and the following additional household level variables:
whether household own the house, own any other house, own agricultural land, have a be-
low poverty level card, number of females in the household, whether the household head
is a muslim. Individual equations control for the village and household level control vari-
ables, person's age, person's age at marriage, and whether the individual attended school.
By controlling for D
1
in the Second stage (A), we account for the jump in the outcome
Y
ivd
that might arise because of the discontinuous jump in assignment of treatment at 500.
Thus
4
in second stage (A) gives the treatment eect at the cuto of 1; 000. Similarly,

4
in the Second stage (B) provides treatment eect at the cuto of 500. By estimating
two separate second stage equations, we allow the treatment eect to vary at dierent
cutos. Alternatively, we could have estimated a single second stage equation without
including the dummy variable for the cutos. Interpreting the
4
coecient in this case
would require an additional assumption. We would have to assume that the local average
treatment eect at the two cutos is the same or it is some weighted average of the two
local average treatment eects where the weights are not clearly understood. Instead in
this paper, we separately estimate the local average treatment eect at the cuto of 500
and 1,000. Doing this requires less assumptions than the alternate method.
2.5 Estimation Results
To analyze the impact of provision of roads on health care, we use the data from the
village, household and individual surveys of DLHS-3. Using these surveys, we estimate
the impact of provision of roads on usage, awareness, and provision of health care. For
each of the variables discussed below, we estimate the two equations described in the
23
A village is dened as treated if it gets connected by a road before end of December 2007. This
treatment status will not vary across individuals within a village
24
The village equations have no \i' subscript in them
25
Actually it is the maximum of populations of dierent habitations in a village
16
previous section.
2.5.1 Usage of Preventive health care
Results for usage of preventive care are presented in Table 3. Panel A (B) in the table
estimates the average treatment eect at the population cuto of 1,000 (500). In these
regressions we include district xed eects, third degree polynomial in village population
and individual, household, and village level control variables. The rst eight columns of
the table are variables from the individual survey and next two are from the household
survey. The rst three columns presents the results for variables related to child-birth:
whether the mother sought antenatal care, did the delivery happen at home, and, in case
the delivery happened at home, was it done by a formal health care provider? Next
ve variables are related to contraceptive use. We look at various contraceptives used:
female sterilization, male sterilization, pill, condom and rhythm or withdrawal method.
The last two variables in the table are from the household survey: whether the household
treats water and whether a member of the household is enrolled in any government health
scheme.
Our results show a signicant improvement in preventive health care use by women and
household. For villages with the population of 1,000 and above, our results indicate that
women in these villages are 20% more likely to seek antenatal care. We do not observe any
change in the probability of the child delivery at the formal health care center. However,
when women have delivery at home it is 8% more likely that the delivery was conducted
by a trained health care personnel. Results on the contraceptive methods used show that
women in treatment villages rely more on female sterilization and substitute away from the
rhythm or withdrawal method. Women are 12% less likely to use rhythm or withdrawal
method.
This move away from traditional contraceptive methods is an important result in the
context of rural India where literacy rate amongst women is still low. Rosenzweig &
Schultz (1989) show that all women in the United States have a comparable success rate
with passive contraception methods such as the pill but women with a higher education
level are much more successful at using the rhythm method. One puzzling observation we
make is a drop in likelihood of women using pill method of contraception. We do not have
a good explanation for this result but we do observe an increase in female sterilization
by a similar magnitude. Results on the household variables show that households in the
treatment villages are 3% more likely to be enrolled in a government health scheme. We
see a positive, but insignicant eect on the likelihood of treatment of water by these
households.
For the villages with the population of 500 and above, we see a positive eect on female
sterilization, and male sterilization. The likelihood that a women uses pill increases by
3.5%. Households are 5% more likely to treat water. We do not see any signicant eect
17
on other variables.
Next, we present results on some of the channels through which use of preventive
health care might increase.
2.5.2 Supply
As discussed before, usage of preventive health care has been shown to increase with
increase in income, improvement in health care supply, information and awareness, and
social interaction. Previous studies on road provision and improvement have shown that
provision of roads leads to increase in income and consumption. We do not pursue these
variables in this paper. We do, however, estimate the impact of road provision on other
factors that can possibly aect preventive health care usage. Table 4 presents the results
for some of the supply side variables. For villages with a population of 1,000 or more, we
see that the likelihood of having an information health worker in the village increases by
30%. Information health worker is known as the Accredited Social Health Activist (ASHA)
worker. ASHA's
26
are local women trained to act as health educators and promoters in
their communities. For the treatment villages, the likelihood of them having an auxiliary
nurse mid-wife increases by 25%. We observe a negative, but insignicant, eect on the
likelihood of these villages having a traditional healer.
For the villages with a population of 500 and more, we nd an increase in the likelihood
of the village having a health guide (increase of 11%), ASHA worker (12% increase) and
having a health camp organized in village (16% increase). We also nd a positive (but
insignicant) impact on the presence of an auxiliary nurse midwife and mother and child
health worker
27
.
2.5.3 Information and Awareness
Table 5 presents the results on the impact of roads on awareness and information. In the
household survey, the respondent was asked about her awareness of various government-run
health-related programs. We report here the results for awareness on AIDS, TB, prevention
of sex selection, and personal hygiene. For the villages with population of 1,000 or more,
we observe that the likelihood that a household is aware of the TB program increases by
12% and that has heard about the prevention of sex selection program increases by 13.8%.
Results for AIDS and personal hygiene are positive but insignicant.
26
The Indian Ministry of Health and Family Welfare describes them as health activist(s) in the commu-
nity who will create awareness on health and its social determinants and mobilize the community towards
local health planning and increased utilization and accountability of the existing health services.
27
known as ICDS worker; ICDS is a government of India sponsored program. It is a social welfare
scheme to tackle malnutrition and health problems in children below 6 years of age and their mothers.
The main beneciaries of the program are children below 6 years of age, pregnant and lactating mothers,
and adolescent girls.
18
For the households with the population of 500 or more, we nd that the likelihood that
the households are aware of the AIDS program increases by 6%, TB program increases by
3.8%, and prevention of sex selection increases by 3%.
Results discussed in this section are of great importance in the developing country
context. Previous studies have argued that information about preventive techniques can
aect the behavior of the households and that people respond to information about health
care. Success of any health program not only depends on the quality of the program
but also on the awareness about its costs and benets. Improvement in awareness is an
important rst step towards changing the behavior of households in low-income countries
towards preventive health care.
2.5.4 Social Interaction
Household might not only learn from their own experimentation, but also from others.
Increased social interaction could lead to increased information and awareness. Results in
this sub-section show the impact of provision of roads on social committees and groups
present in the village. Panel A of Table 6 presents the results for villages with population
of 1,000 or more. We see that for the treatment villages, provision of roads increases the
likelihood of the presence of a youth club by 37%, a women's body by 6%
28
, a self help
group by 25%, and a welfare committee for sick by 31%. The likelihood that the inter-
village assembly takes a decision related to health increases by 35%.
The eects are similar for the villages with population of 500 or more; the likelihood that
a village has a women's body increases by 18% and has a self-help group increases by 22%.
The results for other variables are positive but insignicant.
These changes in preventive health care usage have signicant implications in context
of low-income countries. Studies have shown that changes in preventive health care be-
havior leads to improvement in health and other economic outcomes. Use of prenatal
care have been shown to improve child's birth weight (Gajate-Garrido (2013), Jewell and
Triunfo (2006)). Delivery at a health facility reduces child mortality (Maitra (2004)). Use
of contraception have been shown to reduce the likelihood of maternal death, postpone
the timing of birth of the rst child, and increase the number of years of schooling for
women. (Schultz (2007), Miller (2010), Ahmed et all (2012)). These results suggest, that
provision of roads can lead to improvement in health, reduction in mortality and increase
in educational attainment.
2.6 Discussion and Conclusion
This paper evaluates the impact of a massive nationwide road construction project (PMGSY)
on health care use, awareness and provision. For our analysis, we match the third wave of
28
the result is positive but insignicant
19
DLHS data set with the program placement data at the village level. Matching the data
set at the village level is important for our analysis as the treatment is provided at the
village level. To the best of our knowledge this is the rst paper to match and use DLHS
dataset at the village level.
Our results show that connecting villages with an all-weather road increases the usage
of preventive health care. Women are more likely to use antenatal care, to have the
delivery of their child performed by a trained health personnel, and are more likely to use
modern contraceptive methods. Households are more likely to treat water and are more
likely to be covered by health insurance. This increase in health care usage can come from
various channels. Earlier studies have shown that provision of roads lead to lowering of
travel cost and an increase in income. These are important factors, however, these direct
eects are not the only channels that can explain this increase in health care usage. In this
paper, we show three other channels (awareness, supply, and social interaction) through
which provision of roads can lead to an increase in health care usage. Although these
additional channels might operate through the lowering of cost but they deserve their own
mention and analysis. We nd that provision of roads: a) Improves supply; the likelihood
of presence of various formal health care workers is higher in the treatment villages. These
villages are more likely to have a health information worker, a village health guide, child
and women's health worker, and an Auxiliary Nurse Midwife (ANM). It is more likely
that a health camp is organized in these villages. b) Increases social interaction; there is
an increase in various group activities in the village. Villages are more likely to have a
women's assembly, welfare committee for sick, youth club and it is more likely that the
village assembly takes decisions on health related issues. c) Increases awareness; we nd
the likelihood that households are aware of the government-run health programs is higher
in the treatment villages. To the best of our knowledge, this is the rst paper to estimate
the impact of road provision on transmission of knowledge. It appears that roads not
only create physical pathways but also improves the informational connectivity between
regions.
There are few qualications of this paper, that also opens up various future research
questions that need to be answered for a better understanding of the benets of physical
connectivity. First, in this paper the inter-linkages between various aspects of health care
use, service and awareness is not analyzed. The data set we use, does not allow us to
distinguish between the dierent possible mechanisms at work. For instance, it is possible
that the presence of health care workers leads to more awareness and, consequently, higher
use of health care. However, it is also possible that improved connectivity can lead to
higher income and, consequently, higher investment in preventive health care. Second,
our results only provide the evidence of short run benets of road provision. It would be
important to evaluate the longer run benets of such a program. Benets in the longer run
could be signicantly dierent than what is observed in the short run. The road provision
might lead to a higher income in the longer run and can increase the investments in
20
preventive health care further. Third, due to lack of data, we are unable to study the
impact of road provision on health outcome variables.
Despite the above mentioned qualications, results in this paper can serve as impor-
tant guidelines for improving health care use in developing countries. It is important for
optimal policy to know the benets and costs of such a massive road-building program.
This paper provides insight into the health care benets of providing road connectivity
to a village. We show that in addition to the already studied benets, like reduction in
poverty, increase in income, consumption, and availability of markets, provision of roads
also positively impacts preventive health care usage, provision and awareness. These ad-
ditional benets should be incorporated while evaluating the costs and benets of such
investment intensive project.
21
2.7 Tables and Figures
(1) (2) (3)
UnMatched Matched Dierence
Village has a Drain .282 .353 -.070

(.0055) ( .0038 ) (.0068)
Village has Electricity .796 .850 -.054

(.0049) (.0028) (.0054)
Distance to nearest town (km) 16.48 15.06 1.42

(.2165) (.1132) (.2245)
Distance to district head quarter(km) 48.15 48.55 -.397
(.5531) (.3554) (.6575)
Distance to nearest railway station(km) 64.42 51.87 12.55

(1.686) (.803) (1.655)
Distance to nearest bus station(km) 8.60 7.87 .73

(.163) (.098) (.186)
Has a road to Sub-Center .774 .801 -.027

(.0051) (.0031) (.0059)
Has a road to Primary Health Center .724 .745 -.021

(.0055) (.0034) (.0064)
Has a road to Block Primary Health Center .633 .626 .007

(.0060) (.0038) (.0070)
Has a road to Community Health Center or Rural Hospital .660 .694 -.034

(.0058) (.0036) (.0067)
Has a road to District Hospital .680 .713 -.033

(.0057) (.0035) (.0066)
I.C.D.S present .90 .94 -.04

(.0037) (.0019) (.0038)
Sub-Center present .38 .42 -.04

(.0060) (.0039) (.0071)
Primary Health Center present .15 .118 .03

(.0043) (.0025) (.0048)
Government. dispensary present .106 .062 .043

(.0037) (.0019) (.0038)
Observations 6,666 16,158
Standard errors in parentheses. For binary variables the gures are proportions.

signicant at 10 percent level,

signicant at 5 percent level,

signicant at 1 percent level
Table 1: Mean Dierence of Matched and Unmatched Villages
22
Linear Regression
Y: Roads (Treatment) Coef. Std. Err. t p value
Cuto1 (500) 0.225*** 0.0171 13.16 0.000
Cuto2 (1,000) 0.154*** 0.022 6.97 0.000
District Fixed eects Yes
Third degree Population polynomial Yes
Controls Yes
Mean of Dep. 0.32
SD of Dep. 0.466
N 5,331
F (Cuto1) 173.22
F (Cuto1) 48.53
Controls for district xed eects, total number of households in the village, whether
village has drain, electricity, ICDS center, Sub-Center (health center), Primary Health
Center, Government Dispensary, distance to the nearest town, district head quarter
and railway station.
Robust Standard Errors are in the Parenthesis.
* signicant at 10 percent level, ** signicant at 5 percent level ,*** signicant at 1
percent level
First Stage: T
vd
=0 +1X
vd
+2X
2
vd
+3X
3
vd
+4D1 +5D2 +
d
+H
vd
+
vd
.
Where T
vd
is Treatment status of an village v located in district d , X
vd
is Pop-
ulation of village v located in district d, D1 = I(Population >= 500), D2 =
I(Population>= 1000),
d
are district xed eects andH
vd
are village level controls
Table 2: Village Level, First Stage regression: Treatment on Cutos
23
Panel A-Cuto 1,000
Individual: Birth Individual: Contraceptive Use Household
Used Ante-Natal Place of Person of Female Male Pill Condom Rhythm Treat Health
Care Delivery, Delivery, Sterilization Sterilization and Water Scheme
Home Formal Withdrawal
Roads .205*** -.003 .080* .070* -.007 -.057* -.003 -.126** 0.037 .031*
(.080) (.063) (.048) (.041) (.007) (.031) (.024) (.054) (.049) (.018)
R-Squared .190 .166 .052 .242 .062 .129 .095 .205 .345 097
Mean of Dep. .624 .709 .068 .302 .010 .108 .080 .197 .244 .025
SD of Dep. .484 .454 .252 .459 .098 .310 .271 .398 .430 .155
F (First Stage) 47.03 47.04 35.87 50.10 50.10 50.10 50.10 50.10 46.62 46.64
N 46,346 46,345 33,251 115,090 115,090 115,090 115,090 115,090 135,751 135,870
Panel B-Cuto 500
Individual: Birth Individual: Contraceptive Use Household
Used Ante-Natal Place of Person of Female Male Pill Condom Rhythm Treat Health
Care Delivery, Delivery, Sterilization Sterilization and Water Scheme
Home Formal Withdrawal
Roads .003 -.016 -.003 .044* .015** .035** .011 .001 .050* .013
(.053) (.042) (.033) (.024) (.006) (.017) (.015) (.029) (.029) (.010)
R-Squared .215 .166 .064 .245 .060 .133 .095 .218 .344 .101
Mean of Dep. .624 .709 .068 .302 .010 .108 .080 .197 .244 .025
SD of Dep. .484 .454 .252 .459 .098 .310 .271 .398 .430 .155
F (First Stage) 118.92 118.81 92.05 166.40 166.40 166.40 166.40 166.40 167.29 167.64
N 46,346 46,345 33,251 115,090 115,090 115,090 115,090 115,090 135,751 135,870
Controls for district xed eects, age, age at marriage, whether attended school, whether household own the house, own any other house,
own agricultural land, have a below poverty level card, number of females in the household, religion of the household head, total number of
households in the village, whether village has drain, ICDS in village, Sub-Center (health center) in village, Primary health center, Government
dispensary, distance to the nearest town, district head quarter and railway station.
Treat Water and Health Scheme are questions at the household level. Household level regression do not control for individual level controls.
Robust Standard Errors Clustered at the Village Level are in the Parenthesis.
The First Stage for the all Models is Tivd =0 +1Xvd +2X
2
vd
+3X
3
vd
+4D1 +5D2 +d +Hivd +ivd.
Panel A, Cuto 1,000 Second Stage: Yivd =
0 +
1Xvd +
2X
2
vd
+
3X
3
vd
+
4Tivd +
5D1 +d +Hivd +ivd

4 is the Treatment eect at 1000
Panel B, Cuto 500 Second Stage: Yivd =
0 +
1Xvd +
2X
2
vd
+
3X
3
vd
+
4Tivd +
5D2 +d +Hivd +ivd,

4 is the Treatment eect at 500
Where Tivd is Treatment status for an individual (household) living in village v located in district d , Xvd is Population of village v located
in district d, D1 =I(Population>= 500), D2 =I(Population>= 1000), d are district xed eects and Hivd are individual, household and
village level controls
* signicant at 10 percent level, ** signicant at 5 percent level ,*** signicant at 1 percent level.
Table 3: Preventive Care
24
Panel A-Cuto 1,000
Village Health Information Auxiliary Nurse Mother and Child Traditional Health
Guide Health Worker Midwife Health Worker Healer Camps
Roads .181 .308** .251* .033 -.099 -.023
(.124) (.123) (.146) (.051) (.136) (.113)
R-Squared .211 .317 .265 .556 .247 .258
Mean of Dep. .189 .681 .582 .902 .254 .172
SD of Dep. .392 .466 .493 .298 .435 .378
F (First Stage) 48.55 48.55 48.55 48.55 48.55 48.55
N 5,328 5,328 5,328 5,328 5,328 5,328
Panel B-Cuto 500
Village Health Information Auxiliary Nurse Mother and Child Traditional Health
Guide Health Worker Midwife Health Worker Healer Camps
Roads .113* .122* .087 .027 -.054 .164***
(.064) (.070) (.079) (.035) (.073) (.063)
R-Squared .228 .371 .292 .556 .254 .235
Mean of Dep. .189 .681 .582 .902 .254 .172
SD of Dep. .392 .466 .493 .298 .435 .378
F (First Stage) 173.55 173.55 173.55 173.55 173.55 173.55
N 5,328 5,328 5,328 5,328 5,328 5,328
Controls for district xed eects, total number of households in the village, whether village has drain, ICDS center, Sub-Center
(health center), Primary Health Center, Government Dispensary, distance to the nearest town, district head quarter and railway
station.
Robust Standard Errors are in the Parenthesis.
* signicant at 10 percent level, ** signicant at 5 percent level ,*** signicant at 1 percent level
The First Stage for the both models is Tvd =0 +1Xvd +2X
2
vd
+3X
3
vd
+4D1 +5D2 +d +Hvd +vd.
Panel A, Cuto 1,000 Second Stage: Yvd =
0 +
1Xvd +
2X
2
vd
+
3X
3
vd
+
4Tvd +
5D1 +d +Hvd +vd

4 is the Treatment eect at 1000
Panel B, Cuto 500 Second Stage: Yvd =
0 +
1Xvd +
2X
2
vd
+
3X
3
vd
+
4Tvd +
5D2 +d +Hvd +vd,

4 is the Treatment eect at 500
Where Tvd is Treatment status of an village v located in district d , Xvd is Population of village v located in district d,
D1 =I(Population>= 500), D2 =I(Population>= 1000), d are district xed eects and Hvd are village level controls
Mother and Child health worker is the Integrated Child Development Service (ICDS) health worker
Information Health worker is an Accredited Social Health Activists. ASHAs are local women trained to act as health educators
and promoters in their communities .
Table 4: Health Povider in the Villages
25
Panel A-Cuto 1,000
Heard About AIDS Heard About DOTS (TB) Heard About Prevention Heard messages on Personal
Prevention Program Sex Selection Hygiene
Roads .079 .121* .138** .058
(.056) (.066) (.063) (.065)
R-Squared .198 .235 .163 .189
Mean of Dep. .425 .524 .388 .758
SD of Dep. .494 .499 .487 .428
F (First Stage) 46.64 46.64 46.64 46.64
N 135,870 135,870 135,870 135,870
Panel B-Cuto 500
Heard About AIDS Heard About DOTS (TB) Heard About Prevention Heard messages on Personal
Prevention Program Sex Selection Hygiene
Roads .060* .038 .030 .034
(.030) (.036) (.034) (.037)
R-Squared .199 .242 .173 .191
Mean of Dep. .425 .524 .388 .758
SD of Dep. .494 .499 .487 .428
F (First Stage) 167.64 167.64 167.64 167.64
N 135,870 135,870 135,870 135,870
Controls for district xed eects, age, age at rst marriage, whether individual attended school, whether household own the house, own
any other house, own agricultural land, have a below poverty level card, number of females in the household, religion of the household
head, total number of households in the village, whether village has drain, ICDS in village, Sub-Center (health center), Primary Health
Center, Government Dispensary, distance to the nearest town, district head quarter and railway station.
The rst four columns are information at the household level. Household level regression does not control for individual level controls.
* signicant at 10 percent level, ** signicant at 5 percent level ,*** signicant at 1 percent level.
Robust Standard Errors Clustered at the Village Level are in the Parenthesis.
The First Stage for the both models is Tivd =0 +1Xvd +2X
2
vd
+3X
3
vd
+4D1 +5D2 +d +Hivd +ivd.
Panel A, Cuto 1,000 Second Stage: Yivd =
0 +
1Xvd +
2X
2
vd
+
3X
3
vd
+
4Tivd +
5D1 +d +Hivd +ivd

4 is the Treatment eect at 1; 000
Panel B, Cuto 500 Second Stage: Yivd =
0 +
1Xvd +
2X
2
vd
+
3X
3
vd
+
4Tivd +
5D2 +d +Hivd +ivd

4 is the Treatment eect at 500
Where Tivd is Treatment status of an individual (household) living in village v located in district d , Xvd is Population of village v
located in district d, D1 =I(Population>= 500), D2 =I(Population>= 1000), d are district xed eects and Hivd are individual,
household and village level controls
Table 5: Information and Awareness
26
Panel A-Cuto 1,000
Youth Women's Self Help Welfare Committee Improvement Inter-Village Assembly
Club body Group for Sick in Clinic takes Decision on Health
Roads .369*** .062 .254* .311** .205 .347**
(.118) (.138) (.139) (.126) (.151) (.164)
R-Squared .305 .303 .357 .234 .177 .185
Mean of Dep. .19 .313 .497 .209 .623 .554
SD of Dep. .393 .464 .50 .407 .485 .497
F (First Stage) 48.55 48.55 48.55 48.55 48.55 44.62
N 5,328 5,328 5,328 5,328 5,328 3,970
Panel B-Cuto 500
Youth Women's Self Help Welfare Committee Improvement Inter-Village Assembly
Club body Group for Sick in Clinic takes Decision on Health
Roads .062 .184** .221*** .094 .056 .045
(.056) (.074) (.078) (.066) (.084) (.096)
R-Squared .426 .283 .366 .300 .201 .243
Mean of Dep. .19 .313 .497 .209 .623 .554
SD of Dep. .393 .464 .50 .407 .485 .497
F (First Stage) 173.55 173.55 173.55 173.55 173.55 128.10
N 5,328 5,328 5,328 5,328 5,328 3,970
Controls for district xed eects, number of households in the village, whether village has drain, ICDS center, Sub-Center (health
center), Primary Health Center, Government Dispensary, distance to the nearest town, district head quarter and railway station.
Robust Standard Errors are in the Parenthesis.
* signicant at 10 percent level, ** signicant at 5 percent level ,*** signicant at 1 percent level.
First Stage for the both models: Tvd =0 +1Xvd +2X
2
vd
+3X
3
vd
+4D1 +5D2 +d +Hvd +vd.
Panel A, Cuto 1,000 Second Stage: Yvd =
0 +
1Xvd +
2X
2
vd
+
3X
3
vd
+
4Tvd +
5D1 +d +Hvd +vd

4 is the Treatment eect at 1; 000
Panel B, Cuto 500 Second Stage: Yvd =
0 +
1Xvd +
2X
2
vd
+
3X
3
vd
+
4Tvd +
5D2 +d +Hvd +vd,

4 is the Treatment eect at 500
Where Tvd is Treatment status of a village v located in district d , Xvd is Population of village v located in district d,
D1 =I(Population>= 500), D2 =I(Population>= 1; 000), d are district xed eects and Hvd are village level controls
Table 6: Social Interaction in a village
27
Figure 2: Probability of a Sanctioned road with respect to village population
It is a non-parametric t of probability of a road being sanctioned. Scatter plots in the gure indicate for
every population bin (for example 0 to 100), proportion of the villages with a sanctioned road.
28
Figure 3: Distribution of Villages with Population
Each bin shows number of villages in that population bin. There is no jump of bin sizes at population of
500 and 1000
29
Figure 4: Auxiliary Nurse Midwife(ANM)
It is a non-parametric t of probability of a village having a Auxiliary Nurse Midwife. Scatter plots in the
gure indicate for every population bin (for example 0 to 100), proportion of the villages with a Auxiliary
Nurse Midwife. The gure shows probability of a village having a Auxiliary Nurse Midwife jumps around
population of 500 and 1000
30
Figure 5: Information Health Worker
It is a non-parametric t of probability of a village having a Information Health Worker. Scatter plots
in the gure indicate for every population bin (for example 0 to 100), proportion of the villages with a
Information Health Worker. The gure shows probability of a village having a Information Health Worker
jumps around population of 500 and 1000
31
Figure 6: Self Help Group
It is a non-parametric t of probability of a village having a Self Help Group. Scatter plots in the gure
indicate for every population bin (for example 0 to 100), proportion of the villages with a Self Help
Group.The gure shows probability of a village having a Self Help Group jumps around population of 500
and 1000
32
Figure 7: Village Health Guide
It is a non-parametric t of probability of a village having a Village Health Guide. Scatter plots in the gure
indicate for every population bin (for example 0 to 100), proportion of the villages with a Village Health
Guide.The gure shows probability of a village having a Village Health Guide jumps around population
of 500 and 1000
33
3 The Path to Equilibrium in Sequential and Simultaneous
games
29
The order of moves is key in game theory. Despite its importance, our empirical knowledge
of the eect of pure sequencing on choice and reasoning is still incomplete. The goal of
this paper is to improve our understanding of the fundamental dierences both in choices
and decision processes between sequential and simultaneous versions of a game. To this
purpose, we study a dominance solvable game. In the simultaneous move version, the
equilibrium is most naturally found by the successive elimination of strictly dominated
strategies. In the sequential move version, the equilibrium is most naturally found by
backward induction. Because of dominance solvability, the equilibrium actions are iden-
tical in both cases. We also abstract from framing eects arising from normal-form vs.
extensive-form representations. Instead, we provide the same formal representation in
both versions.
To be precise, we conduct a laboratory experiment where subjects play three- and four-
player games of complete information. The payo of each player depends on her action and
the action of exactly one other player. One (and only one) player has a dominant strategy
so that, starting from the choice of that player, the game is dominance solvable with a
unique Nash equilibrium. We consider two treatments, sequential and simultaneous, with
identical presentation: one matrix for each player that represents her payo as a function
of the actions of the two relevant players. Furthermore, in the sequential treatment, the
player with a dominant strategy moves last and the payo of a player depends on her
action and the action of the player who moves next. This way, observing the choice(s)
of previous mover(s) does not provide a direct help in nding the equilibrium. Finally
but importantly, we also get information about decision processes by hiding the payos in
opaque cells. These are only revealed when the subject moves the computer mouse into
the cell and clicks-and-holds the button down.
We perform an aggregate analysis (section 3.2), a model-based cluster analysis (section
3.3) and a structural estimation of individual types (section 3.4). We are interested in three
broad questions: (1) Are choices dierent between sequential and simultaneous? (2) Are
decision processes dierent between equilibrium and non-equilibrium players? (3) Most
importantly, are decision processes conditional on equilibrium choices dierent between
sequential and simultaneous? We next describe the answers to these questions.
Equilibrium choice is higher in sequential than in simultaneous, but not widely so.
Dierences are signicant only for the second mover in four-player games. Hence, the
combination of two factors helps individuals nd the equilibrium and payo maximizing
action: the cue implied by sequential order together with the observation of the choice
made by the rst mover. Either factor alone does not warrant a better decision.
By contrast, decision processes are vastly dierent between non-equilibrium and equi-
librium players. Two attentional variables are especially predictive of behavior. A measure
of lookup occurrence, MIN (minimum information necessary), captures whether the sub-
ject has opened all the payo cells that are essential to compute her equilibrium action,
29
This chapter is co-authored with Isabelle Brocas and Juan Carrillo
34
independently how many non-essential cells have also been opened. A measure of lookup
transitions, COR (correct sequence), captures whether at some point in the decision pro-
cess the subject has looked at payos in the order predicted by sequential elimination
of strategies (from the matrix of the player with a dominant strategy all the way to the
player's own matrix). We show that for subjects in non-trivial situations, those who satisfy
MIN are 1.4 to 3.4 times more likely to play Nash than those who do not, and those who
satisfy COR are 1.8 to 3.9 times more likely to play Nash than those who do not (note
for comparison that rational players are 2 times more likely to play Nash than random
players). These aggregate dierences are similar across treatments.
Perhaps more strikingly, the decision process among equilibrium players is also dif-
ferent across treatments. In simultaneous, subjects are erratic in their rst few lookups,
with a mix of forward and backward lookup transitions. As a result, it takes them a sub-
stantially longer time to reach the payo matrix of the player with a dominant strategy
(what we call \wandering") than in sequential. However, once this matrix is reached, the
subsequent lookup transitions are remarkably similar in both treatments and follow the
natural sequence of elimination of dominated strategies. The result has interesting policy
implications. It suggests that even if behavior in both treatments is similar when the
setting is suciently simple, the reasoning process is not: unveiling the logic of iterated
elimination proves harder in simultaneous than in sequential. Hence, as complexity grows,
one would expect to observe increasing dierences in choices.
Finally, the paper also shows heterogeneity in both decision processes and choices
among our subjects. A cluster analysis based on the two measures of lookup transitions
previously mentioned (correct sequence and wandering) naturally divides the population
in four groups: one extremely rational with perfect correct sequence and almost no wan-
dering, two with intermediate levels of correct sequence (of which one has low wandering
and the other has high wandering), and one with hardly ever correct sequence and dis-
persed wandering. Choices within a cluster match reasonable well those predicted by level
k theory in the simultaneous treatment but not in the sequential. A structural estima-
tion of individual types based on choices conrms those ndings, with more than 70%
of subjects in simultaneous mapping into levels 1, 2 and 4 and fewer classied types in
sequential. We also establish some learning eects.
The paper is related to three strands of the experimental literature. The rst two
study the eect of sequencing and formal presentation of the game but ignore decision
processes. The third one focuses on attentional data but does not compare timings.
There is a literature comparing behavior in sequential vs. simultaneous versions of
games that predict the same equilibrium actions. Katok et al. (2002) analyze nitely
repeated two-player coordination games and nd that subjects apply only a limited num-
ber of iterations of dominance (simultaneous) and a limited number of steps of backward
induction (sequential), with deviation being more prevalent in sequential than simultane-
ous. Carrillo and Palfrey (2009) study games of incomplete information and show that
equilibrium actions are more frequent when subjects observe their rival's choice before
acting (second player in sequential) than when they do not (simultaneous or rst player
in sequential). Our game is substantially simpler, in an attempt to isolate the eects of
backward induction and elimination of dominated strategies. Also, by studying attentional
35
data, our paper can unveil dierences in cognitive reasoning between treatments.
Relatedly, there is a literature that reports systematic dierences in behavior when
the same game is presented in extensive- vs. normal-form. Schotter et al. (1994) argue
that dierences occur because deductive arguments are more prominent in extensive-form
representations. Rapoport (1997) suggests that knowing the order induces players to frame
the game as if it was sequential even if the actions of previous players are not observed.
McCabe et al. (2000) claim that \mindreading" is at the origin of this result because
intentions are more salient in extensive form representations. Cooper and Van Huyck
(2003) argue that extensive-form induces players to choose the branch where the action of
the other player has meaningful consequences.
30
Our game focuses on the mirror problem
since we propose dierent timings (hence, dierent strategy sets) but the same formal
representation.
Finally, limited use of iterative dominance is typical of experimental results and has
been studied in combination with attentional data. In one-shot games, Costa-Gomes et
al. (2001) nd that compliance with equilibrium is high when the game is solvable by
one or two rounds of iterated dominance, but much lower when the game requires three
rounds or more. Costa-Gomes and Crawford (2006) reach similar conclusions in two-
person beauty contest games.
31
In dynamic games, there is also evidence of the limited
predictive power of backward induction in alternating oer bargaining games (Camerer et
al. (1993); Johnson et al. (2002)). Attentional data has been also used to study forward
induction (Camerer and Johnson, 2004). These experiments point to consistent violations
of both iterated dominance and backward induction, and show that attentional data can
help understand the cognitive limitations of subjects. However, they have not studied
whether there is a relationship in terms of choice and attention between the two.
3.1 Theory and Design
3.1.1 The Game
Game structure. We consider the following four-player game of complete information.
Player in role i2f0; 1; 2; 3g has two possible actions a
i
2fX
i
;Y
i
g. Her payo depends
on her action and the action of exactly one other player. More precisely the payo of role
i2f0; 1; 2g depends on the actions of role i and role i + 1 whereas the payo of role 3
depends on the actions of role 3 and role 0. Payos can be displayed in a series of four
2 2 matrices, one for each role, where each cell in matrix i displays the payo for role i
from a particular pair of actions. Table 7 shows a generic representation of the game with
one of the payo structures used in the experiment.
32
30
These experimental papers are related to the theoretical literature that studies whether the extensive
form representation of a game is the same as the strategic form to which it corresponds (Kohlberg and
Mertens (1986); Luce (1992); Glazer and Rubinstein (1996)).
31
See also the eye-tracking studies by Knoep
e et al. (2009), Wang et al. (2010), Reutskaja et al. (2011)
and Devetag et al. (2013). Armel and Rangel (2008) and Armel et al. (2008) show that manipulation of
visual attention can also aect choices.
32
Kneeland (2013) uses a very similar 4-player, 3-action game for a clever theoretical and experimental
study of epistemic conditions of rationality, beliefs about others' rationality and consistency of beliefs. She
does not compare sequential vs. simultaneous nor uses attentional data, the two key ingredients of our
36
Payo of 0
X
1
Y
1
X
0
15 25
Y
0
30 14
Payo of 1
X
2
Y
2
X
1
38 18
Y
1
18 32
Payo of 2
X
3
Y
3
X
2
14 36
Y
2
30 10
Payo of 3
X
0
Y
0
X
3
34 26
Y
3
20 12
Table 7: Four-player, type-H game (shaded cell is Nash equilibrium).
Dominance solvable. A key element of the game is that payos are chosen in a way that
role 3 (and only role 3) has a dominant strategy. Since all roles have only two actions, this
makes the game dominance-solvable which dramatically reduces the diculty to compute
the Nash equilibrium. For example, with the payos of Table 7 and applying iterated
elimination of strictly dominated strategies it is immediate to see that the equilibrium
actions of roles 3, 2, 1 and 0 are X
3
, Y
2
, Y
1
and X
0
respectively. At the same time,
the level of strategic sophistication required to compute the equilibrium is monotonically
increasing as we move from the rightmost role to the leftmost role. Role 3 faces a trivial
game with a dominant strategy and no need for strategic thinking. By contrast, roles 2, 1
and 0 need to perform one, two and three steps of dominance respectively, which requires
paying attention to the payos of one, two and three other players in the game. The
design thus gives signicant variation across roles for a study of cognitive sophistication
and strategic thinking.
Cognitive limitations. Based on previous research with attentional data (Costa-Gomes
et al. (2001); Costa-Gomes and Crawford (2006); Camerer et al. (1993); Johnson et al.
(2002)), we expect deviations from equilibrium behavior due to cognitive limitations. It
is therefore important to construct the game in a way that we can disentangle between
dierent theories of limited attention. Two leading theories are steps of dominance and
level k. In steps of dominance, a D
s
individual eliminates iteratively s dominated strate-
gies. If this proves insucient to determine the equilibrium, the player assumes that rivals
choose uniformly among the remaining strategies and best responds to that belief. In
levelk, a level 0 player is assumed to follow a simple, non-strategic choice rule and a level
k ( 1) player, or L
k
, assumes that every other player is L
k1
and best responds to that
belief (see Crawford et al. (2013) for a survey of theoretical models of strategic thinking).
Following a signicant portion of the levelk literature, we take the simplest approach and
assume thatL
0
uniformly randomizes between all the available strategies. With cognitive
limitations, the outcome assuming best response to rival's randomization anchors many
choices and therefore plays an important role. For this reason we use two dierent payo
structures in our games. In the \high cognition" type of game (H), payos are chosen in a
way that only role 3 (the one with the dominant strategy) plays the equilibrium action if
she best responds to uniform random behavior of her rival. This corresponds for example
to the payos of the game described in Table 7. In the \low cognition" type of game (L),
two roles, 3 and 2, play the equilibrium action if they best respond to uniform random
behavior of their rival. In a sense, in type-L games an individual who performs no or
analysis.
37
basic strategic reasoning is more likely to play Nash than in type-H games. An example
of payos for the low cognition type of games is presented in Table 8.
Payo of 0
X
1
Y
1
X
0
32 16
Y
0
22 30
Payo of 1
X
2
Y
2
X
1
16 34
Y
1
30 22
Payo of 2
X
3
Y
3
X
2
18 6
Y
2
8 22
Payo of 3
X
0
Y
0
X
3
10 8
Y
3
18 14
Table 8: Four-player, type-L game (shaded cell is Nash equilibrium).
We can then determine for each role and each type of game, the minimum number of
steps of dominance s and the minimum cognitive level k needed to play the equilibrium
action. With the structure of our game, if D
s
and L
k
subjects play Nash, then D
s+1
and
L
k+1
subjects also play Nash and if D
s
and L
k
subjects do not play Nash, then D
s1
and L
k1
subjects do not play Nash. It means that, in our game, higher s and k are
unambiguously associated to greater degree of sophistication. Table 9 shows that for all
roles, the sophistication needed to solve the game is (weakly) greater in type-H than in
type-L games, supporting the hypothesis of a dierence in cognitive diculty between
these two types of games.
Theory Type Role 0 Role 1 Role 2 Role 3
Dominance
H D
3
D
2
D
1
D
0
L D
3
D
2
D
0
D
0
Level
H L
4
L
3
L
2
L
1
L L
3
L
2
L
1
L
1
Table 9: Minimum steps of dominance D
s
and cognitive level L
k
necessary to play Nash.
Notice that with only type-H games, we would be unable to distinguish between steps
of dominance and levelk sinceD
j
L
j+1
. If all subjects can perform at least one step of
dominance, then with only type-L games we would again be unable to distinguish between
the two theories since D
j
L
j
for all j 1. Only the combination of type-H and type-L
provides enough richness in the data to disentangle between the two theories. In particular,
for role 0 and role 1, steps of dominance predicts the same behavior across game types
whereas level k predicts dierent behavior between H and L. This will prove crucial in
our analysis.
Sequential vs. simultaneous. A main objective of the experiment is to compare cog-
nition and behavior in sequential vs. simultaneous games. We therefore consider two
treatments. In the rst one, all roles choose their actions simultaneously. In the second
one, role i + 1 chooses her action a
i+1
after observing the actions of roles 0 to i.
33
Since
33
In the experiment, we do not use numerical indexes on roles to avoid cues related to the order of play.
Instead, roles are called \red", \green", \orange and \blue".
38
the game is dominant solvable, the Nash equilibrium is unique and identical in both treat-
ments (that is, we do not need to worry about Nash equilibria of the sequential game
that are not subgame perfect). This is key for a meaningful comparison. The formal pre-
sentation of the game is also the same in both treatments, with a payo matrix for each
role as depicted in Tables 7 and 8. Although the equilibrium is the same, the strategy
space is dierent and, we conjecture, so are the mental processes likely to be employed by
subjects. For individuals who realize the dominance solvability of the game, there may be
no dierence between the sequential and simultaneous treatments, but for the others we
expect dierences in both behavior and cognition due to two related eects:
Observation. Prior to their decision, roles 1, 2 and 3 observe the actions of one, two
and three other players, respectively. Observing these actions does not help nding
the equilibrium since rolei is only aected by the choices of roles i + 1 to 3 and role
3 has a dominant strategy. However, they still reduce the set of feasible outcomes,
and thus the complexity of the analysis.
Anticipation. Even the reasoning of role 0 can be facilitated by the knowledge of a
sequential order. Indeed, she may realize that her action will be observed by role
3, which will trigger a sequence of choices by roles 3, 2 and 1, with predictable
consequences for her own payo. This \linear" train of thought is arguably simpler
than the \xed point" argument needed to solve the simultaneous version.
Notice, however, that the limited cognition theories presented above predict identical
behavior in the sequential and simultaneous treatments. Therefore, empirical dierences in
choices due to sequencing cannot be attributed to steps of dominance or levelk reasoning.
Group size. So far we have considered four-player games. In the experiment, we also
study three-player games. These games are obtained by performing exactly two changes:
(i) role 0 is removed and (ii) role 3's payo is set to depend on the actions of roles 3 and
1 (with still a dominant strategy). It is immediate to notice that for roles 1, 2 and 3, the
Nash equilibrium, as well as the steps of dominance and cognitive levels needed to reach
the equilibrium are identical under both group sizes. Thus, dierences in behavior by role
i2f1; 2; 3g between the three- and four-player versions of the sequential treatment should
be attributed to the observation of role 0's choice and not to cognitive limitations.
3.1.2 Non-choice data
Following some of the recent literature, we analyze not only the choices made by subjects
in the experiment but also the lookup patterns prior to the decision. To this purpose we
use the same \mousetracking" technique as in Brocas et al. (2013), which is a variant of
the methodology rst introduced by Camerer et al. (1993) and further developed by Costa-
Gomes et al. (2001), Johnson et al. (2002), Costa-Gomes and Crawford (2006) and others
(see Crawford (2008) for a survey). During the experiment, information is hidden behind
blank cells. The information can be revealed by moving a mouse into the payo cell and
clicking-and-holding the left button down. There is no restriction in the amount, sequence
or duration of clicks and no cost associated to it, except for the subject's eort which
39
we argue is negligible.
34
The mousetracking software records the timing and duration
of clicks. Analyzing whether a particular cell has been open at all (\occurrence"), and
then which cell has been open next (\sequence") is an imperfect yet cheap, simple and
informative way to measure what information people might be paying attention to. Some
studies analyze also for how long has a cell been open (\duration"). In our preliminary
data analysis, this measure did not add information to the other two, so we ignored it. We
will study lookup patterns separately for each role (0; 1; 2; 3), each type of game (H;L),
each group size (3; 4) and each treatment (sequential, simultaneous).
3.1.3 Design and procedures
In the experiment, we consider type-H and type-L games with group sizes of 3 and 4
players, which we call 3H, 3L, 4H and 4L. We consider three payo variants of each game
for a total of twelve games. Subjects play each game twice, hence a total of 24 paid trials.
To avoid habituation to a certain game structure, we intertwine games of dierent types
and group sizes. For reference, Table 25 in Appendix A shows the twelve payo variants
used in the experiment and the order of presentation.
We ran 6 sessions of the sequential treatment and 6 sessions of the simultaneous treat-
ment in the Los Angeles Behavioral Economics Laboratory (LABEL) at the University
of Southern California. All participants were undergraduate students at USC. All inter-
actions between subjects were computerized using a mousetracking extension of the open
source software package `Multistage Games' developed at Caltech.
35
In each session, 12
participants played the 24 trials as described before, for a total of 72 subjects playing
the sequential treatment and 72 subjects playing the simultaneous treatment. No subject
participated in more than one session, so that the comparison of results between sequen-
tial and simultaneous is performed between subjects.
36
After each trial, subjects learned
their payo and the actions of the other participants in their group. This information was
recorded in a \history" screen that was visible for the entire session. Subjects were then
randomly reassigned to a new group (of three or four subjects depending on the game),
a new type of game and a new role. Before beginning the 24 paid trials, subjects had to
pass a short comprehension quiz. They also played a practice round to ensure that they
understood the rules and also to familiarize themselves with the click-and-hold method
for revealing payos. A survey including questions about major, years at school, demo-
graphics and experience with game theory was administered at the end of each session.
A sample of the instructions can be found in Appendix B. Figure 1 provides screenshots
of the computer interface used in the experiment. The left screenshot shows the game
the way our subjects see it (with close cells). The right screenshot shows the traditional
34
Earlier experiments have always run additional treatments with open boxes. They have typically found
no signicant behavioral dierences between open and closed box treatments, so we decided not to run the
open box version.
35
Documentation and instructions for downloading the software can be found at the website
http://multistage.ssel.caltech.edu.
36
We conjecture that learning may carry over from sequential to simultaneous and vice versa. Although
this is a fascinating possibility, it makes the data analysis substantially more complicated. We therefore
opted to have subjects playing only one treatment.
40
Figure 1
Figure 8: Sample screenshots of the game with close cells (left) and open cells (right)
version (with open cells). Sessions lasted about 1hr45min for the sequential treatment
and 1hr15min for the simultaneous treatment. Individual earnings (not including the $5
show-up fee) averaged $17.5 in the sequential and $17.2 in the simultaneous treatment,
with a minimum of $12.5 and a maximum of $20.2.
3.2 Aggregate analysis
3.2.1 Equilibrium play
The rst cut at the data consists in an aggregate analysis of Nash behavior in the 24 trials.
Table 10 reports the probability of equilibrium behavior by role (0; 1; 2; 3), type of game
and group size (4H, 3H, 4L, 3L), and treatment (simultaneous, sequential), pooling in
each case the three payo variants that are played twice each. For each subject, we have
144 observations of 3H and 3L games and 108 observations of 4H and 4L games.
simultaneous
0 1 2 3
4H :59 :61 :83 :99
3H | :72 :83 :99
4L :64 :80 :95 :99
3L | :88 :90 :99
sequential
0 1 2 3
4H :58 :78 :85 :96
3H | :77 :86 :99
4L :71 :90 :94 :98
3L | :81 :96 :99
Table 10: Probability of Nash (darker shade re
ects higher level k needed for Nash play).
Subjects realize the basics of the game and, just like in previous experiments, almost
invariably play the equilibrium action when it is suciently simple (Costa-Gomes et al.
(2001); Brocas et al. (2013)). In our case, whenever there is a dominant strategy (role
3), that strategy is played 98% of the time. When the decision requires a higher level of
sophistication, that is, as we move from role i + 1 to role i, compliance to equilibrium
decreases, and it becomes rather low (around 59%) for the most dicult choice, role 0 in
4H (recall that random choice predicts equilibrium behavior 50% of the time). In other
41
words, consistent with theories of limited reasoning as well as with previous experiments on
dominance solvable games, Nash behavior is inversely related to the number of strategies
that need to be iteratively eliminated in order to nd the equilibrium.
However, a closer look at choices across types of games suggests that level k ts the
data better than steps of dominance, although the support for levelk should be interpreted
with caution as we will recurrently notice all along our analysis. Indeed, recall from Table
9 that the steps of dominance required for Nash behavior are the same for role 0 in H
and L games (D
3
) and also the same for role 1 in H and L games (D
2
) whereas the
hierarchy levels are dierent. We use increasingly darker shades of gray in Table 10 to
capture higher levelk needed to play Nash (with no shade for level 1 and darkest shade for
level 4). We pooled the observations of the sequential and simultaneous treatments and
performed a comparison of means. The results show that, for both three- and four-player
games, dierences in equilibrium choices are not statistically signicant between role 2 in
type-H and role 1 in type-L games, and also not statistically signicant between role 1
in type-H and role 0 in type-L games. By contrast, dierences in equilibrium choices are
statistically signicant between type-H and type-L games for role 2 (p-value .000), role 1
(p-value .000) and marginally for role 0 (p-value .058). All ve results are consistent with
level k theory and inconsistent with steps of dominance.
At the same time, there are some dierences in aggregate behavior between the se-
quential and simultaneous treatments that shed light on the cues provided by sequencing.
Comparisons of means reveal signicantly higher Nash choices in sequential than in si-
multaneous treatments by role 1 in 4H games (p-value .007) and by role 1 in 4L games
(p-value .037). No other signicant dierences are found at the 5% level. Thus, contrary
to level k predictions, sequentiality sometimes helps reaching the equilibrium. It remains
to determine which eect, anticipation (knowing the order of play), observation (knowing
the choice of some player(s)) or a combination of both, is key for the dierence in behav-
ior, since both are present in the comparison. The fact that no signicant dierences are
found for role 0 in four-player games and for role 1 in three-player games suggests that
anticipation is not sucient. Also, when we look only at sequential games, we notice that
dierences in behavior by role 1 between 4H and 3H are not signicant and dierences
between 4L and 3L are marginally signicant (p-value .045). Hence, observation alone
may sometimes be sucient. However, the largest increases in equilibrium choice occur
when we combine observation of role 0's action and anticipation of the order of play.
37
These results will be conrmed and further expanded when we study attentional data.
From the analysis so far, it looks like decision-making for role 3 and for role 2 (especially
in type-L games) are straightforward. Dierences across subjects are not important enough
for meaningful comparisons. Therefore, from now on we will focus the analysis on roles 0
and 1 where heterogeneity in choice is more signicant.
Finally, a natural question is to determine if individuals learn to play Nash over the
course of the experiment. To address it, we compute the aggregate probability of equilib-
rium behavior in roles 0 and 1 separately for the rst twelve (early) and the last twelve
37
Notice that we do not nd dierences between sequential and simultaneous choices for role 2. This
may happen because Nash compliance is close to the boundary in both cases.
42
(late) matches of the game, pooling type-H and type-L games.
38
The results are summa-
rized in Table 11.
simultaneous sequential
Size Role Early Late Early Late
4 0 .47 :76

.56 :74

1 .59 :81

.76 :92

3 1 .72 :88

.76 .82
Table 11: Equilibrium choice in early (rst 12) and late (last 12) matches for roles 0 and 1
(dierence between early and late signicant at the 10% (*), 5% (**) and 1% (***) level)
Our subjects do learn how to play this game and that, by the end of the experiment,
Nash compliance is relatively high even in the most dicult situations. Learning is more
pronounced in the simultaneous than in the sequential treatment, due in part to lower
Nash choices at the beginning of the game.
3.2.2 Alternative theories: empirical best response and social preferences
Best-responding to subjects who do not play the equilibrium strategy may involve devia-
tions from Nash behavior. After all, only for role 3 it is optimal to play Nash independently
of the choices by others and, in that case, equilibrium compliance is ubiquitous. For each
role in each payo-variant of each game, we compare the expected payo of playing each
action given the empirical behavior of the other players. We do this separately for sequen-
tial and simultaneous. In our data, Nash is the empirical best-response for all roles in
all games in simultaneous (30 variants) and in 29 out of 30 variants in sequential (all 12
games for roles 1 and 2 and 5 out 6 games for role 0). We conclude that a sophisticated
subject who anticipates the behavior of other roles should still play Nash consistently.
The dierence in behavior across roles also sheds light on social preference theories.
Suppose that players are willing to sacrice money to reduce inequality, benet the worst-
o player or increase total payo (Fehr and Schmidt, 1999; Charness and Rabin, 2002).
Payos in our experiment are designed in a way that even with some degree of social
preferences equilibrium behavior is optimal. Furthermore, since the payo structures
are similar for roles 0, 1 and 2, deviations due to social preferences should be similar
across roles, types of games and treatments. This is not what we observe in Table 10.
Overall, we argue that with the parameters of social preferences typically estimated in
previous experiments, we should not observe signicant deviations from equilibrium. More
importantly, it would be dicult to explain with this theory the dierences between Nash
behavior across roles, types of games and treatments observed in our game. We later
support this conclusion with the attentional data.
38
Similar results are obtained if we use a dierent partition (e.g., rst eight and last eight matches).
43
3.2.3 Occurrence of lookups
Having established the existence of deviations from equilibrium, we now jointly study
attention and behavior. The simplest measure of attention is occurrence of lookups. Oc-
currence is a binary variable that takes value 1 if a payo cell has been open and 0
otherwise.
For each role (0; 1; 2; 3), each type (H;L), each group size (3; 4) and each treatment
(sequential, simultaneous) we can determine which cells must imperatively be open in
order to nd the Nash equilibrium. We call this set of cells the \Minimum Information
Necessary" or MIN. A subject who looks at MIN may or may not compute and play the
Nash equilibrium. More importantly, we can know for sure that a subject who does not
look at MIN cannot have played the Nash equilibrium after performing a traditional game
theoretic reasoning. For example, role 3 in simultaneous games needs to open all 4 cells
of her payo matrix. In the sequential treatment, she observes the action of the player in
the rst role and needs to open only the two cells in her payo matrix which correspond
to that action. MIN for roles 2, 1 and 0 can be determined using a simple backward
induction algorithm. In Appendix C, we display for each role, group size and treatment
the cells that belong to MIN (these cells are the same in type-H and type-L games).
Notice that MIN is a very conservative measure since opening a cell is a necessary but
not sucient condition for a subject to pay attention to it and understand the implica-
tions. Notice also that MIN is dened from the perspective of an outside observer (the
experimenter) who is aware of the payos behind all cells. A subject cannot know ex ante
what the MIN set of a given game is, and therefore she will likely open more cells than
those exact ones. For this reason, we choose to classify an observation as MIN as long as
the subject opens all the cells in the MIN set, independently of how many of the other
non-essential cells she also opens. An observation is classied as `notMIN' if the subject
does not open all the cells in the MIN set, again independently of how many of the other
non-essential cells she opens.
Table 12 presents for roles 0 and 1 the percentage of observations where subjects look at
the MIN set (Pr[MIN]). It also shows the probability of equilibrium behavior conditional
on MIN and conditional on notMIN (Pr[Nashj MIN] and Pr[Nashj notMIN]). Since we
identied some learning over time, we present the data separately for the rst 12 matches
(early), the last 12 matches (late) and all together (total). Finally, we pool together
type-H and type-L games because they have the same lookup predictions and distinguish
between the sequential and simultaneous treatments.
The aggregate likelihood of Nash when subjects look at MIN is high (84% to 96%) and
decreases dramatically when they do not look at MIN (26% to 67%). Overall, equilibrium
choices are 1.4 to 3.4 more likely for the observations where subjects look at all the
essential cells. This is high and in line with the more positive results in the existing
mousetracking literature (Brocas et al. (2013)). It suggests that, for our experiment, MIN
lookup is a very good predictor of equilibrium choice. In the simultaneous treatment,
the increase in Nash choices over the course of the experiment documented in Table 11
is due both to a substantial increase in correct lookups (Pr[MIN]) and a more accurate
transformation of this directed attention into equilibrium choice (Pr[Nashj MIN]). In the
44
simultaneous
Pr[MIN] Pr[Nashj MIN] Pr[Nashj notMIN]
Size Role early late all early late all early late all
4 0 .44 .69 .57 .77 .96 .89 .23 .30 .26
1 .49 .68 .58 .83 .93 .89 .36 .57 .44
3 1 .61 .78 .70 .82 .97 .91 .55 .56 .56
sequential
Pr[MIN] Pr[Nashj MIN] Pr[Nashj notMIN]
Size Role early late all early late all early late all
4 0 .48 .67 .57 .85 .83 .84 .29 .56 .39
1 .56 .59 .58 .95 .97 .96 .51 .84 .67
3 1 .68 .75 .72 .88 .94 .91 .50 .47 .49
Table 12: Equilibrium choice based on lookup occurrence (MIN)
sequential treatment, it is mainly due to an increase in correct lookups.
39
Next, we determine whether the likelihood of equilibrium behavior is aected by the
time the subject spends looking at the payo matrices of players in the dierent roles.
Previous research in the alternate bargaining oers game (Camerer et al. (1993); Johnson
et al. (2002)) suggests that subjects who play o-equilibrium tend to exhibit a more
self-centered behavior, with a majority of lookups in their own payo-cells. We want to
determine if similar biases occur in our experiment. To this purpose, we look at two
measures. First, the percentage of lookups on the subject's own payo matrix, with
the conjecture that self-centeredness is an indication of insuciently strategic thinking.
Second, the percentage of observations with one or more lookups at the matrix of role
3. This payo matrix is farthest away from the subject's own payo and yet it is key to
initiate the elimination of dominated strategies. Table 13 summarizes the ndings.
Perhaps not surprisingly, the subject's own payo is a focal point that needs to be
overcome for strategic thinking. In our experiment, subjects who play Nash spend on
average less than 40% of the time on their own payo whereas those who do not play Nash
spend more than 50%. The dierence in the likelihood of looking at role 3's matrix is even
more striking. Supporting the ndings in Table 12, subjects who reach the equilibrium
strategy fail to look at the crucial payo matrix of role 3 only 15% of the time. By contrast,
those who do not play Nash miss that matrix about 64% of the time.
39
In both treatments, we also observe some instances of increases in Pr[Nashj notMIN]. We speculate
that some subjects may have realized after some trials that role 3 has a dominant strategy. They may
choose not to open all the cells in that matrix but still play the equilibrium. This highlights that lookup,
while instructive and interesting, is still an imperfect measure.
45
% of total lookups % observations where
at own payo subject looks at role 3
Treatment Size Role Nash Not Nash Nash Not Nash
4 0 33% 48% 89% 27%
simultaneous 4 1 42% 55% 80% 25%
3 1 39% 58% 82% 47%
4 0 38% 52% 85% 43%
sequential 4 1 37% 55% 88% 26%
3 1 42% 56% 89% 45%
Table 13: Lookup behavior of subjects who play and do not play Nash.
3.2.4 Transitions of lookups
In section 3.2.1 we have established that aggregate behavior is dierent in the simultaneous
and sequential treatments only for role 1 in four-player games. Attentional data can inform
us if dierences in the cognitive processes are at the origin of these dierences in choices.
It may even be the case that behavior of role 0 in four-player games and role 1 in three-
player games is similar but the cognitive processes are not. To study this question in more
detail, we analyze the sequence of lookups.
Mousetracking provides an enormous amount of data that can be disaggregated in
many ways. Here, we propose the following analysis. For each subject in each game we
determine which role's payo matrix a subject opens (independently of the cell within
that matrix), and then record all the transitions between matrices (from a cell in role i's
payo matrix to a cell in role j's payo matrix, etc.).
40
This means that we ignore the
number of clicks in a cell as well as the transitions within a role i's matrix.
Denotingij the transition from the payo matrix of role i to the payo matrix of role
j, we can group these transitions in three main categories. First, \action" transitions.
These are the transitions from the matrix of rolei to the matrix of the role aected by the
action of rolei: (32; 21; 10; 03) in four-player games and (32; 21; 13) in three-player games.
They include all backward adjacent transitions as well as the transition from rst to last
role, which wraps up the argument.
41
These transitions follow the induction argument
which is key to solve the game: \ifi choses actiona
i
, theni 1 should choose actiona
i1
,
etc." Second, \payo" transitions. These are the transitions from the matrix of role i to
the matrix of the role whose action will aect the payo of role i: (01; 12; 23; 30) in four-
player games and (12; 23; 31) in three-player games. They include all forward adjacent
transitions as well as the transition from last to rst role. These are natural transitions
to look at, in order to determine potential payos associated to the action of a certain
40
For this particular analysis of lookup transitions, it is key that each matrix contains payos of one and
only one role.
41
For a subject who realizes that role 3 has a dominant strategy, the transition from rst to last role is
unnecessary. However, we should not presuppose that our subjects have such sophisticated knowledge.
46
role, but they are misleading in that they do not help solving the game. All transitions
in three-player games are either action or payo transitions. The remaining transitions in
four-player games are what we call \non-adjacent" transitions: (02; 13; 20; 31).
Table 14 presents for role 0 in four-player games and for role 1 in three- and four-player
games, the fraction of between-matrices transitions that are of the action, payo and non-
adjacent type, respectively. We are interested in studying dierences in cognitive processes
between simultaneous and sequential treatments by subjects who play the equilibrium
strategy. We therefore consider the two treatments separately and restrict attention to
observations consistent with equilibrium. Finally, we also disaggregate the data into early,
late and all matches together.
simultaneous
action payo non-adjacent
Size Role early late all early late all early late all
4 0 .56 .58 .57 .42 .41 .41 .02 .01 .02
1 .55 .57 .57 .41 .38 .39 .05 .05 .05
3 1 .53 .63 .58 .47 .37 .42 { { {
sequential
action payo non-adjacent
Size Role early late all early late all early late all
4 0 .67 .81 .75 .31 .16 .22 .02 .03 .03
1 .62 .78 .69 .31 .19 .26 .07 .03 .06
3 1 .72 .82 .76 .28 .18 .24 { { {
Table 14: Percentage of action, payo and non-adjacent transitions for Nash players
According to Table 14, the pattern of transitions is very dierent between the sequential
and simultaneous treatments, even though we consider only observations where subjects
play the equilibrium action. At the same time, dierences are stable across roles and
group size. As expected, non-adjacent transitions are always rare. More interestingly, the
overall ratio between action and payo transitions is around 3 in the sequential treatment
(75%-25%) and 1.5 in the simultaneous treatment (60%-40%), whereas random transitions
would predict a ratio of 1. The dierence is even more dramatic if we consider only the last
12 matches since the ratio remains constant in the simultaneous treatment and reaches
4.5 in the sequential. The result suggests that imposing a sequential order of play directs
subjects into looking at the matrices in the \right way", and that this cue provided by
sequentiality becomes more helpful over time. The transitional attentional data is key in
obtaining this result since it holds even when we look exclusively at individuals who choose
the equilibrium (and payo maximizing) strategy. We conjecture that in more complex
games, the cue would translate into larger choice dierences (some players who are not
47
directed to look in the right way, would simply never succeed in nding the equilibrium)
although new data would be necessary to test this hypothesis.
To further investigate the dierences in lookup transitions between sequential and
simultaneous treatments, we construct the same table of transitions, except that we con-
dition on the subject having reached the payo matrix of role 3. More precisely, we remove
all the transitions between matrices that occur before reaching the matrix of role 3 for the
rst time. We also remove the observations of individuals who never look at role 3's ma-
trix.
42
The reason for such analysis is the conjecture that a main diculty in nding the
equilibrium lies in realizing how the behavior of role 3 is the key to unravel the choices of
roles 2, 1 and 0. The outcome is summarized in Table 15.
simultaneous
action payo non-adjacent
Size Role early late all early late all early late all
4 0 .83 .92 .89 .16 .07 .11 .01 .01 .01
1 .81 .82 .82 .14 .13 .13 .06 .05 .05
3 1 .79 .89 .85 .21 .11 .15 { { {
sequential
action payo non-adjacent
Size Role early late all early late all early late all
4 0 .80 .85 .83 .19 .13 .15 .01 .02 .02
1 .77 .85 .81 .15 .12 .14 .07 .02 .05
3 1 .77 .85 .81 .23 .15 .19 { { {
Table 15: Percentage of action, payo and non-adjacent transitions for Nash players con-
ditional on reaching the payo matrix of role 3
Once the subject has looked at the payo matrix of role 3 for the rst time, action
transitions become overwhelmingly prevalent (between 81% and 89% of the total). Perhaps
more surprisingly in light of Table 14, the ratio between action and payo transitions is
now very similar in both treatments. If anything, it is now higher in simultaneous. Also,
the ratio increases in both treatments over the course of the experiment. Overall, Tables 14
and 15 conrm that the reasoning process is very dierent in sequential and simultaneous,
even for subjects who play the equilibrium strategy. It also provides an indication of what
these dierences are. In simultaneous games, it is harder to realize that the choice of role
3 is key to determine the optimal behavior of roles 2, 1 and 0. As a result, transitions are
more erratic than in sequential games. However, once the payo matrix of role 3 is hit,
the connection is made and the transition sequence 3-2-1-0 is triggered fast and eciently
42
These are only 14% of the observations (recall that we are focusing only on subjects who play Nash).
48
in both treatments.
43
3.2.5 Regression analysis: predicting choice from lookups
The last step of the aggregate analysis consists in using the lookup data to predict choices.
We treat each trial as a separate observation and run Probit regressions to predict whether
the subject plays the equilibrium action (= 1) or not (= 0) in roles 0 and 1. We run six
regressions to study separately the behavior of role 0 in 4H and 4L and role 1 in 4H, 4L,
3H and 3L.
Since we are interested in the predictive power of attentional data, we include variables
related to lookup occurrence and transitions. For occurrence, we introduce a dummy vari-
able that takes value 1 if the subject looked at all the MIN cells, independently of how
many other cells he looked at, and 0 otherwise (min). For transitions, we introduce two
variables: the total number of transitions (total-t) and the percentage of transitions that
are action transitions (action-t). We choose these variables because, according to the re-
sults in sections 3.2.3 and 3.2.4, they are good candidates to explain equilibrium behavior.
We can think of other interesting lookup variables, but they will be highly correlated with
the variables in our regression. Finally but crucially, we also add a treatment dummy
variable that takes value 1 in sequential and 0 in simultaneous (seq). The goal is to de-
termine if dierences in behavior across treatments are fully captured by the three lookup
variables described above or if we are still missing some lookup aspect that dierentiates
equilibrium choice between treatments. Results are presented in Table 16.
Role 0 Role 0 Role 1 Role 1 Role 1 Role 1
4H 4L 4H 4L 3H 3L
seq -.135 .103 .213 .460 -.010 -.512

(.207) (.211) (.240) (.269) (.180) (.220)
min 1.14

1.55

1.83

1.01

.872

1.29

(.251) (.256) (.322) (.275) (.234) (.268)
total-t .007 -.006 -.016

.004 -.009

-.004
(.005) (.004) (.006) (.006) (.004) (.004)
action-t 7.10

5.60

8.76

4.84

5.31

4.31

(1.84) (1.64) (2.00) (1.92) (1.55) (1.68)
const. -1.19 -.496

-.769

-.110 .008 .229
(.243) (.233) (.245) (.278) (.173) (.220)
# obs. 215 216 216 214 288 287
Pseudo R
2
0.340 0.314 0.430 0.217 0.177 0.307
Standard errors in parentheses.

p< 0:05,

p< 0:01,

p< 0:001
Table 16: Probit regression of Nash behavior as a function of lookups
43
Given that we observe learning and that reaching the matrix of role 3 is key, we studied whether
subjects who played in role 3 early in the experiment learned faster to play the Nash equilibrium. We
found no signicant dierences.
49
The sign and signicance of the parameters are remarkably similar across regressions.
The coecient for MIN occurrence and action transitions are always highly signicant
and indicative of Nash behavior (at the 5% and often at the 0.1% level). This conrms
our previous results that these measures of attention are good predictors of equilibrium
choice. We also nd that `total transitions' is either not signicant or a negative indicator
of equilibrium choice. It means that, conditional on looking at MIN and having a high
fraction of transitions in the right direction, subjects who spend more time looking at
payos perform (weakly) worse. This captures an interesting kind of misguided search (or
wandering) that we will explore in more detail in the next section. Finally but importantly,
the sequence treatment variable is signicant in only one regression (role 1 in 3L) and at
the 5% level. It suggests that most dierences in choices between the sequential and
simultaneous treatments can be accounted with only two simple attentional measures,
MIN occurrence and action transitions.
3.2.6 Summary of aggregate analysis
(i) Choice. Nash compliance is reasonably high and increases over time. Level k ts the
aggregate data well though, contrary to the theory, choices for role 1 in four-player games
is dierent across treatments. (ii) Lookup occurrence. For roles 0 and 1, looking at the
relevant cells is a good predictor of equilibrium behavior: Nash is close to 1 for subjects
who look at MIN and substantially lower for those who do not. (iii) Lookup transition.
The sequence of lookups conditional on equilibrium choice diers across treatments. The
matrix of role 3 is reached faster in sequential. However, once the subject arrives at this
payo matrix, the unraveling logic of elimination of dominated strategies is performed
equally eciently in both treatments. (iv) Regression. Probit regressions conrm these
results: MIN occurrence and action transitions have a signicant eect in explaining Nash
choices, and there is no treatment eect once we control for these variables.
3.3 Cluster analysis
In this section we use the attentional data to group individuals with the objective of
nding common patterns of lookups. We follow the clustering methodology introduced by
Camerer and Ho (1999) and further developed by Brocas et al. (2013). An advantage of
clustering is that it does not impose any structure of heterogeneity, but rather describes
the heterogeneity found in the data as it is.
As highlighted in section 3.2, there are many attentional variables that contribute to
explain behavioral choices and these variables are often correlated with each other. In
our experiment, the most promising measures relate to lookup transitions. Indeed, action
transitions are very indicative that the subject is following the logic of strategy elimination.
We will therefore focus on this aspect of attention at the expense of lookup occurrence,
which may be more noisy and variable.
44
In any case, which attentional variable (oc-
44
In particular, subjects who spend a lot of cognitive eort but are ultimately lost will very likely look
at MIN. By contrast, transitions will look chaotic. Also, subjects who inadvertently miss just one of the
cells in the MIN set will be coded as notMIN and yet they may often play the equilibrium.
50
currence, transitions or a combination of both) explains choices better is ultimately an
empirical question that our data may be able to answer. We will also concentrate on the
choices of roles 0 and 1 for the same reasons as previously.
3.3.1 Lookup transitions: correct sequence and wandering
One challenge with attentional measures is the large amount of data they provide. For
example, subjects in our experiment open as many as 228 payo cells in one single trial.
To lter the transition data, we construct a measure analogous to the one we used in
section 3.2.4. For each observation, we record the string of transitions between the payo
matrices of the dierent roles. As before, this ignores the number of clicks as well as the
transitions within a role's payo matrix. So, for example, a string `132' for a subject in
role 1 would capture an individual who rst opens one or several cells in his own payo
matrix, then moves to the payo matrix of role 3 before nally stopping at the matrix of
role 2. For reference, strings in our experiment contain between 0 and 50 digits.
Once these strings are created, we construct two variables for each observation. First,
a dummy variable that takes value 1 if the string contains what we code as the \correct
sequence:" 3210 or 321210 for role 0 and 321 for role 1. The variable takes value 0 otherwise.
The idea is that these sequences are strong indicators that the subject follows the logic
of elimination of dominated strategies from role 3 backwards.
45
The second variable is
the number of matrices open before reaching the correct sequence. This includes the
whole string if the correct sequence is never reached. It provides a measure of how much
the subject looked around before realizing (or not) the correct sequence, which we will
informally refer to as \wandering". So, for example, strings 01232101 and 13231 for role
1 would be coded as 1 and 0 respectively for the correct sequence variable and 3 and
5 for the wandering variable. Finally, for each individual we compute the percentage of
observations where the correct sequence takes value 1, called %-correct, and the average
number of matrices open before reaching the correct sequence, called pre-correct.
46
The
choice of these two variables relies heavily on the analysis in section 3.2.4, where we
reached two conclusions. First, that lookup transitions widely dier across treatments
even among subjects who play the equilibrium strategy. And second, that heterogeneity
is concentrated on transitions before reaching the matrix of role 3.
47
To provide an initial idea of the relationship between correct sequence and equilibrium
behavior, we display in Table 17 the probability that a subject performs the correct se-
quence (Pr[COR]), the probability of Nash conditional on performing the correct sequence
(Pr[Nashj COR]) and the probability of Nash conditional on not performing the correct
sequence (Pr[Nashj notCOR]) for roles 0 and 1. This is the analogue of Table 12 with the
45
For role 0, we allow one forward adjacent transition (12) because a subject may forget some payo
and double check it before restarting the reasoning. Results are almost identical if we allow two forward
adjacent transitions (32121210) or more.
46
We chose average rather than percentage of pre-correct matrices to distinguish between subjects who
do not reach the correct sequence after opening few boxes v. after opening many boxes.
47
We also explored a third variable: the number of matrices open after the correct sequence (which we
called \post-wandering"). We found little variance across subjects and no systematic patterns for this
variable so we nally did not include it in the analysis.
51
lookup transition variable COR instead of the lookup occurrence variable MIN.
simultaneous
Pr[COR] Pr[Nashj COR] Pr[Nashj notCOR]
Size Role early late all early late all early late all
4 0 .40 .69 .54 .86 .97 .93 .22 .29 .24
1 .44 .69 .57 .94 .95 .94 .32 .52 .39
3 1 .53 .80 .67 .90 .97 .94 .51 .52 .51
sequential
Pr[COR] Pr[Nashj COR] Pr[Nashj notCOR]
Size Role early late all early late all early late all
4 0 .44 .67 .55 .89 .92 .91 .30 .39 .33
1 .68 .81 .74 .95 .98 .96 .37 .67 .49
3 1 .66 .72 .69 .89 .96 .93 .49 .46 .48
Table 17: Equilibrium choice based on correct sequence (COR)
Correct sequence is an excellent predictor of equilibrium behavior. Nash choices are
1.8 to 3.9 more likely given COR than given notCOR. Pr[Nashj COR] slightly increases
over time but the biggest change is the increase in the likelihood of performing the correct
sequence. When we compare the results to those in Table 12, we notice that the increase in
equilibrium choice from notCOR to COR (Pr[Nashj COR]-Pr[Nashj notCOR]) is 3 to 18
percentage points bigger than from notMIN to MIN (Pr[Nashj MIN]-Pr[Nashj notMIN]).
This suggests that correct sequence is a strong indicator, possibly better than MIN lookup,
that the subject understands the unraveling logic of the game.
48
3.3.2 Cluster based on lookup transitions
Given the signicant dierences in lookup transitions between the simultaneous and se-
quential treatments, we decided to perform a separate cluster analysis for subjects in
those treatments. We group the 72 participants of each treatment in clusters based on
the two variables described above, %-correct and pre-correct. There is a wide array of
heuristic clustering methods that are commonly used but they usually require the number
48
We also conducted an analysis of Nash conditional on performing and not performing the mirror image
\forward sequence" (0123 and 012123 for four-player games and 123 for three-player games). We found
that, after controlling for correct sequence, forward sequence had no explanatory power for Nash behavior.
We also noticed that, in accordance to results in section 3.2.4, subjects in the simultaneous treatment
who performed the correct sequence typically performed also the forward sequence. By contrast, subjects
in the sequential treatment who performed the correct sequence typically did not performed the forward
sequence (data omitted fro brevity).
52
of clusters and the clustering criterion to be set ex-ante rather than endogenously opti-
mized. Mixture models, on the other hand, treat each cluster as a component probability
distribution. Thus, the choice between numbers of clusters and models can be made us-
ing Bayesian statistical methods (Fraley and Raftery, 2002). We implement model-based
clustering analysis with the Mclust package in R (Fraley and Raftery, 2006). We consider
ten dierent models with a maximum of nine clusters each, and determine the combina-
tion that yields the maximum Bayesian Information Criterion (BIC).
49
Technically, this
methodology is the same as Brocas et al. (2013). Conceptually, there are two dierences.
First, Brocas et al. (2013) cluster individuals based on lookups and choice.
50
Clustering
only on lookups allows us to study whether a classication made solely on attentional data
has a good predictive power of choice. Second, Brocas et al. (2013) introduce six variables.
Reducing them to only two makes the predictions sharper. The risk, of course, is to have
an insucient number of variables to adequately discriminate behavior.
For the simultaneous data, the model with diagonal distribution, equal volume, vari-
able shape and coordinate axes orientation (EVI) that endogenously yields four clusters
maximizes the BIC. `For the sequential data, the model with ellipsoidal distribution, vari-
able volume, equal shape and variable orientation (VEV) that endogenously yields four
clusters maximizes the BIC. Table 18 shows for each treatment the summary statistics of
the average value within each cluster of the two variables considered in the analysis (%-
correct and pre-correct) as well as the number of subjects in each cluster. For reference, it
also shows the average performance of subjects within a cluster in terms of percentage of
equilibrium choice in roles 0 and 1 (% Nash) and percentage of MIN lookups also in roles
0 and 1 (% MIN). Recall, however, that these two variables are not used in the clustering.
Figure 2 provides a graphical representation of the four clusters in the simultaneous (left)
and sequential (right) treatments.
simultaneous
Cluster A B C D all
%-correct 96 62 54 02 59
pre-correct 2.0 2.7 4.0 3.1 2.8
# subjects 25 15 16 16 72
% Nash 95 69 67 39 71
% MIN 91 61 62 14 61
sequential
Cluster A B C D all
%-correct 100 81 47 06 67
pre-correct 0.98 2.3 4.3 2.6 2.3
# subjects 21 25 13 13 72
% Nash 98 83 55 53 77
% MIN 86 73 59 12 63
Table 18: Summary statistics by cluster.
The optimal number of clusters is the same in both treatments (four) and all clusters
49
Specically, hierarchical agglomeration rst maximizes the classication likelihood and nds the clas-
sication for up to nine clusters for each model. This classication then initializes the Expectation-
Maximization algorithm which does maximum likelihood estimation for all possible models and num-
ber of clusters combinations. Finally, the BIC is calculated for all combinations with the Expectation-
Maximization generated parameters.
50
In the appendix, they perform clustering based only on lookups and obtain similar but weaker results.
53
Figure 2
Figure 9: Cluster based on correct sequence (percent correct) and wandering (pre-correct)
for simultaneous (left) and sequential (right) treatments.
are of dierent but comparable size (between 13 and 25 subjects). In both treatments, we
observe one cluster with perfect or near perfect percentage of correct sequence, one with
almost no correct sequence, and two with intermediate levels.
As noted above, the frequency of correct sequence is highly correlated both with equi-
librium choice and MIN lookup. More precisely, subjects in cluster A reach rapidly the
correct sequence and play Nash whereas subjects in cluster D are lost. They wander
for some time (not much), rarely perform the correct sequence and occasionally play
Nash. Between these two extremes we have two groups of subjects. Cluster B is a weaker
version of cluster A, with fewer correct sequence and more wandering. Cluster C tries
hard, performs long strings of transitions but reaches the correct sequence only half of the
time, which translates into equilibrium choice only slightly more often than random choice
would dictate. Overall, there is a hump shaped relationship between correct sequence and
wandering, especially in sequential. In the extremes, subjects do not wander because they
either know where to look or they are clueless and give up. In the middle, subjects struggle
to nd the equilibrium and sometimes succeed.
Despite the similarity of patterns across treatments, we can also notice interesting
dierences. Cluster A in the sequential treatment is the absolute portrait of rationality:
correct sequence, extremely low wandering and consistent Nash choice.
51
Clusters B and C
are more dierentiated in sequential than in simultaneous. More generally and consistent
with the results in section 3.2.4, correct sequence is on average higher in sequential while
51
Recall that a subject who rst looks at his own payo matrix and then performs the correct sequence
would show a value of 1 in pre-correct.
54
wandering is on average higher in simultaneous.
Finally, although clustering is performed in the entire sample and based only on tran-
sition variables, it may still be informative about the learning trends documented in the
previous section. In Table 19 we present the same information as in Table 18 with the
data split between early and late matches.
simultaneous
Cluster A B C D all
early late early late early late early late early late
%-correct 90 100 37 86 32 77 02 03 46 70
pre-correct 2.5 1.6 3.0 2.3 4.9 3.0 3.3 3.0 3.3 2.4
% Nash 90 99 49 87 52 83 36 46 61 81
% MIN 87 95 41 81 43 81 18 09 52 70
sequential
Cluster A B C D all
early late early late early late early late early late
%-correct 100 100 65 97 39 53 04 10 59 74
pre-correct 1.4 0.7 3.4 0.9 4.2 4.4 3.1 2.3 2.9 1.7
% Nash 99 98 71 95 46 65 49 58 70 83
% MIN 88 85 66 81 53 68 05 18 58 68
Table 19: Statistics by cluster in early (rst 12) and late (last 12) matches.
There is substantial heterogeneity in learning across subjects. The amount of learning{
in terms of more correct sequences, less wandering and more Nash choices{ by subjects in
clusters B and C is important. Over time, subjects in cluster B play almost as well as the
highly rational cluster A subjects. This means that, by the end of the experiment, 56%
of subjects in the simultaneous treatment and 64% in the sequential treatment perform
the correct sequence, limit the wandering, and play Nash, providing an excellent template
for rational choice and information processing. The improvement is less pronounced for
subjects in cluster C (especially in the sequential treatment) but still signicant. By
contrast, subjects in the other clusters exhibit very limited learning, which is natural
since their level of understanding of the game is either complete from the outset (cluster
A) or extremely limited by the end (cluster D).
3.3.3 Clusters and level k
In section 3.2.1 we argued that levelk theory provides a reasonably good t of the aggregate
data. We now study if subjects who belong to a certain cluster exhibit choices consistent
with a specic level of reasoning. This is a stringent test because clustering is performed
55
on attentional variables that are only indirectly related to level k.
In Table 20 we present the probability of Nash choices by role and type of game for
each cluster separately, with darker shades re
ecting a substantial drop in Nash choice.
This is the analogue of Table 10 for each subpopulation.
cluster A
0 1 2 3
4H .89 .91 .97 1.0
3H | .95 .96 1.0
4L .97 .91 1.0 .98
3L | .98 .92 1.0
cluster A
0 1 2 3
4H .92 1.0 .93 1.0
3H | 1.0 1.0 1.0
4L .96 1.0 1.0 1.0
3L | .98 .98 1.0
simultaneous
cluster B
0 1 2 3
4H :52 :63 1.0 1.0
3H | :66 .97 1.0
4L :50 .85 1.0 1.0
3L | .97 .97 1.0
sequential
cluster B
0 1 2 3
4H :73 :80 .91 1.0
3H | :85 .93 1.0
4L :76 .92 1.0 .97
3L | .89 .98 1.0
cluster C
0 1 2 3
4H :60 :54 .89 1.0
3H | :62 .94 .97
4L :56 .86 1.0 1.0
3L | .88 .97 1.0
cluster C
0 1 2 3
4H :37 :56 .82 1.0
3H | :52 .88 1.0
4L :42 .83 .90 .96
3L | :56 1.0 1.0
cluster D
0 1 2 3
4H :21 :22 :46 .96
3H | :46 :47 .96
4L :35 :54 .80 1.0
3L | :52 .79 .97
cluster D
0 1 2 3
4H :33 :50 :59 .81
3H | :44 :52 .96
4L :61 :71 .75 1.0
3L | :61 .79 .94
Table 20: Probability of Nash choice by cluster (darker shade re
ects substantial drop in
Nash rates).
If all subjects in a cluster perfectly tted a certain level, we would observe Nash choices
with probabilities either 1 or 0 depending on role and type. More realistically, we expect
a signicant drop in Nash between the situations where a certain level k predicts Nash
behavior and those where it predicts non-Nash behavior, and that the drop will correspond
to a dierent combination of role and type of game in dierent clusters.
The results for the simultaneous treatment are sharp. Cluster A consistently plays
Nash in all roles and types of games, with probabilities ranging from .89 to 1.0. They
correspond to equilibrium (or, equivalently, level 4) players. Clusters B and C are similar
in terms of choice. They play Nash with very high probability when equilibrium requires
to be a level 2 player (.85 and above), and signicantly less often when equilibrium requires
to be a level 3 or 4, although these probabilities are still a long way from 0 (.50 to .66).
Combined with Table 18, we notice that the main characteristic that dierentiates these
two clusters is not their choice, MIN occurrence or correct sequence; it is mostly the time
they spend wandering before realizing (or not) the logic of strategy elimination. These
clusters either mix level 2 and level 4 players or have players starting as level 2 and
become level 4 by the end of the experiment. Given the results in Table 19, we favor
the rst explanation for cluster C and the second for cluster B, although we do not have
56
enough data for a proper test of this conjecture.
52
Finally, cluster D is a good prototype
of level 1 players, with high Nash compliance when there is a dominant strategy (role 3)
or when equilibrium requires best response to random behavior (role 2 in type-L games),
and a signicant drop when nding the equilibrium requires any sophisticated reasoning.
Levelk theory does not t the data nearly as sharply in the sequential treatment. For
example, cluster C subjects play Nash less often than predicted by level 2 theory in 3L role
1 (.56) and cluster D subjects play Nash more often than predicted by level 1 theory in
4L role 1 (.71). Cluster B does not t any level: equilibrium choice consistently decreases
with complexity but without a sharp drop at any given role. This is in part due to the
subjects' ability to learn since, as we highlighted previously, their behavior is very close
to equilibrium (or level 4) in the second-half of the experiment. The link between clusters
and level k theory will be further investigated in the next section.
3.3.4 Summary of cluster analysis
Two measures of lookup transitions, correct sequence and wandering, naturally divide the
population into four clusters in both treatments: one that reaches the correct sequence
fast, does it systematically, and always plays Nash; one that wanders for a while, rarely
reaches the correct sequence and do not play Nash; and two with intermediate levels of
correct sequence, of which one has signicantly more wandering than the other. These
measures correlate well with level k choices in the simultaneous treatment but not in the
sequential treatment. There is learning over time by some subjects. By the end of the
experiment, 60% of the population exhibits rational choice and well-directed attention.
3.4 Individual analysis
In this section we perform a structural estimation of individual behavior. Following Costa-
Gomes et al. (2001), we assume that subjects have a type that is drawn from a common
prior distribution, and that this type remains constant over the 24 matches.
53
The sub-
ject's behavior is determined by her type, possibly with some error. We also assume that
subjects treat each match as strategically independent. In specifying the possible types, we
use some of the general behavioral principles that have been emphasized in the literature
as being most relevant. We consider the following set of types. Pessimistic [Pes] (subjects
who maximize the minimum payo over the rival's decision), Optimistic [Opt] (subjects
who maximize the maximum payo over the rival's decision), Sophisticated [Sop] (sub-
jects who best respond to the aggregate empirical distribution of choices) and Equilibrium
[NE] (subjects who play Nash). We also include the types corresponding to the steps of
dominance and level k theories: L
1
, L
2
, L
3
, L
4
, D
1
, D
2
, D
3
as described in section 3.1.1.
This set of 11 types is chosen to be large and diverse enough to accommodate a variety
of possible strategies without overly constraining the data analysis, yet small enough to
52
For a structural estimation of learning in beauty contest games based on level k reasoning, see Gill
and Prowse (2012).
53
Given the documented learning, this is unsatisfactory. Unfortunately, we do not have enough obser-
vations to perform an individual estimation if we use only the last 12 matches.
57
avoid overtting.
54
Each of our types predicts an action for each role in each game.
3.4.1 Econometric model
For the econometric analysis we focus exclusively on decisions.
55
In order to determine
how distinctive the behavior of each type is, we rst compute the matrix of correlations
of choices for the dierent types. More precisely, for each observation of an individual
and given the role and type of game, we determine whether the action chosen by the
subject is consisted with each of the considered types (coded as 1) or not (coded as 0).
Naturally, actions will typically be consisted with a subset of types. We then sum up the
24 observations of the individual and calculate the partial correlation matrix for all our
types across all individuals. Since D
3
and L
4
subjects play Nash in all games, they are
indistinguishable from [NE], so we omit them from the analysis. The results are presented
in Table 21 separately for the simultaneous and sequential treatments.
simultaneous
L
1
L
2
L
3
NE D
1
D
2
Sop Pes Opt
L
1
1.0
L
2
.24 1.0
L
3
-.63 .32 1.0
NE -.72 .17 .93 1.0
D
1
.78 .67 -.29 -.40 1.0
D
2
-.43 .56 .91 .79 -.05 1.0
Sop -.71 .20 .95 .98 -.36 .83 1.0
Pes .16 -.17 -.12 -.07 -.02 -.10 -.04 1.0
Opt .96 .25 -.52 -.61 .72 -.38 -.60 .11 1.0
sequential
L
1
L
2
L
3
NE D
1
D
2
Sop Pes Opt
L
1
1.0
L
2
.33 1.0
L
3
-.42 .45 1.0
NE -.64 .23 .90 1.0
D
1
.74 .69 .04 -.24 1.0
D
2
-.24 .64 .92 .77 .22 1.0
Sop -.64 .23 .90 1.0 -.24 .77 1.0
Pes .39 .08 -.13 -.14 .15 -.05 -.14 1.0
Opt .94 .30 -.35 -.55 .68 -.25 -.55 .33 1.0
Table 21: Matrix of types correlation (shaded cells for correlations >:90)
As we already knew from section 3.2.2, [Sop] play Nash in almost all games and roles,
hence the high correlation with [NE]. [Opt] are also rarely separated from L
1
and so
are D
2
from L
3
. Given these correlations, for the econometric analysis we keep 6 types:
2T =fPes;D
1
;L
1
;L
2
;L
3
; NEg.
56
We conduct a maximum likelihood error-rate analysis of subjects' decisions with the
6 types of players discussed above using the econometric model of Costa-Gomes et al.
(2001). A subject of type is expected to make a decision consistent with type , but in
54
Costa-Gomes and Crawford (2006) also include \pseudo types," dened as types constructed from
each of the subjects' empirical behavior in their experiment (for a total of 88 types). Pseudo types had
little explanatory power in their data so we decided not to follow that route.
55
Ideally, we would like to classify individuals according to choices and lookups. In a previous version
(omitted for brevity) we performed such exercise. However, the results were not robust mainly because we
do not have enough observations to estimate the large number of parameters.
56
We realize this biases the results in favor of level k theory since all 4 relevant levels are kept. We
performed the analysis (i) withD2 instead ofL3 and (ii) with neitherD2 norL3 and found similar results
mostly because, as we will see below, L3 and D2 subjects are rare in the sequential treatment and almost
non-existent in the simultaneous.
58
each game makes an error with probability"

2 (0; 1). This error rate may be dierent for
dierent types. Given that our games have only two actions, for a subject of type the
probability of taking the action consistent with type is (1"

) and the probability of
taking the other action is"

. We assume errors are i.i.d. across games and across subjects.
Let i2I =f1; 2;:::; 72g index the subjects in a treatment. Denote by N be the total
number of games an individual plays (24 in our experiment) and by x
i

the total number
of actions consistent with type for subject i. The probability of observing a particular
sample with x
i

type decisions when subject i is type can be written as:
L
i

("

x
i

) = [1"

]
x
i

["

]
Nx
i

Let p

denote the subjects' common prior type probabilities, with 2T and
P

p

= 1.
Weighting the above equation byp

, summing over types, taking logarithms, and summing
over players yields the log-likelihood function for the entire sample:
lnL(p;"

x) =
X
i2I
ln
X
2T
p

[1"

]
x
i

["

]
Nx
i

:
With 6 types, we have 11 parameters to estimate: 5 independent probabilities and 6 error
rates.
3.4.2 Estimation results
We compute parameter estimates separately for the sequential and simultaneous treat-
ments. Under our assumptions, maximum likelihood yields consistent parameter estimates
(the complexity of the estimation made it impractical to compute standard errors). Table
22 shows the estimated type probabilities and type-dependent error rates.
simultaneous
Type Prob. p

Error "

NE .60 .06
L
3
.02 .02
L
2
.22 .11
L
1
.15 .25
D
1
.00 .87
Pes .01 .04
sequential
Type Prob. p

Error "

NE .59 .04
L
3
.12 .12
L
2
.18 .16
L
1
.07 .26
D
1
.05 .41
Pes .00 .64
Table 22: Estimated type probabilities in simultaneous and sequential treatments
The distribution of types is similar in both treatments, with more than half of the
observations corresponding to [NE], and the rest distributed among L
1
, L
2
and L
3
. D
1
and [Pes] are virtually non-existent, lending support for level k.
57
Behavior is more
sophisticated in the sequential than the simultaneous treatment, with more L
3
and fewer
57
This support, however, should be interpreted with caution. First, the vast majority are Nash players,
59
L
2
and L
1
types. Finally, the errors are small for three out of four of the relevant types
(L
2
,L
3
, NE) and somewhat higher for the last one (L
1
). Overall, the estimation is stable,
reasonably accurate and supportive of our previous results.
Given those estimates, we can also characterize the model's implications for the types
of individual subjects. To do this, we calculate the Bayesian posterior conditional on
each subject's decision history. Formally, let x
i
be the sequence of actions taken by an
individual. By Bayes rule, the probability of this individual being of type given x
i
is:
Pr(

x
i
) =
Pr(x
i

)p

P
2T
Pr(x
i

)p

Naturally, the number of subjects that can be classied into a type depends on how harsh
is the requirement for a classication. In Table 23 we report the results for the 72 subjects
in each treatment when a subject is classied into a given type if the posterior estimate
of that type, Pr(

x
i
), is highest and at least .70, .80, and .90, respectively.
simultaneous
min. criterion Pr(

x
i
)
Type .70 .80 .90
NE 42 40 40
L
3
{ { {
L
2
13 13 11
L
1
10 10 9
D
1
{ { {
Pes 1 1 1
N/C 6 8 11
sequential
min. criterion Pr(

x
i
)
Type .70 .80 .90
NE 40 36 36
L
3
3 1 1
L
2
9 8 4
L
1
4 2 {
D
1
2 2 2
Pes { { {
N/C 14 23 29
Table 23: Individual classication in types (N/C = not classied)
In simultaneous, 55% of subjects are classied as equilibrium players and 28% as L
1
or L
2
, even under the tightest requirement of .90 probability of choices tting a type. In
line with previous results, the individual classication is much less accurate in sequential
(50% classied as equilibrium players and only 7% as another level k) and tilted towards
higher sophistication (fewer L
1
and L
2
and more L
3
and unclassied subjects).
In the nal step of the analysis, we put together the results of the individual and cluster
analyses and determine whether subjects classied as a certain type are more prevalent
in some clusters than in others. We present the results for the case of .90 probability of
choices tting a type but the results are similar for .70 and .80. Table 24 summarizes the
ndings.
The results for the simultaneous treatment are remarkably in line with previous nd-
ings. Cluster A is entirely made of Nash players. Clusters B and C are a mix of Nash and
and therefore also consistent with any behavioral theory for which equilibrium is a special case. Second,
we observe few L3 types, and these types could be classied as D2 as well.
60
simultaneous
Cluster
Type A B C D
NE 24 7 9 {
L
3
{ { { {
L
2
{ 4 4 3
L
1
{ { { 9
D
1
{ { { {
Pes { { { 1
N/C 1 4 3 3
sequential
Cluster
Type A B C D
NE 19 15 2 {
L
3
{ 1 { {
L
2
{ { 3 1
L
1
{ { { {
D
1
{ { { 2
Pes { { { {
N/C 2 9 8 10
Table 24: Individual classication in types by cluster
level 2 players as conjectured in section 3.3.3, which explains the within cluster percentage
of Nash choices by role and type presented in Table 20. Finally, a majority of subjects in
cluster D are na ve L
1
players.
Once again, the results are less clear cut in the sequential treatment, possibly due to
signicant learning over the experiment. Clusters A and B are mostly equilibrium players,
with many unclassied subjects in the case of cluster B. Clusters C and D are largely
unclassied. This is not surprising for C but one would have expected some subjects in
cluster D to be categorized as L
1
(or D
1
).
3.4.3 Summary of individual analysis
Choices in the simultaneous treatment map well into types. We nd equilibrium players
in clusters A, B and C, L
2
players in clusters B, C and D and L
1
players in cluster
D. Other types are rarely represented. The mapping is not as sharp in the sequential
treatment (except for cluster A which consists of equilibrium players), possibly due to
learning eects.
3.5 Conclusion
In this paper, we have studied equilibrium behavior in dominance solvable games. We
have found that Nash compliance was slightly higher in sequential than simultaneous
treatments, suggesting that the cue implied by the order of moves is helpful, but only
moderately, in the search for the optimal way to play. The paper has also shown that
attentional data can be highly predictive of behavior. In particular, looking at all the
payos necessary to compute the equilibrium and looking at payos in the order predicted
by elimination of strategies are strong indicators of Nash choices. Also, when we focused
on subjects who play the equilibrium, we noticed that they look more eciently and
systematically (less wandering and more correct sequence) in sequential than simultaneous.
61
Several issues deserve further investigation. First, the discrepancy in \lookup e-
ciency" across treatments suggests that the dierences in equilibrium choices between
treatments could be exacerbated when the complexity of the game grows. A proper test
of this conjecture would lend support to the value of attentional data as an indicator
for out-of-sample predictions. Second, the diculty to nd the player with a dominant
strategy in the simultaneous treatment, together with its importance in determining equi-
librium compliance, is intriguing. It would be interesting to know if directing the attention
of our subjects to that player can have a long lasting eect on choice.
58
Third, decisions
could be aected by the presentation of the game. In our design, it is always the right-
most player who has the dominant strategy. We believe that subjects would be cued if
the last mover always had the dominant strategy (which we have to for comparison with
simultaneous) but her position in the screen (rightmost, center, leftmost) changed from
game to game. However, this is an empirical question. Overall, we believe that choice and
non-choice data are strongly complementary measures and that experimental research in
that direction will improve our understanding of (the limits to) human cognition.
58
Naturally, the challenge is to devise an ecologically valid mechanism which is powerful yet subtle
enough to avoid demand eects from the experimenter.
62
Supplementary Appendix
Appendix 3 A. Payo variants used in the experiment
payoffs
Variant Matches Size Type Role 0 Role 1 Role 2 Role 3
1 1, 7 4 H 28 12 4 25 10 20 10 14
10 24 20 5 25 10 20 26
2 10, 19 4 H 15 25 38 18 14 36 34 26
30 14 18 32 30 10 20 12
3 20, 23 4 H 15 30 16 28 15 35 18 24
24 16 30 20 32 10 10 12
4 2, 14 4 L 15 25 8 18 14 6 10 14
26 10 20 10 6 18 18 24
5 5, 11 4 L 10 22 25 15 28 14 22 32
18 10 15 30 12 24 14 20
6 15, 21 4 L 32 16 16 34 18 6 10 8
22 30 30 22 8 22 18 14
7 3, 9 3 H 4 25 10 20 10 14
20 5 25 10 24 30
8 6, 13 3 H 6 22 12 28 18 12
28 8 22 10 10 6
9 12, 17 3 H 4 20 8 22 10 8
15 5 25 10 26 22
10 4, 24 3 L 22 8 10 28 12 10
10 25 22 12 24 20
11 8, 18 3 L 12 22 10 16 18 14
28 10 18 10 10 8
12 16, 22 3 L 4 25 10 25 12 20
20 5 20 12 22 32
Table 25: Payo-Variants
63
Appendix 3 B. Sample of Instructions (simultaneous treatment)
Thanks for participating in this experiment on group decision-making. During the experiment we would
like to have your undistracted attention. Do not open other applications on your computer, chat with
other students, use headphones, read, etc. Make sure to turn your phone to silent mode and not use it
during the experiment.
You will be paid for your participation in cash at the end of the experiment. Dierent participants
may earn dierent amounts. What you earn depends partly on your decisions, partly on the decisions of
others, and partly on chance. The entire experiment will take place through computer terminals, and all
interaction between participants will take place through the computers. Do not talk or in any way try to
communicate with other participants during the experiment.
We will start with a brief instruction period. During the instruction period, you will be given a
complete description of the experiment and will be shown how to use the computers. It is very important
that you listen carefully and fully understand the instructions since your decisions will aect your earnings.
You will be asked some review questions after the instructions, which have to be answered correctly before
we can begin the experiment. If you have any questions during the instruction period, raise your hand
and your question will be answered so everyone can hear. If any diculties arise after the experiment has
begun, raise your hand, and an experimenter will come and assist you.
At the end of the session, you will be paid the sum of what you have earned in all matches, plus the
show-up fee of $5. Your earnings during the experiment are denominated in tokens. Depending on your
decisions, you can earn more or less tokens. At the end of the experiment, we will count the number of
tokens you have and you will be paid $1.00 for every 30 tokens. Everyone will be paid in private and you
are under no obligation to tell others how much you earned.
The experiment consists of 24 matches. In each match, you will be grouped with either two or three
other participants, which means there will be either 3 or 4 participants in a group. Group size will be
dierent for each match. Since there are 12 participants in today's session, in a match there will be either
3 groups of 4 participants or 4 groups of 3 participants. You are not told the identity of the participants
you are grouped with. Your payo depends only on your decisions, the decisions of the participants you
are grouped with and on chance. What happens in the other groups has no eect on your payo and vice
versa. Your decisions are not revealed to participants in the other groups.
We will present the game using screenshots. Your instruction package includes two separate pages,
which are screenshots of computer screens. Look at the rst page. I will now describe the screenshot in
\Display 1". Do you have the Display 1 in front of you? Raise your hand high if you do. If you don't raise
your hand we will come around and guide your attention to the separate Display 1 page.
In this match each participant is grouped with two other participants. At the beginning of the match,
the computer randomly assigns a role to each of the three members in your group as RED or GREEN or
BLUE. In each match, each role is asked to make a choice from two possible actions, XR or YR for the
subject in the RED role, XG or YG for the subject in the GREEN role and XB or YB for the subject in
the BLUE role. You will choose an action without knowing which actions the other players in your group
have chosen.
You will see a screen like the one in Display 1. In this example, you have the GREEN role. The screen
says `GREEN, please choose an action'. Your action can be either XG or YG.
The payos you may obtain are the numbers inside the boxes in the left table. In this example, your
payo depends on your action (the rows, XG or YG) and on the action of RED (the columns, XR or YR).
For example, if you choose YG and RED chooses XR, then you will earn 80 tokens. If RED chooses YR
instead, then you will earn 132 tokens.
If you are Role RED, you will see a screen similar to Display 1 but it will read, 'RED, please choose
an action'. RED must respond by clicking on the XR orYR button. The payos RED may obtain are the
numbers inside the middle table. In this example, the payos RED may obtain depend on his action and
the action of BLUE. For example, if RED chooses YR and BLUE chooses XB, RED will earn 96 tokens.
Finally, the payos BLUE may obtain are the numbers inside the right table. Payos that BLUE may
obtain depend on his action and the action of GREEN.
Once every member in the group has made a choice, the computer screen will display the actions for
all members of your group and your payo for the match. The payo is added to your total. This will end
64
Figure 10: Screenshot of the game: Display 1
the current match.
When a match is nished, we proceed to the next match. For the next match, the computer randomly
reassigns all participants to a new group and to a new role. The new assignments do not depend in any
way on the past decisions of any participant including you, and are done completely randomly by the
computer. The assignments are independent across groups, across participants and across matches. This
second match then follows the same rules as the rst match with two exceptions. First, the payos inside
the tables are now dierent. Second, in the new match you may be grouped with 3 (rather than 2) other
participants. If you are grouped with three other participants the roles are \RED", \GREEN", \BLUE"
and \ORANGE".
The same procedure continues for 24 matches, after which the experiment ends.
A history screen at the bottom will show a rolling history of your role in that match, the actions of
all subjects in your group and your payo.
Now turn to the Display 2. Do you have the Display 2 page in front of you? Raise your hand high if
you do. If you don't raise your hand we will come around and guide you.
This is a similar game but the payos are now hidden in boxes. This is the type of screen you will
observe during the experiment. In order to nd out what your possible payos are, or what the other roles'
payos are, you must move your mouse into the box that shows the payo from a particular pair of actions
in the table, and click-and-hold one of the mouse buttons. If you do not hold down the mouse button the
payo will disappear. When you move the mouse away from the box, the payo will also disappear. If
you move your mouse back into a box, click-and-hold, the exact same payo will appear again. Clicking
does not aect your earnings and you can look at as many of the possible payos as you care to, or as few,
for as long or as brie
y as you like. If you have trouble guring out how to use the mouse to temporarily
reveal the hidden payos during the experiment, raise your hand right away and we will come around and
help you.
Are there any questions? If there are any problems or questions from this point on, raise your hand
and an experimenter will come and assist you.
We will now begin a Practice session and go through one practice match to familiarize you with the
computer interface and the procedures. The tokens accumulated in this match do not count towards your
nal dollar earnings. The practice match is similar to the matches in the experiment. During the practice
match, please do not hit any keys until you are asked to, and when you enter information, please do exactly
as asked. You are not paid for this practice match. At the end of the practice match you will have to
answer some review questions.
65
Figure 11: Screenshot of the game: Display 2
[START game]
You now see the rst screen of the experiment on your computer. Raise your hand high if you do.
At the top left of the screen, you see your subject ID. Please record that ID in your record sheet. You
have been grouped by the computer with two other participants and assigned a role as RED or GREEN
or BLUE, which you can see on your screen. The pair assignment and role will remain the same for the
entire match. You can also see on the top left of the screen that you are in match 1.
You will see a screen similar to the Display 2 with the payos hidden in boxes. Please do not hit any
key. Now, use your mouse button to reveal the payos in the dierent boxes. Familiarize yourself with the
click-and-hold method. If you have problems revealing the payos raise your hand and we will come and
assist you.
If you are Role BLUE, please select YB. Note that it does not matter which one you choose since you
will not be paid for this round. You must wait for other participants in your group to make a choice. If
you are Role GREEN, please select YG. If you are Role RED, please select XR.
Once everyone in your group makes a choice, the computer screen will display the actions for all
members of your group and your payo for the match. Please spend some time familiarizing yourself with
this screen.
Now click \Continue". The practice match is over. Please complete the review questions before we
begin the paid session. Please answer all questions correctly and click to submit. The quiz will disappear
from your screen.
Are there any questions before we begin with the paid session?
We will now begin with the 24 paid matches. If there are any problems or questions from this point
on, raise your hand and an experimenter will come and assist you.
[START MATCH 1]
[After MATCH 24 read]:
This was the last match of the experiment. Your payo is displayed on your screen. Your nal payo
in the experiment is equal to your stock of tokens in the end converted into dollars plus the show-up fee
of $5. Please record this payo in your record sheet and remember to CLICK OK after you are done.
We will pay each of you in private in the next room in the order of your Subject ID number. Remember
you are under no obligation to reveal your earnings to the other participants. Please put the mouse on the
side of the computer and do not use either the mouse or the keyboard. Please remain seated and keep the
dividers pulled out until we call you to be paid. Do not converse with the other participants or use your
cell phone. Thank you for your cooperation.
66
QUIZ
1. In this experiment, your payos are presented in boxes. Please choose the correct option:
i) Payos for all cells are always visible.
ii) Payos for all cells are hidden. They can be viewed by moving your mouse over the cell and
clicking-and-holding one of the mouse buttons. There is no cost of opening a cell.
iii) Payos of some cells are hidden and payos of other cells are visible.
iv) Payos for all cells are hidden. They can be viewed by moving your mouse over the cell and
clicking-and-holding one of the mouse buttons. However, tokens are subtracted from your payo when you
view a cell.
2. Look at Display 1. Suppose you are role GREEN. What will be your payo if you choose XG and
RED chooses YR?
i) 72
ii) 66
iii) It depends on what BLUE chooses
3. What will be the payo of RED?
i) It depends of what BLUE chooses
ii) 96
iii) 112
4. What will be the payo of BLUE?
i) 66
ii) 40 if BLUE chooses XB and 66 if BLUE chooses YB
iii) 144 if BLUE chooses XB and 94 if BLUE chooses YB
5. Look at Display 1. If actions chosen by all members of the group are XG, YR, YB what will be the
earnings of the three roles?
i) GREEN: 72 tokens, RED: 96 tokens, BLUE: 94 tokens.
ii) GREEN: 72 tokens, RED: 112 tokens, BLUE: 66 tokens.
iii) GREEN: 66 tokens, RED: 112 tokens, BLUE: 66 tokens.
6. Look at Display 2. What is your role and which game table hides your own payos
i) My role is GREEN and my payos are hidden in the middle table
ii) My role is BLUE and my payos are hidden in the right table
iii) My role is GREEN and my payos are hidden in the left table
iv) I cannot know what my role is yet.
67
Appendix 3 C. Determination of MIN set
The MIN set depends on the role, treatment and the actions consistent with Nash. In
sequential, it also depends on the action of the rst player (role 0 in 4-player games and
role 1 in 3-player games). We explain MIN with the help of Table 26. The values in this
table are not the payos from the game but, instead, the codes of the cells used here to
support the explanation of MIN.
Role 0
X
1
Y
1
X
0
1 2
Y
0
3 4
Role 1
X
2
Y
2
X
1
5 6
Y
1
7 8
Role 2
X
3
Y
3
X
2
9 10
Y
2
11 12
Role 3
X
0
Y
0
X
3
13 14
Y
3
15 16
Table 26: Support table to nd MIN (values are not payos in the game but instead the
cell codes given to facilitate the explanation of MIN)
MIN for simultaneous. Take the convention that the Nash equilibrium is (X
0
;X
1
;X
2
;X
3
).
MIN for role 3 are cells 13, 14, 15 and 16, since opening this set enables role 3 to gure
out her dominant strategy. MIN for role 2 are cells 13, 14, 15, 16, 9 and 11: opening 13,
14, 15 and 16 enables role 2 to know that X
3
is a dominant strategy for role 3 and then
role 2 only needs to open cells 9 and 11, the cells in her payo matrix corresponding to
X
3
. Using the same logic we get that MIN for role 1 are cells 13, 14, 15, 16, 9, 11, 5 and
7 and MIN for role 0 are cells 13, 14, 15, 16, 9, 11, 5, 7, 1 and 3.
MIN for sequential. MIN for the rst player (role 0 in 4-player games and role 1 in
3-player games) is dened exactly as in the simultaneous treatment. MIN for the other
roles depends on the action taken by the rst player. Let us assume that role 0 chooses
X
0
in 4-player games (or role 1 chooses X
1
in 3-player games). MIN for role 3 are only
cells 13 and 15: role 3 observes the action of role 0 (role 1 in 3-player games) so, in order
to calculate her Nash strategy, she only needs to compare cells 13 and 15 in her payo
matrix. With an analogous reasoning we get that MIN for role 2 are cells 13, 15, 9 and
11 and MIN for role 1 in 4-player games are cells 13, 15, 9, 11, 5 and 7. Naturally, when
we code MIN in each of our games we need to track which action corresponds to the Nash
equilibrium (X
i
or Y
i
) and which action has been taken by the rst player.
68
4 Conclusion
These essays presented empirical evidence on two issues in development economics and
game theory. The rst essay (chapter 2) presents evidence from India on benets of
providing roads on preventive health care usage. The second essay (chapter 3) presents
results from an experimental examination of dierence in choice and decision making
process between sequential and simultaneous games.
4.1 Pathways to Preventive Health
The rst essay estimates in context of India the impact of a nationwide road construction
program on the preventive health care usage. We also try to nd evidence on plausible
mechanism through which roads could impact health care behavior. For our analysis we
use third wave of district level household survey. We match the household survey data
with the program placement data at the treatment level and then use fuzzy regression dis-
continuity to overcome the problem of endogenous road provision. We nd that provision
of roads increases the use of preventive health care usage by women and household. We
provide evidence for some plausible mechanism for this increase. We show provision of
roads leads to an: a) increase in the awareness of government run health care programs
amongst households, b) improvement in health care supply, and c) increase in social in-
teraction within and between villages. Our results show additional benets of providing
roads and provides important insights for increasing preventive health care use in devel-
oping countries. We show that roads not only create physical pathways but also improves
informational availability between regions.
4.2 Choice and Reasoning in Sequential and Simultaneous Games
The second essay looks at dierence in choice and decision making process between se-
quential and simultaneous games. We consider sequential and simultaneous versions of
games that have the same equilibrium actions and requires the same reasoning to reach
to the equilibrium actions. Our objective is to test whether players play dierently in the
sequential games than in the simultaneous games and in case we see a dierence in their
behavior we want to know whether the players also analyze the two games dierently.
There are many reasons why we would expect any dierence between sequential and si-
multaneous games: a) A game may have multiple nash equilibria but unique sub game
perfect nash, b) the dierence in visual representation of the game can lead to dierence in
behavior, c) players in sequential (except the "rst" mover) need to analyze a smaller game
than in the simultaneous games, d) the sequential games by providing the order of moves
may provide a "key" (hint) to solve the game. The game we study is dominance solvable
complete information game with unique nash and therefore unique subgame perfect nash.
We also keep the same visual representation for the sequential and simultaneous version
of the game. We nd slightly more equilibrium choices in sequential than in simultaneous.
Two attentional variables are highly predictive of equilibrium behavior in both versions:
looking at the payos necessary to compute the Nash equilibrium and looking at payos
in the order predicted by sequential elimination of the strategies. Finally, the sequence
69
of lookups reveals dierent cognitive processes between sequential and simultaneous, even
among subjects who play the equilibrium strategy. Subjects have a harder time nding
the player with a dominant strategy in simultaneous than in sequential. However con-
ditional on nding such player, the unraveling logic of iterated elimination of dominated
strategies is performed (equally) fast and ecient in both cases. Although we see not a
huge dierence in equilibrium behavior between sequential and simultaneous versions of
the game, we do see a big dierence in the decision making process. We conjecture when
the game gets more dicult, we will see bigger dierences in choices as well.
70
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