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CYCLICAL MATCHING IN HIGHER DIMENSIONS
by
Brijesh Preston Pinto
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Ful llment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(ECONOMICS)
May 2011
Copyright 2011 Brijesh Preston Pinto
Object Description
| Title | Cyclical matching in higher dimensions |
| Author | Pinto, Brijesh Preston |
| Author email | brijeshp@usc.edu; bpinto@gmail.com |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Economics |
| School | College of Letters, Arts and Sciences |
| Date defended/completed | 2010-11-18 |
| Date submitted | 2011 |
| Restricted until | Restricted until 21 Jan. 2013. |
| Date published | 2013-01-21 |
| Advisor (committee chair) |
Wilkie, Simon J. Magill, Michael J.P. |
| Advisor (committee member) | Alonso, Ricardo |
| Abstract | In this dissertation, we study stable and strongly stable matching for the Cyclic Matching Problem when the number of dimensions (sides) is greater than or equal to three. The following is a summary of the analysis and results.; 1. We offer preliminary results on Pareto optimality in higher dimensions; we also comment on changes in the relationships among stability, strong stability, and Pareto optimality, when we move from the two-sided to the higher-sided case.; 2. We construct a function whose fixed points are exactly the set of strongly stable matchings.; 3. We show how to compute all strongly stable matchings for a given instance of the Cyclic Matching Problem using the methodology of Echenique and Yenmez (2007).; 4. We construct a non-monotonic function whose fixed points are exactly the set of stable matchings.; 5. We investigate an extension of the Adachi program to higher dimensions; in particular, we look at the properties of the fixed points of certain functions constructed so that they are increasing with respect to "natural" partial orders in higher dimensions.; 6. We consider extensions of the Gale-Shapley algorithm to higher dimensions; we design the Hierarchical Gale-Shapley Algorithm and comment on its properties with regard to (1) convergence and (2) stability of the output matching. |
| Keyword | matching; cyclical preferences; stability; strong stability; Pareto optimality; fixed points; Gale-Shapley algorithm |
| Language | English |
| Part of collection | University of Southern California dissertations and theses |
| Publisher (of the original version) | University of Southern California |
| Place of publication (of the original version) | Los Angeles, California |
| Publisher (of the digital version) | University of Southern California. Libraries |
| Provenance | Electronically uploaded by the author |
| Type | texts |
| Legacy record ID | usctheses-m3618 |
| Contributing entity | University of Southern California |
| Rights | Pinto, Brijesh Preston |
| Repository name | Libraries, University of Southern California |
| Repository address | Los Angeles, California |
| Repository email | cisadmin@lib.usc.edu |
| Filename | etd-Pinto-4185 |
| Archival file | uscthesesreloadpub_Volume68/etd-Pinto-4185-1.pdf |
Description
| Title | Page 1 |
| Contributing entity | University of Southern California |
| Repository email | cisadmin@lib.usc.edu |
| Full text | CYCLICAL MATCHING IN HIGHER DIMENSIONS by Brijesh Preston Pinto A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Ful llment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (ECONOMICS) May 2011 Copyright 2011 Brijesh Preston Pinto |
