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Better-Reply Dynamics in Deferred Acceptance Games

27 Pages Posted: 3 Jun 2011  

Guillaume Haeringer

Autonomous University of Barcelona - Department of Economics and Economic History

Hanna Halaburda

Bank of Canada; New York University (NYU); CESifo (Center for Economic Studies and Ifo Institute)

Date Written: June 1, 2011

Abstract

In this paper we address the question of learning in a two-sided matching mechanism that utilizes the deferred acceptance algorithm. We consider a repeated matching game where at each period agents observe their match and have the opportunity to revise their strategy (i.e., the preference list they will submit to the mechanism). We focus in this paper on better-reply dynamics. To this end, we first provide a characterization of better-replies and a comprehensive description of the dominance relation between strategies. Better-replies are shown to have a simple structure and can be decomposed into four types of changes. We then present a simple better-reply dynamics with myopic and boundedly rational agents and identify conditions that ensure that limit outcomes are outcome equivalent to the outcome obtained when agents play their dominant strategies. Better-reply dynamics may not converge, but if they do converge, then the limit strategy profiles constitute a subset of the Nash equilibria of the stage game.

Keywords: better-reply dynamics, deferred acceptance, two-sided matching.

JEL Classification: C72, D41.

Suggested Citation

Haeringer, Guillaume and Halaburda, Hanna, Better-Reply Dynamics in Deferred Acceptance Games (June 1, 2011). Harvard Business School Strategy Unit Working Paper No. 11-126. Available at SSRN: https://ssrn.com/abstract=1856503 or http://dx.doi.org/10.2139/ssrn.1856503

Guillaume Haeringer

Autonomous University of Barcelona - Department of Economics and Economic History ( email )

Edifici B - Campus Bellaterra
Barcelona, 08193
Spain
+34 93 581 12 15 (Phone)
+34 93 581 20 12 (Fax)

Hanna Halaburda (Contact Author)

Bank of Canada ( email )

234 Wellington Street
Ontario, Ottawa K1A 0G9
Canada

New York University (NYU) ( email )

Bobst Library, E-resource Acquisitions
20 Cooper Square 3rd Floor
New York, NY 10003-711
United States

CESifo (Center for Economic Studies and Ifo Institute) ( email )

Munich
Germany

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