Better-Reply Dynamics in Deferred Acceptance Games
Autonomous University of Barcelona - Department of Economics and Economic History
Bank of Canada; New York University (NYU); CESifo (Center for Economic Studies and Ifo Institute)
June 1, 2011
Harvard Business School Strategy Unit Working Paper No. 11-126
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.
Number of Pages in PDF File: 27
Keywords: better-reply dynamics, deferred acceptance, two-sided matching.
JEL Classification: C72, D41.
Date posted: June 3, 2011