Abstract

http://ssrn.com/abstract=1856503
 
 

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Better-Reply Dynamics in Deferred Acceptance Games


Guillaume Haeringer


Autonomous University of Barcelona - Department of Economics and Economic History

Hanna Halaburda


Bank of Canada

June 1, 2011

Harvard Business School Strategy Unit Working Paper No. 11-126

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.

Number of Pages in PDF File: 27

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

JEL Classification: C72, D41.

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Date posted: June 3, 2011  

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: http://ssrn.com/abstract=1856503 or http://dx.doi.org/10.2139/ssrn.1856503

Contact Information

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
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