An algorithm for proper rationalizability

• 成果类型: Article
• 署名作者: Perea, Andres
• 署名单位: Maastricht University
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2010.10.008
• 发表日期: 2011
• 页码: 510-525
• 关键词: Epistemic game theory; Proper rationalizability; algorithms

摘要

Proper rationalizability (Schuhmacher, 1999; Asheim, 2001) is a concept in epistemic game theory based on the following two conditions: (a) a player should be cautious, that is, should not exclude any opponent's strategy from consideration; and (b) a player should respect the opponents' preferences, that is, should deem an opponent's strategy s(i) infinitely more likely than s(i)' if he believes the opponent to prefer s(i) to s(i)'. A strategy is properly rationalizable if it can optimally be chosen under common belief in the events (a) and (b). In this paper we present an algorithm that for every finite game computes the set of all properly rationalizable strategies. The algorithm is based on the new idea of a preference restriction, which is a pair (s(i), A(i)) consisting of a strategy s(i), and a subset of strategies A(i), for player i. The interpretation is that player i prefers some strategy in A(i) to s(i). The algorithm proceeds by successively adding preference restrictions to the game. (C) 2010 Elsevier Inc. All rights reserved.