A new epistemic characterization of ε-proper rationalizability

• 成果类型: Article
• 署名作者: Perea, Andres; Roy, Souvik
• 署名单位: Maastricht University; Indian Statistical Institute; Indian Statistical Institute Kolkata
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2017.04.009
• 发表日期: 2017
• 页码: 309-328
• 关键词: Epistemic game theory; incomplete information; Proper rationalizability

摘要

For a given epsilon > 0, the concept of epsilon-proper rationalizability (Schuhmacher, 1999) is based on two assumptions: (1) every player is cautious, i.e., does not exclude any opponent's choice from consideration, and (2) every player satisfies the epsilon-proper trembling condition, i.e., the probability he assigns to an opponent's choice a is at most epsilon times the probability he assigns to b whenever he believes the opponent to prefer b to a. In this paper we show that a belief hierarchy is epsilon-properly rationalizable in the complete information framework, if and only if, there is an equivalent belief hierarchy within the incomplete information framework that expresses common belief in the events that (1) players are cautious, (2) the players' beliefs about the opponent's utilities are centered around the original utilities in some specific way parametrized by epsilon, and (3) players rationalize each opponent's choice by a utility function that is as close as possible to the original utility function. (C) 2017 Elsevier Inc. All rights reserved.