The implications of finite-order reasoning

• 成果类型: Article
• 署名作者: Brandenburger, Adam; Danieli, Alexander; Friedenberg, Amanda
• 署名单位: New York University; New York University; NYU Shanghai; Arizona State University; Arizona State University-Tempe; University of Arizona
• 刊物名称: THEORETICAL ECONOMICS
• ISSN/ISSBN: 1933-6837
• DOI: 10.3982/TE2889
• 发表日期: 2021-11-01
• 页码: 1605-1654
• 关键词: Epistemic game theory; strategic uncertainty; bounded reasoning; identifying reasoning; D01; D03; D83

摘要

The epistemic conditions of rationality and mth-order strong belief of rationality (RmSBR; Battigalli and Siniscalchi (2002)) formalize the idea that players engage in contextualized forward-induction reasoning. This paper characterizes the behavior consistent with RmSBR across all type structures. In particular, in a class of generic games, R(m-1)SBR is characterized by a new solution concept we call an m-best response sequence (m-BRS). Such sequences are an iterative version of extensive-form best response sets (Battigalli and Friedenberg (2012)). The strategies that survive m rounds of extensive-form rationalizability are consistent with an m-BRS, but there are m-BRS's that are disjoint from the former set. As such, there is behavior that is consistent with R(m-1)SBR but inconsistent with m rounds of extensive-form rationalizability. We use our characterization to draw implications for the interpretation of experimental data. Specifically, we show that the implications are nontrivial in the three-repeated Prisoner's Dilemma and Centipede games.