The implications of finite-order reasoning

Adam Brandenburger (), Alexander Danieli () and Amanda Friedenberg ()
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Adam Brandenburger: Stern School of Business, New York University
Alexander Danieli: School of Business, Arizona State University
Amanda Friedenberg: Department of Economics, University of Arizona

Theoretical Economics, 2021, vol. 16, issue 4

Abstract: 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.

Keywords: Epistemic game theory; strategic uncertainty; bounded reasoning; identifying reasoning (search for similar items in EconPapers)
JEL-codes: D01 D03 D83 (search for similar items in EconPapers)
Date: 2021-11-08
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