Theoretical Economics, Volume 16, Number 4 ( 2021)

Theoretical Economics 16 (2021), 1605–1654

The implications of finite-order reasoning

Adam Brandenburger, Alexander Danieli, Amanda Friedenberg


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

JEL classification: D01, D03, D83

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