The implications of finite-order reasoning

Adam Brandenburger, Alexander Danieli, Amanda Friedenberg

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)1605-1654
Number of pages50
JournalTheoretical Economics
Issue number4
StatePublished - Nov 2021


  • D01
  • D03
  • D83
  • Epistemic game theory
  • bounded reasoning
  • identifying reasoning
  • strategic uncertainty

ASJC Scopus subject areas

  • Economics, Econometrics and Finance(all)


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