Admissibility in games

Adam Brandenburger, Amanda Friedenberg, H. Jerome Keisler

Research output: Chapter in Book/Report/Conference proceedingChapter


Suppose that each player in a game is rational, each player thinks the other players are rational, and so on. Also, suppose that rationality is taken to incorporate an admissibility requirement-that is, the avoidance of weakly dominated strategies. Which strategies can be played? We provide an epistemic framework in which to address this question. Specifically, we formulate conditions of rationality and mth-order assumption of rationality (RmAR) and rationality and common assumption of rationality (RCAR). We show that (i) RCAR is characterized by a solution concept we call a "self-Admissible set"; (ii) in a "complete"type structure, RmAR is characterized by the set of strategies that survive m + 1 rounds of elimination of inadmissible strategies; (iii) under certain conditions, RCAR is impossible in a complete structure.

Original languageEnglish (US)
Title of host publicationWorld Scientific Series in Economic Theory
EditorsAdam Brandenburger
PublisherWorld Scientific
Number of pages52
StatePublished - Sep 1 2023

Publication series

NameWorld Scientific Series in Economic Theory


  • Epistemic game theory
  • admissibility
  • assumption
  • completeness
  • iterated weak dominance
  • rationality
  • self-Admissible sets

ASJC Scopus subject areas

  • Economics and Econometrics
  • Statistics, Probability and Uncertainty
  • Applied Mathematics
  • Statistics and Probability


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