Admissibility in games

Adam Brandenburger, Amanda Friedenberg, H. Jerome Keisler

Research output: Contribution to journalArticlepeer-review

101 Scopus citations

Abstract

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)
Pages (from-to)307-352
Number of pages46
JournalEconometrica
Volume76
Issue number2
DOIs
StatePublished - Mar 2008

Keywords

  • Admissibility
  • Assumption
  • Completeness
  • Epistemic game theory
  • Iterated weak dominance
  • Rationality
  • Self-admissible sets

ASJC Scopus subject areas

  • Economics and Econometrics

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