Iterated dominance revisited

Amanda Friedenberg, H. Jerome Keisler

Research output: Contribution to journalArticlepeer-review

Abstract

Epistemic justifications of solution concepts often refer to type structures that are sufficiently rich. One important notion of richness is that of a complete type structure, i.e., a type structure that induces all possible beliefs about types. For instance, it is often said that, in a complete type structure, the set of strategies consistent with rationality and common belief of rationality are the set of strategies that survive iterated dominance. This paper shows that this classic result is false, absent certain topological conditions on the type structure. In particular, it provides an example of a finite game and a complete type structure in which there is no state consistent with rationality and common belief of rationality. This arises because the complete type structure does not induce all hierarchies of beliefs—despite inducing all beliefs about types. This raises the question: Which beliefs does a complete type structure induce? We provide several positive results that speak to that question. However, we also show that, within ZFC, one cannot show that a complete structure induces all second-order beliefs.

Original languageEnglish (US)
Pages (from-to)377-421
Number of pages45
JournalEconomic Theory
Volume72
Issue number2
DOIs
StatePublished - Sep 2021
Externally publishedYes

Keywords

  • Epistemic game theory
  • Iterated dominance
  • Rationality and common belief of rationality
  • Rationalizability
  • Type structures

ASJC Scopus subject areas

  • Economics and Econometrics

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