The context of the game

Amanda Friedenberg, Martin Meier

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

We study games of incomplete information and argue that it is important to correctly specify the “context” within which hierarchies of beliefs lie. We consider a situation where the players understand more than the analyst: It is transparent to the players—but not to the analyst—that certain hierarchies of beliefs are precluded. In particular, the players’ type structure can be viewed as a strict subset of the analyst’s type structure. How does this affect a Bayesian equilibrium analysis? One natural conjecture is that this doesn’t change the analysis—i.e., every equilibrium of the players’ type structure can be associated with an equilibrium of the analyst’s type structure. We show that this conjecture is wrong. Bayesian equilibrium may fail an Extension Property. This can occur even in the case where the game is finite and the analyst uses the so-called universal structure (to analyze the game)—and, even, if the associated Bayesian game has an equilibrium. We go on to explore specific situations in which the Extension Property is satisfied.

Original languageEnglish (US)
Pages (from-to)1-40
Number of pages40
JournalEconomic Theory
DOIs
Publication statusAccepted/In press - Dec 22 2015

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Keywords

  • Bayesian games
  • Context
  • Hierarchies of beliefs
  • Robustness
  • Universal type structure

ASJC Scopus subject areas

  • Economics and Econometrics

Cite this

Friedenberg, A., & Meier, M. (Accepted/In press). The context of the game. Economic Theory, 1-40. https://doi.org/10.1007/s00199-015-0938-z