Continuity of the value and optimal strategies when common priors change

Ezra Einy, Ori Haimanko, Biligbaatar Tumendemberel

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We show that the value of a zero-sum Bayesian game is a Lipschitz continuous function of the players' common prior belief with respect to the total variation metric on beliefs. This is unlike the case of general Bayesian games where lower semi-continuity of Bayesian equilibrium (BE) payoffs rests on the "almost uniform" convergence of conditional beliefs. We also show upper semi-continuity (USC) and approximate lower semi-continuity (ALSC) of the optimal strategy correspondence, and discuss ALSC of the BE correspondence in the context of zero-sum games. In particular, the interim BE correspondence is shown to be ALSC for some classes of information structures with highly non-uniform convergence of beliefs, that would not give rise to ALSC of BE in non-zero-sum games.

Original languageEnglish
Pages (from-to)829-849
Number of pages21
JournalInternational Journal of Game Theory
Volume41
Issue number4
DOIs
StatePublished - 1 Dec 2012

Keywords

  • Bayesian equilibrium
  • Common prior
  • Ex-ante
  • Interim
  • Lower approximate semi-continuity
  • Optimal strategies
  • Upper semi-continuity
  • Value
  • Zero-sum Bayesian games

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics (miscellaneous)
  • Social Sciences (miscellaneous)
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty

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