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Continuity of the value and optimal strategies when common priors change

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  • Einy, Ezra
  • Haimanko, Ori
  • Tumendemberelz, Biligbaatar

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. Copyright Springer-Verlag 2012
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Suggested Citation

  • Einy, Ezra & Haimanko, Ori & Tumendemberelz, Biligbaatar, 2009. "Continuity of the value and optimal strategies when common priors change," Discussion Papers 2009-09, Graduate School of Economics, Hitotsubashi University.
    • Handle: RePEc:hit:econdp:2009-09
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    File URL: https://hit-u.repo.nii.ac.jp/record/2052776/files/070econDP09-09.pdf
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    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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