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Continuity of the value and optimal strategies when common priors change

Author

Listed:
  • Ezra Einy
  • Ori Haimanko
  • Biligbaatar Tumendemberel

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

Suggested Citation

  • Ezra Einy & Ori Haimanko & Biligbaatar Tumendemberel, 2012. "Continuity of the value and optimal strategies when common priors change," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(4), pages 829-849, November.
  • Handle: RePEc:spr:jogath:v:41:y:2012:i:4:p:829-849
    DOI: 10.1007/s00182-010-0248-4
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    References listed on IDEAS

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    4. Kajii, Atsushi & Morris, Stephen, 1998. "Payoff Continuity in Incomplete Information Games," Journal of Economic Theory, Elsevier, vol. 82(1), pages 267-276, September.
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    More about this item

    Keywords

    Zero-sum Bayesian games; Common prior; Value; Optimal strategies; Interim; Ex-ante; Bayesian equilibrium; Upper semi-continuity; Lower approximate semi-continuity; C72;
    All these keywords.

    JEL classification:

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

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