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On the Stability of Equilibria in Incomplete Information Games under Ambiguity

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Abstract

In this paper, we look at the (Kajii and Ui) mixed equilibrium notion, which has been recognized by previous literature as a natural solution concept for incomplete information games in which players have multiple priors on the space of payoff relevant states. We investigate the problem of stability of mixed equilibria with respect to perturbations on the sets of multiple priors. We find out that the (Painlevé-Kuratowski) convergence of posteriors ensures that stability holds; whereas, convergence of priors is not enough to obtain stability since it does not always implies convergence of posteriors when we consider updating rules (for multiple priors) based on the classical Bayesian approach.

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  • Giuseppe De Marco & Maria Romaniello, 2013. "On the Stability of Equilibria in Incomplete Information Games under Ambiguity," CSEF Working Papers 332, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
  • Handle: RePEc:sef:csefwp:332
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    References listed on IDEAS

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    1. Lo, Kin Chung, 1996. "Equilibrium in Beliefs under Uncertainty," Journal of Economic Theory, Elsevier, vol. 71(2), pages 443-484, November.
    2. Marinacci, Massimo, 2000. "Ambiguous Games," Games and Economic Behavior, Elsevier, vol. 31(2), pages 191-219, May.
    3. Dow James & Werlang Sergio Ribeiro Da Costa, 1994. "Nash Equilibrium under Knightian Uncertainty: Breaking Down Backward Induction," Journal of Economic Theory, Elsevier, vol. 64(2), pages 305-324, December.
    4. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    5. De Marco, Giuseppe & Romaniello, Maria, 2013. "A limit theorem for equilibria under ambiguous belief correspondences," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 431-438.
    6. repec:wsi:igtrxx:v:10:y:2008:i:01:n:s0219198908001741 is not listed on IDEAS
    7. Eichberger, Jurgen & Kelsey, David, 2000. "Non-Additive Beliefs and Strategic Equilibria," Games and Economic Behavior, Elsevier, vol. 30(2), pages 183-215, February.
    8. Stauber, Ronald, 2011. "Knightian games and robustness to ambiguity," Journal of Economic Theory, Elsevier, vol. 146(1), pages 248-274, January.
    9. Friedman, James W. & Mezzetti, Claudio, 2005. "Random belief equilibrium in normal form games," Games and Economic Behavior, Elsevier, vol. 51(2), pages 296-323, May.
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    Cited by:

    1. Giuseppe De Marco & Maria Romaniello, 2013. "Games Equilibria and the Variational Representation of Preferences," CSEF Working Papers 336, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.

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    Keywords

    Incomplete information games; multiple priors; equilibrium stability;

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