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Ambiguous games with contingent beliefs

Author

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  • De Marco, Giuseppe
  • Romaniello, Maria

Abstract

The Nash equilibrium concept combines two fundamental ideas. First, rational players choose the most preferred strategy given their beliefs about what other players will do. Second, it imposes the consistency condition that all players' beliefs are correct. This consistency condition has often been considered too strong and different solution concepts have been introduced in the literature in order to take into account ambiguous beliefs. In this paper, we show, by means of examples, that in some situation beliefs might be dependent on the strategy profile and that this kind of contingent ambiguity affects equilibrium behavior differently with respect to the existing models of ambiguous games. Hence we consider a multiple prior approach and subjective beliefs correspondences which depend on the strategy profile; we investigate existence of the equilibrium concepts corresponding to different attitudes towards ambiguity (namely optimism and pessimism). Finally we analyze particular beliefs correspondences: beliefs given by correlated equilibria and by ambiguity levels on events.

Suggested Citation

  • De Marco, Giuseppe & Romaniello, Maria, 2010. "Ambiguous games with contingent beliefs," MPRA Paper 27507, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:27507
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    File URL: https://mpra.ub.uni-muenchen.de/30800/3/MPRA_paper_30800.pdf
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    References listed on IDEAS

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    1. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, April.
    2. Jürgen Eichberger & David Kelsey & Burkhard C. Schipper, 2009. "Ambiguity and social interaction," Oxford Economic Papers, Oxford University Press, vol. 61(2), pages 355-379, April.
    3. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    4. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    5. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    6. Moreno, Diego & Wooders, John, 1996. "Coalition-Proof Equilibrium," Games and Economic Behavior, Elsevier, vol. 17(1), pages 80-112, November.
    7. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    8. Lo, Kin Chung, 1996. "Equilibrium in Beliefs under Uncertainty," Journal of Economic Theory, Elsevier, vol. 71(2), pages 443-484, November.
    9. Eichberger, Jurgen & Kelsey, David, 2000. "Non-Additive Beliefs and Strategic Equilibria," Games and Economic Behavior, Elsevier, vol. 30(2), pages 183-215, February.
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    Cited by:

    1. 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.

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    More about this item

    Keywords

    Noncooperative games; ambiguity; beliefs correspondence; equilibrium;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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