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Ambiguous games with contingent beliefs

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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.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 27507.

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Date of creation: 20 Dec 2010
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Handle: RePEc:pra:mprapa:27507

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Keywords: Noncooperative games; ambiguity; beliefs correspondence; equilibrium;

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References

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  1. Jürgen Eichberger & David Kelsey & Burkhard C. Schipper, 2007. "Ambiguity and Social Interaction," Working Papers 0443, University of Heidelberg, Department of Economics, revised May 2007.
  2. AUMANN, Robert J., . "Subjectivity and correlation in randomized strategies," CORE Discussion Papers RP -167, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Moreno, Diego & Wooders, John, 1996. "Coalition-Proof Equilibrium," Games and Economic Behavior, Elsevier, vol. 17(1), pages 80-112, November.
  4. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
  5. Lo, Kin Chung, 1996. "Equilibrium in Beliefs under Uncertainty," Journal of Economic Theory, Elsevier, vol. 71(2), pages 443-484, November.
  6. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
  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. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
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Cited by:
  1. Giuseppe De Marco & Maria Romaniello, 2011. "A Limit Theorem for Equilibria under Ambiguous Beliefs Correspondences," CSEF Working Papers 299, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.

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