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A Limit Theorem for Equilibria under Ambiguous Beliefs Correspondences

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  • Giuseppe De Marco

    ()
    (Università di Napoli Parthenope and CSEF)

  • Maria Romaniello

    ()
    (Università di Napoli Federico II)

Abstract

Previous literature shows that, in many different models, limits of equilibria of perturbed games are equilibria of the unperturbed game when the sequence of perturbed games converges to the unperturbed one in an appropriate sense. The question whether such limit property extends to the equilibrium notions in ambiguous games is not yet clear as it seems; in fact, previous literature shows that the extension fails in simple examples. The contribution in this paper is to show that the limit property holds for equilibria under ambiguous beliefs correspondences (presented by the authors in a previous paper). Key for our result is the sequential convergence assumption imposed on the sequence of beliefs correspondences. Counterexamples show why this assumption cannot be removed.

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Bibliographic Info

Paper provided by Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy in its series CSEF Working Papers with number 299.

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Date of creation: 28 Nov 2011
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Publication status: Published in Mathematical Social Sciences, 2013, Vol. 66(3), pp. 431–438
Handle: RePEc:sef:csefwp:299

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Keywords: Ambiguous games; beliefs correspondences; limit equilibria;

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References

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  1. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  2. Burkhard C. Schipper & David Kelsey, 2005. "Ambiguity and Social Interaction," Working Papers 536, University of California, Davis, Department of Economics.
  3. Ehud Lehrer, 2012. "Partially Specified Probabilities: Decisions and Games," American Economic Journal: Microeconomics, American Economic Association, vol. 4(1), pages 70-100, February.
  4. Marinacci, Massimo, 2000. "Ambiguous Games," Games and Economic Behavior, Elsevier, vol. 31(2), pages 191-219, May.
  5. Eichberger, Jurgen & Kelsey, David, 2000. "Non-Additive Beliefs and Strategic Equilibria," Games and Economic Behavior, Elsevier, vol. 30(2), pages 183-215, February.
  6. 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.
  7. Kin Chung Lo, 1995. "Equilibrium in Beliefs Under Uncertainty," Working Papers ecpap-95-02, University of Toronto, Department of Economics.
  8. Dow, James & Werlang, Sérgio Ribeiro da Costa, 1992. "Nash equilibrium under knightian uncertainty: breaking-down backward induction," Economics Working Papers (Ensaios Economicos da EPGE) 186, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  9. De Marco, Giuseppe & Romaniello, Maria, 2010. "Ambiguous games with contingent beliefs," MPRA Paper 27507, University Library of Munich, Germany.
  10. Atsushi Kajii & Takashi Ui, 2004. "Incomplete Information Games with Multiple Priors," KIER Working Papers 583, Kyoto University, Institute of Economic Research.
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Cited by:
  1. 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.
  2. 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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