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A Limit Theorem for Equilibria under Ambiguous Beliefs Correspondences

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  • Giuseppe De Marco

    () (Università di Napoli Parthenope)

  • 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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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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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. Kin Chung Lo, 1995. "Equilibrium in Beliefs Under Uncertainty," Working Papers ecpap-95-02, University of Toronto, Department of Economics.
  2. Eichberger, Jurgen & Kelsey, David, 2000. "Non-Additive Beliefs and Strategic Equilibria," Games and Economic Behavior, Elsevier, vol. 30(2), pages 183-215, February.
  3. 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, Graduate School of Economics, Getulio Vargas Foundation (Brazil).
  4. 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.
  5. De Marco, Giuseppe & Romaniello, Maria, 2010. "Beliefs correspondences and equilibria in ambiguous games," MPRA Paper 27507, University Library of Munich, Germany, revised May 2011.
  6. Marinacci, Massimo, 2000. "Ambiguous Games," Games and Economic Behavior, Elsevier, vol. 31(2), pages 191-219, May.
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