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A Limit Theorem for Equilibria under Ambiguous Beliefs Correspondences

  • Giuseppe De Marco

    ()

    (Università di Napoli Parthenope and CSEF)

  • Maria Romaniello

    ()

    (Università di Napoli Federico II)

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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Publication status: Published in Mathematical Social Sciences, 2013, Vol. 66(3), pp. 431–438
Handle: RePEc:sef:csefwp:299
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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. Lo, Kin Chung, 1996. "Equilibrium in Beliefs under Uncertainty," Journal of Economic Theory, Elsevier, vol. 71(2), pages 443-484, November.
  3. Atsushi Kajii & Takashi Ui, 2005. "Incomplete Information Games With Multiple Priors," The Japanese Economic Review, Japanese Economic Association, vol. 56(3), pages 332-351.
  4. Jürgen Eichberger & David Kelsey & Burkhard C. Schipper, 2007. "Ambiguity and Social Interaction," Working Papers 0443, University of Heidelberg, Department of Economics, revised May 2007.
  5. 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).
  6. De Marco, Giuseppe & Romaniello, Maria, 2010. "Ambiguous games with contingent beliefs," MPRA Paper 27507, University Library of Munich, Germany.
  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. Marinacci, Massimo, 2000. "Ambiguous Games," Games and Economic Behavior, Elsevier, vol. 31(2), pages 191-219, May.
  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.
  10. Ehud Lehrer, 2012. "Partially Specified Probabilities: Decisions and Games," American Economic Journal: Microeconomics, American Economic Association, vol. 4(1), pages 70-100, February.
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