A Limit Theorem for Equilibria under Ambiguous Beliefs Correspondences
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.
|Date of creation:||28 Nov 2011|
|Date of revision:|
|Publication status:||Published in Mathematical Social Sciences, 2013, Vol. 66(3), pp. 431–438|
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- Gilboa, Itzhak & Schmeidler, David, 1989.
"Maxmin expected utility with non-unique prior,"
Journal of Mathematical Economics,
Elsevier, vol. 18(2), pages 141-153, April.
- Burkhard C. Schipper & David Kelsey, 2005.
"Ambiguity and Social Interaction,"
536, University of California, Davis, Department of Economics.
- Jurgen Eichberger & David Kelsey & Burkhard C. Schipper, 2005. "Ambiguity and Social Interaction," Discussion Papers 0504, Exeter University, Department of Economics.
- Juergen Eichberger & David Kelsey & Burkhard C. Schipper, 2003. "Ambiguity and Social Interaction," Bonn Econ Discussion Papers bgse23_2003, University of Bonn, Germany.
- Jürgen Eichberger & David Kelsey & Burkhard C. Schipper, 2007. "Ambiguity and Social Interaction," Working Papers 0443, University of Heidelberg, Department of Economics, revised May 2007.
- Eichberger, Jürgen & Kelsey, David & Schipper, Burkhard, 2007. "Ambiguity and Social Interaction," Sonderforschungsbereich 504 Publications 07-19, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
- Eichberger, Jürgen & Kelsey, David & Schipper, Burkhard C., 2005. "Ambiguity and Social Interaction," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 59, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
- Eichberger, Jürgen & Kelsey, David & Schipper, Burkhard, 2003. "Ambiguity and Social Interaction," Sonderforschungsbereich 504 Publications 03-30, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
- Ehud Lehrer, 2012. "Partially Specified Probabilities: Decisions and Games," American Economic Journal: Microeconomics, American Economic Association, vol. 4(1), pages 70-100, February.
- Lo, Kin Chung, 1996.
"Equilibrium in Beliefs under Uncertainty,"
Journal of Economic Theory,
Elsevier, vol. 71(2), pages 443-484, November.
- 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).
- Dow James & Werlang Sergio Ribeiro Da Costa, 1994. "Nash Equilibrium under Knightian Uncertainty: Breaking Down Backward Induction," Journal of Economic Theory, Elsevier, vol. 64(2), pages 305-324, December.
- Marinacci, Massimo, 2000. "Ambiguous Games," Games and Economic Behavior, Elsevier, vol. 31(2), pages 191-219, May.
- 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.
- Atsushi Kajii & Takashi Ui, 2004.
"Incomplete Information Games with Multiple Priors,"
KIER Working Papers
583, Kyoto University, Institute of Economic Research.
- Eichberger, Jurgen & Kelsey, David, 2000. "Non-Additive Beliefs and Strategic Equilibria," Games and Economic Behavior, Elsevier, vol. 30(2), pages 183-215, February.
- De Marco, Giuseppe & Romaniello, Maria, 2010. "Ambiguous games with contingent beliefs," MPRA Paper 27507, University Library of Munich, Germany.
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