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Sequential Two-Player Games With Ambiguity

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Author Info
Jürgen Eichberger
David Kelsey

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Abstract

If players' beliefs are strictly nonadditive, the Dempster-Shafer updating rule can be used to define beliefs off the equilibrium path. We define an equilibrium concept in sequential two-person games where players update their beliefs with the Dempster-Shafer updating rule. We show that in the limit as uncertainty tends to zero, our equilibrium approximates Bayesian Nash equilibrium. We argue that our equilibrium can be used to define a refinement of Bayesian Nash equilibrium by imposing context-dependent constraints on beliefs under uncertainty. Copyright 2004 by the Economics Department Of The University Of Pennsylvania And Osaka University Institute Of Social And Economic Research Association.

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Article provided by Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association in its journal International Economic Review.

Volume (Year): 45 (2004)
Issue (Month): 4 (November)
Pages: 1229-1261
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Handle: RePEc:ier:iecrev:v:45:y:2004:i:4:p:1229-1261

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Gilboa Itzhak & Schmeidler David, 1993. "Updating Ambiguous Beliefs," Journal of Economic Theory, Elsevier, vol. 59(1), pages 33-49, February. [Downloadable!] (restricted)
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  2. Sujoy Mukerji, 1996. "Understanding the nonadditive probability decision model (*)," Economic Theory, Springer, vol. 9(1), pages 23-46.
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  3. Ryan, Matthew J., 2002. "Violations of Belief Persistence in Dempster-Shafer Equilibrium," Games and Economic Behavior, Elsevier, vol. 39(1), pages 167-174, April. [Downloadable!] (restricted)
  4. Banks Jeffrey & Camerer Colin & Porter David, 1994. "An Experimental Analysis of Nash Refinements in Signaling Games," Games and Economic Behavior, Elsevier, vol. 6(1), pages 1-31, January. [Downloadable!] (restricted)
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  5. Eichberger, Jurgen & Kelsey, David, 2000. "Non-Additive Beliefs and Strategic Equilibria," Games and Economic Behavior, Elsevier, vol. 30(2), pages 183-215, February. [Downloadable!] (restricted)
  6. 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. [Downloadable!]
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  7. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May. [Downloadable!] (restricted)
  8. Lo, Kin Chung, 1999. "Extensive Form Games with Uncertainty Averse Players," Games and Economic Behavior, Elsevier, vol. 28(2), pages 256-270, August. [Downloadable!] (restricted)
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  9. Eichberger, Jurgen & Kelsey, David, 1996. "Uncertainty Aversion and Preference for Randomisation," Journal of Economic Theory, Elsevier, vol. 71(1), pages 31-43, October. [Downloadable!] (restricted)
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  10. Brandts, Jordi & Holt, Charles A, 1992. "An Experimental Test of Equilibrium Dominance in Signaling Games," American Economic Review, American Economic Association, vol. 82(5), pages 1350-65, December. [Downloadable!] (restricted)
  11. Bebchuk, Lucian Arye, 1988. "Suing Solely to Extract a Settlement Offer," Journal of Legal Studies, University of Chicago Press, vol. 17(2), pages 437-50, June.
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  12. Sarin, Rakesh K & Wakker, Peter, 1992. "A Simple Axiomatization of Nonadditive Expected Utility," Econometrica, Econometric Society, vol. 60(6), pages 1255-72, November. [Downloadable!] (restricted)
  13. Eichberger, Jurgen & Kelsey, David, 2002. "Strategic Complements, Substitutes, and Ambiguity: The Implications for Public Goods," Journal of Economic Theory, Elsevier, vol. 106(2), pages 436-466, October. [Downloadable!] (restricted)
  14. Lo, Kin Chung, 1996. "Equilibrium in Beliefs under Uncertainty," Journal of Economic Theory, Elsevier, vol. 71(2), pages 443-484, November. [Downloadable!] (restricted)
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  15. Eichberger, J. & Kelsey, D., 1996. "E-Capacities and the Ellsberg Paradox," Discussion Papers 96-13, Department of Economics, University of Birmingham.
  16. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-37, September. [Downloadable!] (restricted)
  17. Marinacci, Massimo, 2000. "Ambiguous Games," Games and Economic Behavior, Elsevier, vol. 31(2), pages 191-219, May. [Downloadable!] (restricted)
  18. Brandts, Jordi & Holt, Charles A, 1993. "Adjustment Patterns and Equilibrium Selection in Experimental Signaling Games," International Journal of Game Theory, Springer, vol. 22(3), pages 279-302.
  19. Spence, A Michael, 1973. "Job Market Signaling," The Quarterly Journal of Economics, MIT Press, vol. 87(3), pages 355-74, August. [Downloadable!] (restricted)
  20. Battigalli, Pierpaolo, 1997. "On Rationalizability in Extensive Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 40-61, May. [Downloadable!] (restricted)
  21. 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. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Jürgen Eichberger & David Kelsey, 2008. "Are the Treasures of Game Theory Ambiguous?," Working Papers 0469, University of Heidelberg, Department of Economics, revised Jul 2008. [Downloadable!]
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