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Equilibrium in Beliefs Under Uncertainty

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Author Info
Kin Chung Lo

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Abstract

Existing equilibrium concepts for games make use of the subjective expected utility model axiomatized by Savage (1954) to represent players' preferences. Accordingly, each player's beliefs about the strategies played by opponents are represented by a probability measure. Motivated by experimental findings such as the Ellsberg Paradox demonstrating that the beliefs of a decision maker may not be representable by a probability measure, this paper generalizes equilibrium concepts for normal form games to allow for the beliefs of each player to be representable by a closed and convex set of probability measures. The implications of this generalization for the strategy choices and welfare of players are studied.

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Publisher Info
Paper provided by University of Toronto, Department of Economics in its series Working Papers with number ecpap-95-02.

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Length: 41 pages
Date of creation: 11 Mar 1995
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Handle: RePEc:tor:tecipa:ecpap-95-02

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Related research
Keywords: uncertainty; Ellsberg Paradox; multiple priors; Nash Equilibrium; equilibrium in beliefs;

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Find related papers by JEL classification:
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January. [Downloadable!] (restricted)
  2. Crawford, Vincent P., 1990. "Equilibrium without independence," Journal of Economic Theory, Elsevier, vol. 50(1), pages 127-154, February. [Downloadable!] (restricted)
  3. Dow, James & Werlang, Sergio Ribeiro da Costa, 1992. "Uncertainty Aversion, Risk Aversion, and the Optimal Choice of Portfolio," Econometrica, Econometric Society, vol. 60(1), pages 197-204, January. [Downloadable!] (restricted)
  4. Brandenburger, Adam, 1992. "Knowledge and Equilibrium in Games," Journal of Economic Perspectives, American Economic Association, vol. 6(4), pages 83-101, Fall. [Downloadable!] (restricted)
  5. Epstein, Larry G & Wang, Tan, 1994. "Intertemporal Asset Pricing Under Knightian Uncertainty," Econometrica, Econometric Society, vol. 62(2), pages 283-322, March. [Downloadable!] (restricted)
  6. Tan, Tommy Chin-Chiu & da Costa Werlang, Sergio Ribeiro, 1988. "The Bayesian foundations of solution concepts of games," Journal of Economic Theory, Elsevier, vol. 45(2), pages 370-391, August. [Downloadable!] (restricted)
  7. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April. [Downloadable!] (restricted)
  8. Machina, Mark J & Schmeidler, David, 1992. "A More Robust Definition of Subjective Probability," Econometrica, Econometric Society, vol. 60(4), pages 745-80, July. [Downloadable!] (restricted)
    Other versions:
  9. Dekel, Eddie & Safra, Zvi & Segal, Uzi, 1991. "Existence and dynamic consistency of Nash equilibrium with non-expected utility preferences," Journal of Economic Theory, Elsevier, vol. 55(2), pages 229-246, December. [Downloadable!] (restricted)
  10. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May. [Downloadable!] (restricted)
  11. Machina, Mark J, 1989. "Dynamic Consistency and Non-expected Utility Models of Choice under Uncertainty," Journal of Economic Literature, American Economic Association, vol. 27(4), pages 1622-68, December. [Downloadable!] (restricted)
  12. Aumann, Robert & Brandenburger, Adam, 1995. "Epistemic Conditions for Nash Equilibrium," Econometrica, Econometric Society, vol. 63(5), pages 1161-80, September. [Downloadable!] (restricted)
  13. Segal, Uzi, 1990. "Two-Stage Lotteries without the Reduction Axiom," Econometrica, Econometric Society, vol. 58(2), pages 349-77, March. [Downloadable!] (restricted)
    Other versions:
  14. 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)
    Other versions:
Full references

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 & Burkhard C. Schipper, 2005. "Ambiguity and Social Interaction," Discussion Papers 59, SFB/TR 15 Governance and the Efficiency of Economic Systems, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich. [Downloadable!]
    Other versions:
  2. Bailey, Ralph W. & Eichberger, Jürgen & Kelsey, David, 2004. "Ambiguity and Public Good Provision in Large Societies," Sonderforschungsbereich 504 Publications 04-54, Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim.
    Other versions:
  3. Jürgen Eichberger & David Kelsey & Burkhard Schipper, 2008. "Granny Versus Game Theorist: Ambiguity in Experimental Games," Theory and Decision, Springer, vol. 64(2), pages 333-362, March. [Downloadable!] (restricted)
    Other versions:
  4. Ludovic Renou & Karl H. Schlag, 2008. "Minimax regret and strategic uncertainty," Discussion Papers in Economics 08/2, Department of Economics, University of Leicester, revised Apr 2008. [Downloadable!]
    Other versions:
  5. Eichberger, Jürgen & Kelsey, David, 2008. "Are the Treasures of Game Theory Ambiguous?," Sonderforschungsbereich 504 Publications 08-08, Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim. [Downloadable!]
    Other versions:
  6. Atsushi Kajii & Takashi Ui, 2004. "Incomplete Information Games with Multiple Priors," KIER Working Papers 583, Kyoto University, Institute of Economic Research. [Downloadable!]
    Other versions:
  7. Kin Chung Lo, 1998. "Epistemic Conditions for Agreement and Stochastic Independence of epsilon-Contaminated Beliefs," Working Papers 1998_02, York University, Department of Economics. [Downloadable!]
  8. Takao Asano, 2004. "Portfolio Inertia under Ambiguity," ISER Discussion Paper 0609, Institute of Social and Economic Research, Osaka University. [Downloadable!]
  9. Werlang, Sérgio Ribeiro da Costa, 2000. "A Notion Of Subgame Perfect Nash Equilibrium Under Knightian Uncertainty," Economics Working Papers (Ensaios Economicos da EPGE) 376, Graduate School of Economics, Getulio Vargas Foundation (Brazil). [Downloadable!]
  10. Eichberger, Jürgen & Kelsey, David, 2003. "Sequential Two-Player Games with Ambiguity," Sonderforschungsbereich 504 Publications 03-27, Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim. [Downloadable!]
    Other versions:
  11. Alexander Zimper, 2007. "Strategic games with security and potential level players," Theory and Decision, Springer, vol. 63(1), pages 53-78, August. [Downloadable!] (restricted)
  12. David Dequech, 2006. "Towards An Alternative To The Game-Theoretic Concept Of Conventions," Anais do XXXIV Encontro Nacional de Economia [Proceedings of the 34th Brazilian Economics Meeting] 77, ANPEC - Associação Nacional dos Centros de Pósgraduação em Economia [Brazilian Association of Graduate Programs in Economics].
  13. Jürgen Eichberger & David Kelsey, 2007. "Ambiguity," Working Papers 0448, University of Heidelberg, Department of Economics, revised Jul 2007. [Downloadable!]
    Other versions:
  14. Nicola Dimitri, 2005. "Cooperation with Strategy-Dependent Uncertainty Attitude," Department of Economics University of Siena 457, Department of Economics, University of Siena. [Downloadable!]
  15. Zimper, Alexander, 2004. "On the Existence of Strategic Solutions for Games with Security- and Potential Level Players," Sonderforschungsbereich 504 Publications 04-04, Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim. [Downloadable!]
  16. Takao Asano, 2004. "Portfolio Inertia and [Epsilon]-Contaminations," ISER Discussion Paper 0610, Institute of Social and Economic Research, Osaka University. [Downloadable!]
  17. repec:bep:theadv:v:2:y:2002:i:1:p:1011-1011 is not listed on IDEAS
  18. Vitaly Pruzhansky, 2004. "A Discussion of Maximin," Tinbergen Institute Discussion Papers 04-028/1, Tinbergen Institute. [Downloadable!]
  19. Xiao Luo & Yi-Chun Chen, 2004. "A Unified Approach to Information, Knowledge, and Stability," Econometric Society 2004 Far Eastern Meetings 472, Econometric Society. [Downloadable!]
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