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Extensive Form Games with Uncertainty Averse Players

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  • Kin Chung Lo

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 the Ellsberg Paradox and relevant experimental findings demonstrating that the beliefs of a decision maker may not be representable by a probability measure, this paper generalizes Nash Equilibrium in finite extensive form games to allow for preferences conforming to the multiple priors model developed in Gilboa and Schmeidler (1989). The implications of this generalization for strategy choices and welfare are studied.

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Bibliographic Info

Paper provided by University of Toronto, Department of Economics in its series Working Papers with number ecpap-95-03.

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Length: 27 pages
Date of creation: 09 Jul 1995
Date of revision:
Handle: RePEc:tor:tecipa:ecpap-95-03

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References

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  1. Machina, Mark J & Schmeidler, David, 1992. "A More Robust Definition of Subjective Probability," Econometrica, Econometric Society, vol. 60(4), pages 745-80, July.
  2. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
  3. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-37, September.
  4. Kin Chung Lo, 1995. "Nash Equilibrium without Mutual Knowledge of Rationality," Working Papers ecpap-95-04, University of Toronto, Department of Economics.
  5. Epstein Larry G. & Le Breton Michel, 1993. "Dynamically Consistent Beliefs Must Be Bayesian," Journal of Economic Theory, Elsevier, vol. 61(1), pages 1-22, October.
  6. Karni, E. & Safra, Z., 1988. "Ascending Bid Auctions With Behaviorally Consistent Bidders," Papers 1-88, Tel Aviv.
  7. Itzhak Gilboa & David Schmeidler, 1991. "Updating Ambiguous Beliefs," Discussion Papers 924, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  8. 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.
  9. Daniel Ellsberg, 2000. "Risk, Ambiguity and the Savage Axioms," Levine's Working Paper Archive 7605, David K. Levine.
  10. Camerer, Colin & Weber, Martin, 1992. " Recent Developments in Modeling Preferences: Uncertainty and Ambiguity," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 325-70, October.
  11. F J Anscombe & R J Aumann, 2000. "A Definition of Subjective Probability," Levine's Working Paper Archive 7591, David K. Levine.
  12. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, December.
  13. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
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Citations

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Cited by:
  1. Nicola Dimitri, 2005. "Cooperation with Strategy-Dependent Uncertainty Attitude," Department of Economics University of Siena 457, Department of Economics, University of Siena.
  2. Takao Asano, 2010. "Precautionary Principle and the Optimal Timing of Environmental Policy Under Ambiguity," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 47(2), pages 173-196, October.
  3. Lo, Kin Chung, 2009. "Correlated Nash equilibrium," Journal of Economic Theory, Elsevier, vol. 144(2), pages 722-743, March.
  4. Matthias Lang & Achim Wambach, 2010. "The fog of fraud – mitigating fraud by strategic ambiguity," Working Paper Series of the Max Planck Institute for Research on Collective Goods 2010_24, Max Planck Institute for Research on Collective Goods.
  5. Takao Asano, 2004. "Portfolio Inertia and [Epsilon]-Contaminations," ISER Discussion Paper 0610, Institute of Social and Economic Research, Osaka University.
  6. De Waegenaere, A.M.B. & Wakker, P.P., 1997. "Choquet Integrals With Respect to Non-Monotonic Set Functions," Discussion Paper 1997-44, Tilburg University, Center for Economic Research.
  7. 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].
  8. Asano, Takao, 2006. "Portfolio inertia under ambiguity," Mathematical Social Sciences, Elsevier, vol. 52(3), pages 223-232, December.
  9. Takao Asano, 2004. "Portfolio Inertia under Ambiguity," ISER Discussion Paper 0609, Institute of Social and Economic Research, Osaka University.
  10. Werlang, Sérgio Ribeiro da Costa, 2000. "A Notion Of Subgame Perfect Nash Equilibrium Under Knightian Uncertainty," Economics Working Papers (Ensaios Economicos da EPGE) 376, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  11. Xiao Luo & Yi-Chun Chen, 2004. "A Unified Approach to Information, Knowledge, and Stability," Econometric Society 2004 Far Eastern Meetings 472, Econometric Society.
  12. Rieger, Marc Oliver, 2014. "Evolutionary stability of prospect theory preferences," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 1-11.
  13. Takao Asano, 2010. "Portfolio Inertia and Epsilon-Contaminations," Theory and Decision, Springer, vol. 68(3), pages 341-365, March.
  14. Luo, Xiao & Ma, Chenghu, 2001. "Stable equilibrium in beliefs in extensive games with perfect information," Journal of Economic Dynamics and Control, Elsevier, vol. 25(11), pages 1801-1825, November.
  15. Lo, Kin Chung, 2002. "Correlated equilibrium under uncertainty," Mathematical Social Sciences, Elsevier, vol. 44(2), pages 183-209, November.
  16. Jorn Rothe, 2000. "Uncertainty Aversion and Backward Induction," Econometric Society World Congress 2000 Contributed Papers 1610, Econometric Society.
  17. Gaurab Aryal & Ronald Stauber, 2013. "Trembles in Extensive Games with Ambiguity Averse Players," ANU Working Papers in Economics and Econometrics 2013-606, Australian National University, College of Business and Economics, School of Economics.
  18. Linda Sass, 2013. "Kuhn's Theorem for extensive form Ellsberg games," Working Papers 478, Bielefeld University, Center for Mathematical Economics.

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