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Extensive Form Games with Uncertainty Averse Players

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  • Lo, Kin Chung

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

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 28 (1999)
Issue (Month): 2 (August)
Pages: 256-270

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Handle: RePEc:eee:gamebe:v:28:y:1999:i:2:p:256-270

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Web page: http://www.elsevier.com/locate/inca/622836

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References

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  1. Machina,Mark & Schmeidler,David, 1991. "A more robust definition of subjective probability," Discussion Paper Serie A 365, University of Bonn, Germany.
  2. Kin Chung Lo, 1999. "Nash equilibrium without mutual knowledge of rationality," Economic Theory, Springer, vol. 14(3), pages 621-633.
  3. Gilboa Itzhak & Schmeidler David, 1993. "Updating Ambiguous Beliefs," Journal of Economic Theory, Elsevier, vol. 59(1), pages 33-49, February.
  4. 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.
  5. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  6. KOHLBERG, Elon & MERTENS, Jean-François, . "On the strategic stability of equilibria," CORE Discussion Papers RP -716, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
  8. Karni, E. & Safra, Z., 1988. "Ascending Bid Auctions With Behaviorally Consistent Bidders," Papers 1-88, Tel Aviv.
  9. 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.
  10. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, December.
  11. Daniel Ellsberg, 2000. "Risk, Ambiguity and the Savage Axioms," Levine's Working Paper Archive 7605, David K. Levine.
  12. F J Anscombe & R J Aumann, 2000. "A Definition of Subjective Probability," Levine's Working Paper Archive 7591, David K. Levine.
  13. 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.
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Citations

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Cited by:
  1. Linda Sass, 2013. "Kuhn's Theorem for extensive form Ellsberg games," Working Papers 478, Bielefeld University, Center for Mathematical Economics.
  2. Takao Asano, 2010. "Portfolio Inertia and Epsilon-Contaminations," Theory and Decision, Springer, vol. 68(3), pages 341-365, March.
  3. Asano, Takao, 2006. "Portfolio inertia under ambiguity," Mathematical Social Sciences, Elsevier, vol. 52(3), pages 223-232, December.
  4. 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).
  5. 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.
  6. Rieger, Marc Oliver, 2014. "Evolutionary stability of prospect theory preferences," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 1-11.
  7. Kin Chung Lo, 2007. "Correlated Nash Equilibrium," Working Papers 2007_5, York University, Department of Economics.
  8. 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.
  9. 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.
  10. Lang, Matthias & Wambach, Achim, 2013. "The fog of fraud – Mitigating fraud by strategic ambiguity," Games and Economic Behavior, Elsevier, vol. 81(C), pages 255-275.
  11. 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.
  12. Frank Riedel & Linda Sass, 2014. "Ellsberg games," Theory and Decision, Springer, vol. 76(4), pages 469-509, April.
  13. Jorn Rothe, 2000. "Uncertainty Aversion and Backward Induction," Econometric Society World Congress 2000 Contributed Papers 1610, Econometric Society.
  14. Takao Asano, 2004. "Portfolio Inertia under Ambiguity," ISER Discussion Paper 0609, Institute of Social and Economic Research, Osaka University.
  15. Xiao Luo & Yi-Chun Chen, 2004. "A Unified Approach to Information, Knowledge, and Stability," Econometric Society 2004 Far Eastern Meetings 472, Econometric Society.
  16. Takao Asano, 2004. "Portfolio Inertia and [Epsilon]-Contaminations," ISER Discussion Paper 0610, Institute of Social and Economic Research, Osaka University.
  17. 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].
  18. Lo, Kin Chung, 2002. "Correlated equilibrium under uncertainty," Mathematical Social Sciences, Elsevier, vol. 44(2), pages 183-209, November.
  19. Nicola Dimitri, 2005. "Cooperation with Strategy-Dependent Uncertainty Attitude," Department of Economics University of Siena 457, Department of Economics, University of Siena.

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