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Extensive Form Games with Uncertainty Averse Players

  • Kin Chung Lo

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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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
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Handle: RePEc:tor:tecipa:ecpap-95-03
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  1. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, March.
  2. 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.
  3. Mailath, G.J. & Samuelson, L. & Swinkels, J., 1990. "Extensive Form Reasoning In Normal Form Games," Papers 1-90-1, Pennsylvania State - Department of Economics.
  4. F J Anscombe & R J Aumann, 2000. "A Definition of Subjective Probability," Levine's Working Paper Archive 7591, David K. Levine.
  5. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, Oxford University Press, vol. 75(4), pages 643-669.
  6. Ebbe Groes & Hans Jørgen Jacobsen & Birgitte Sloth & Torben Tranaes, 1998. "Nash Equilibrium with Lower Probabilities," Theory and Decision, Springer, vol. 44(1), pages 37-66, January.
  7. Daniel Ellsberg, 2000. "Risk, Ambiguity and the Savage Axioms," Levine's Working Paper Archive 7605, David K. Levine.
  8. Epstein, Larry G & Wang, Tan, 1994. "Intertemporal Asset Pricing Under Knightian Uncertainty," Econometrica, Econometric Society, vol. 62(2), pages 283-322, March.
  9. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-37, September.
  10. Epstein, Larry G., 1997. "Preference, Rationalizability and Equilibrium," Journal of Economic Theory, Elsevier, vol. 73(1), pages 1-29, March.
  11. Mark J. Machina & David Schmeidler, 1990. "A More Robust Definition of Subjective Probability," Discussion Paper Serie A 306, University of Bonn, Germany.
  12. 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).
  13. Mukerji, S., 1995. "A theory of play for games in strategic form when rationality is not common knowledge," Discussion Paper Series In Economics And Econometrics 9519, Economics Division, School of Social Sciences, University of Southampton.
  14. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  15. 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.
  16. Fudenberg, Drew & Levine, David K, 1993. "Self-Confirming Equilibrium," Econometrica, Econometric Society, vol. 61(3), pages 523-45, May.
  17. Itzhak Gilboa & David Schmeidler, 1991. "Updating Ambiguous Beliefs," Discussion Papers 924, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  18. Eichberger, Jurgen & Kelsey, David, 1996. "Uncertainty Aversion and Preference for Randomisation," Journal of Economic Theory, Elsevier, vol. 71(1), pages 31-43, October.
  19. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
  20. Eichberger, J. & Kelsey, D., 1994. "Non-additive beliefs and game theory," Discussion Paper 1994-10, Tilburg University, Center for Economic Research.
  21. Karni, E. & Safra, Z., 1988. "Ascending Bid Auctions With Behaviorally Consistent Bidders," Papers 1-88, Tel Aviv.
  22. Kin Chung Lo, 1995. "Equilibrium in Beliefs Under Uncertainty," Working Papers ecpap-95-02, University of Toronto, Department of Economics.
  23. Kin Chung Lo, 1999. "Nash equilibrium without mutual knowledge of rationality," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 14(3), pages 621-633.
  24. Epstein, Larry G & Wang, Tan, 1996. ""Beliefs about Beliefs" without Probabilities," Econometrica, Econometric Society, vol. 64(6), pages 1343-73, November.
  25. 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.
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