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Strategic games with security and potential level players

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Author Info
Alexander Zimper ()

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Abstract

This paper examines the existence of strategic solutions to finite normal form games under the assumption that strategy choices can be described as choices among lotteries where players have security- and potential level preferences over lotteries (e.g., Cohen, Theory and Decision, 33, 101–104, 1992, Gilboa, Journal of Mathematical Psychology, 32, 405–420, 1988, Jaffray, Theory and Decision, 24, 169–200, 1988). Since security- and potential level preferences require discontinuous utility representations, standard existence results for Nash equilibria in mixed strategies (Nash, Proceedings of the National Academy of Sciences, 36, 48–49, 1950a, Non-Cooperative Games, Ph.D. Dissertation, Princeton University Press, 1950b) or for equilibria in beliefs (Crawford, Journal of Economic Theory, 50, 127–154, 1990) do not apply. As a key insight this paper proves that non-existence of equilibria in beliefs, and therefore non-existence of Nash equilibria in mixed strategies, is possible in finite games with security- and potential level players. But, as this paper also shows, rationalizable strategies (Bernheim, Econometrica, 52, 1007–1028, 1984, Moulin, Mathematical Social Sciences, 7, 83–102, 1984, Pearce, Econometrica, 52, 1029–1050, 1984) exist for such games. Rationalizability rather than equilibrium in beliefs therefore appears to be a more favorable solution concept for games with security- and potential level players. Copyright Springer Science+Business Media, LLC 2007

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File URL: http://hdl.handle.net/10.1007/s11238-007-9036-4
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Publisher Info
Article provided by Springer in its journal Theory and Decision.

Volume (Year): 63 (2007)
Issue (Month): 1 (August)
Pages: 53-78
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Handle: RePEc:kap:theord:v:63:y:2007:i:1:p:53-78

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Web page: http://www.springerlink.com/link.asp?id=100341

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Related research
Keywords: Allais paradoxes; equilibrium in beliefs; Nash equilibrium; non-expected utility theories; rationalizability; C72; D81;

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  1. Green, Jerry R & Jullien, Bruno, 1988. " Ordinal Independence in Nonlinear Utility Theory," Journal of Risk and Uncertainty, Springer, vol. 1(4), pages 355-87, December.
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  2. Essid, Samir, 1997. "Choice under risk with certainty and potential effects: A general axiomatic model," Mathematical Social Sciences, Elsevier, vol. 34(3), pages 223-247, October. [Downloadable!] (restricted)
  3. Schmidt, Ulrich & Zimper, Alexander, 2003. "Security And Potential Level Preferences With," Sonderforschungsbereich 504 Publications 03-29, Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim. [Downloadable!]
  4. 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)
  5. Crawford, Vincent P., 1990. "Equilibrium without independence," Journal of Economic Theory, Elsevier, vol. 50(1), pages 127-154, February. [Downloadable!] (restricted)
  6. Segal, Uzi, 1993. " The Measure Representation: A Correction," Journal of Risk and Uncertainty, Springer, vol. 6(1), pages 99-107, January.
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  7. 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)
  8. Quiggin John & Wakker Peter, 1994. "The Axiomatic Basis of Anticipated Utility: A Clarification," Journal of Economic Theory, Elsevier, vol. 64(2), pages 486-499, December. [Downloadable!] (restricted)
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  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. Ghirardato, Paolo & Le Breton, Michel, 2000. "Choquet Rationality," Journal of Economic Theory, Elsevier, vol. 90(2), pages 277-285, February. [Downloadable!] (restricted)
  12. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-28, July. [Downloadable!] (restricted)
  13. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December. [Downloadable!] (restricted)
  14. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July. [Downloadable!] (restricted)
  15. Gul, Faruk, 1991. "A Theory of Disappointment Aversion," Econometrica, Econometric Society, vol. 59(3), pages 667-86, May. [Downloadable!] (restricted)
  16. Moulin, Herve, 1984. "Dominance solvability and cournot stability," Mathematical Social Sciences, Elsevier, vol. 7(1), pages 83-102, February. [Downloadable!] (restricted)
  17. R. Guesnerie, 2002. "Anchoring Economic Predictions in Common Knowledge," Econometrica, Econometric Society, vol. 70(2), pages 439-480, March. [Downloadable!] (restricted)
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  18. 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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  19. Karni, Edi & Schmeidler, David, 1991. "Utility theory with uncertainty," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 33, pages 1763-1831 Elsevier. [Downloadable!] (restricted)
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