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Nash rationalization of collective choice over lotteries

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  • Demuynck, Thomas
  • Lauwers, Luc

Abstract

To test the joint hypothesis that players in a noncooperative game (allowing mixtures over pure strategies) consult an independent preference relation and select a Nash equilibrium, it suffices to study the reaction of the revealed collective choice upon changes in the space of strategies available to the players. The joint hypothesis is supported if the revealed choices satisfy an extended version of Richter's congruence axiom together with a contraction-expansion axiom that models the noncooperative behavior. In addition, we provide sufficient and necessary conditions for a binary relation to have an independent ordering extension, and for individual choices over lotteries to be rationalizable by an independent preference relation.

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Bibliographic Info

Article provided by Elsevier in its journal Mathematical Social Sciences.

Volume (Year): 57 (2009)
Issue (Month): 1 (January)
Pages: 1-15

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Handle: RePEc:eee:matsoc:v:57:y:2009:i:1:p:1-15

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Web page: http://www.elsevier.com/locate/inca/505565

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Keywords: Independence condition Binary extensions Rationalizability Nash equilibrium with mixed strategies;

References

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  1. Kim, Taesung, 1996. "Revealed preference theory on the choice of lotteries," Journal of Mathematical Economics, Elsevier, vol. 26(4), pages 463-477.
  2. Conlisk, John, 1989. "Three Variants on the Allais Example," American Economic Review, American Economic Association, vol. 79(3), pages 392-407, June.
  3. Shachat, Jason M., 2002. "Mixed Strategy Play and the Minimax Hypothesis," Journal of Economic Theory, Elsevier, vol. 104(1), pages 189-226, May.
  4. Indrajit Ray & Lin Zhou, . "Game Theory Via Revealed Preferences," Discussion Papers 00/15, Department of Economics, University of York.
  5. Adam Galambos, 2005. "Revealed Preference in Game Theory," 2005 Meeting Papers 776, Society for Economic Dynamics.
  6. Oliver, Adam, 2003. "A quantitative and qualitative test of the Allais paradox using health outcomes," Journal of Economic Psychology, Elsevier, vol. 24(1), pages 35-48, February.
  7. Suzumura, Kataro, 1976. "Remarks on the Theory of Collective Choice," Economica, London School of Economics and Political Science, vol. 43(172), pages 381-90, November.
  8. Sen, Amartya K, 1971. "Choice Functions and Revealed Preference," Review of Economic Studies, Wiley Blackwell, vol. 38(115), pages 307-17, July.
  9. Sopher & Narramore, 2000. "Stochastic Choice and Consistency in Decision Making Under Risk: An Experimental Study," Theory and Decision, Springer, vol. 48(4), pages 323-349, June.
  10. Sprumont, Yves, 2000. "On the Testable Implications of Collective Choice Theories," Journal of Economic Theory, Elsevier, vol. 93(2), pages 205-232, August.
  11. Clark, Stephen A., 1995. "Indecisive choice theory," Mathematical Social Sciences, Elsevier, vol. 30(2), pages 155-170, October.
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Citations

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Cited by:
  1. Susan Snyder & Indrajit Ray, 2004. "Observable implications of Nash and subgame-perfect behavior in extensive games," Econometric Society 2004 North American Summer Meetings 407, Econometric Society.
  2. Demuynck, Thomas, 2011. "The computational complexity of rationalizing boundedly rational choice behavior," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 425-433.
  3. Lee, SangMok, 2012. "The testable implications of zero-sum games," Journal of Mathematical Economics, Elsevier, vol. 48(1), pages 39-46.
  4. T. Demuynck, 2009. "Common ordering extensions," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 09/593, Ghent University, Faculty of Economics and Business Administration.

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