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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.

Suggested Citation

  • Demuynck, Thomas & Lauwers, Luc, 2009. "Nash rationalization of collective choice over lotteries," Mathematical Social Sciences, Elsevier, vol. 57(1), pages 1-15, January.
  • Handle: RePEc:eee:matsoc:v:57:y:2009:i:1:p:1-15
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    References listed on IDEAS

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    1. Clark, Stephen A., 1995. "Indecisive choice theory," Mathematical Social Sciences, Elsevier, vol. 30(2), pages 155-170, October.
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    10. Amartya K. Sen, 1971. "Choice Functions and Revealed Preference," Review of Economic Studies, Oxford University Press, vol. 38(3), pages 307-317.
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    Cited by:

    1. Lee, SangMok, 2012. "The testable implications of zero-sum games," Journal of Mathematical Economics, Elsevier, vol. 48(1), pages 39-46.
    2. Ray, Indrajit & Snyder, Susan, 2013. "Observable implications of Nash and subgame-perfect behavior in extensive games," Journal of Mathematical Economics, Elsevier, vol. 49(6), pages 471-477.
    3. Demuynck, Thomas, 2011. "The computational complexity of rationalizing boundedly rational choice behavior," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 425-433.
    4. Athanasios Andrikopoulos, 2017. "Generalizations of Szpilrajn's Theorem in economic and game theories," Papers 1708.04711, arXiv.org.
    5. 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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