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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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  • 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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    Cited by:

    1. 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.
    2. Thomas Demuynck, 2014. "The computational complexity of rationalizing Pareto optimal choice behavior," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(3), pages 529-549, March.
    3. Mabrouk, Mohamed, 2018. "On the Extension and Decomposition of a Preorder under Translation Invariance," MPRA Paper 90537, University Library of Munich, Germany.
    4. 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.
    5. Mabrouk, Mohamed, 2009. "On the extension of a preorder under translation invariance," MPRA Paper 15407, University Library of Munich, Germany.
    6. Mikhail Freer & Cesar Martinelli, 2018. "A Functional Approach to Revealed Preference," Working Papers ECARES 2018-29, ULB -- Universite Libre de Bruxelles.
    7. Mikhail Freer & César Martinelli, 2023. "An algebraic approach to revealed preference," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(3), pages 717-742, April.
    8. Athanasios Andrikopoulos, 2017. "Generalizations of Szpilrajn's Theorem in economic and game theories," Papers 1708.04711, arXiv.org.
    9. Lee, SangMok, 2012. "The testable implications of zero-sum games," Journal of Mathematical Economics, Elsevier, vol. 48(1), pages 39-46.
    10. Athanasios Andrikopoulos, 2019. "On the extension of binary relations in economic and game theories," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(1), pages 277-285, June.
    11. Mikhail Freer & Cesar Martinelli, 2018. "A Functional Approach to Revealed Preference," Working Papers 1070, George Mason University, Interdisciplinary Center for Economic Science.
    12. Demuynck, Thomas, 2011. "The computational complexity of rationalizing boundedly rational choice behavior," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 425-433.
    13. Rehbeck, John, 2018. "Note on unique Nash equilibrium in continuous games," Games and Economic Behavior, Elsevier, vol. 110(C), pages 216-225.
    14. 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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