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Nash rationalizability of collective choice over lotteries

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  • T. DEMUYNCK

    ()

  • L. LAUWERS

Abstract

To test the joint hypothesis that players in a noncooperative game (allowing mixed strategies) maximize expected utilities 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.

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Paper provided by Ghent University, Faculty of Economics and Business Administration in its series Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium with number 05/301.

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Length: 21 pages
Date of creation: Apr 2005
Date of revision:
Handle: RePEc:rug:rugwps:05/301

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Keywords: independence condition; binary extensions; rationalizability; Nash equilibrium in mixed strategies;

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  1. Sen, Amartya K, 1971. "Choice Functions and Revealed Preference," Review of Economic Studies, Wiley Blackwell, vol. 38(115), pages 307-17, July.
  2. Conlisk, John, 1989. "Three Variants on the Allais Example," American Economic Review, American Economic Association, vol. 79(3), pages 392-407, June.
  3. Indrajit Ray & Lin Zhou, . "Game Theory Via Revealed Preferences," Discussion Papers 00/15, Department of Economics, University of York.
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