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The testable implications of zero-sum games

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  • Lee, SangMok
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    Abstract

    We study collective choices from the revealed preference theory viewpoint. For every product set of individual actions, joint choices are called Nash-rationalizable if there exists a preference relation for each player such that the selected joint actions are Nash equilibria of the corresponding game. We characterize Nash-rationalizable joint choice behavior by zero-sum games, or games of conflicting interests. If the joint choice behavior forms a product subset, the behavior is called interchangeable. We prove that interchangeability is the only additional empirical condition which distinguishes zero-sum games from general non-cooperative games.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Mathematical Economics.

    Volume (Year): 48 (2012)
    Issue (Month): 1 ()
    Pages: 39-46

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    Handle: RePEc:eee:mateco:v:48:y:2012:i:1:p:39-46

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    Web page: http://www.elsevier.com/locate/jmateco

    Related research

    Keywords: Interchangeability; Nash-rationalizability; Revealed preference; Zero-sum game;

    References

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    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. Echenique, Federico & Ivanov, Lozan, 2011. "Implications of Pareto efficiency for two-agent (household) choice," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 129-136, March.
    3. Peter Duersch & Joerg Oechssler & Burkhard C. Schipper, 2011. "Unbeatable Imitation," Working Papers, University of California, Davis, Department of Economics 103, University of California, Davis, Department of Economics.
    4. Andrés Carvajal & Rahul Deb & James Fenske & John K.‐H. Quah, 2013. "Revealed Preference Tests of the Cournot Model," Econometrica, Econometric Society, Econometric Society, vol. 81(6), pages 2351-2379, November.
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    7. Forges, Françoise & Minelli, Enrico, 2009. "Afriat's theorem for general budget sets," Economics Papers from University Paris Dauphine 123456789/4099, Paris Dauphine University.
    8. Indrajit Ray & Lin Zhou, . "Game Theory Via Revealed Preferences," Discussion Papers, Department of Economics, University of York 00/15, Department of Economics, University of York.
    9. Sen, Amartya K, 1971. "Choice Functions and Revealed Preference," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 38(115), pages 307-17, July.
    10. Demuynck, Thomas & Lauwers, Luc, 2009. "Nash rationalization of collective choice over lotteries," Mathematical Social Sciences, Elsevier, Elsevier, vol. 57(1), pages 1-15, January.
    11. Xu, Yongsheng & Zhou, Lin, 2007. "Rationalizability of choice functions by game trees," Journal of Economic Theory, Elsevier, vol. 134(1), pages 548-556, May.
    12. Sprumont, Yves, 2000. "On the Testable Implications of Collective Choice Theories," Journal of Economic Theory, Elsevier, vol. 93(2), pages 205-232, August.
    13. Wilson, Robert B., 1970. "The finer structure of revealed preference," Journal of Economic Theory, Elsevier, vol. 2(4), pages 348-353, December.
    14. Suzumura, Kataro, 1976. "Remarks on the Theory of Collective Choice," Economica, London School of Economics and Political Science, London School of Economics and Political Science, vol. 43(172), pages 381-90, November.
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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. Walter Bossert & Yves Sprumont, 2013. "Every Choice Function Is Backwards‐Induction Rationalizable," Econometrica, Econometric Society, Econometric Society, vol. 81(6), pages 2521-2534, November.

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