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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

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

    References

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    1. Xu, Yongsheng & Zhou, Lin, 2007. "Rationalizability of choice functions by game trees," Journal of Economic Theory, Elsevier, Elsevier, vol. 134(1), pages 548-556, May.
    2. Forges, Françoise & Minelli, Enrico, 2009. "Afriat's theorem for general budget sets," Economics Papers from University Paris Dauphine, Paris Dauphine University 123456789/4099, Paris Dauphine University.
    3. Peter Duersch & Joerg Oechssler & Burkhard Schipper, 2012. "Unbeatable Imitation," Working Papers, University of California, Davis, Department of Economics 125, University of California, Davis, Department of Economics.
    4. Sen, Amartya K, 1971. "Choice Functions and Revealed Preference," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 38(115), pages 307-17, July.
    5. Radzik, Tadeusz, 1991. "Saddle Point Theorems," International Journal of Game Theory, Springer, Springer, vol. 20(1), pages 23-32.
    6. Peleg, Bezalel & Tijs, Stef, 1996. "The Consistency Principle for Games in Strategic Forms," International Journal of Game Theory, Springer, Springer, vol. 25(1), pages 13-34.
    7. 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.
    8. Demuynck, Thomas & Lauwers, Luc, 2009. "Nash rationalization of collective choice over lotteries," Mathematical Social Sciences, Elsevier, Elsevier, vol. 57(1), pages 1-15, January.
    9. Wilson, Robert B., 1970. "The finer structure of revealed preference," Journal of Economic Theory, Elsevier, Elsevier, vol. 2(4), pages 348-353, December.
    10. Indra Ray & Susan Snyder, 2003. "Observable Implications of Nash and Subgame-Perfect Behavior in Extensive Games," Working Papers, Brown University, Department of Economics 2003-02, Brown University, Department of Economics.
    11. Sprumont, Yves, 2000. "On the Testable Implications of Collective Choice Theories," Journal of Economic Theory, Elsevier, Elsevier, vol. 93(2), pages 205-232, August.
    12. Ray, Indrajit & Zhou, Lin, 2001. "Game Theory via Revealed Preferences," Games and Economic Behavior, Elsevier, Elsevier, vol. 37(2), pages 415-424, November.
    13. 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.
    14. Echenique, Federico & Ivanov, Lozan, 2011. "Implications of Pareto efficiency for two-agent (household) choice," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 47(2), pages 129-136, March.
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    Cited by:
    1. Indra Ray & Susan Snyder, 2003. "Observable Implications of Nash and Subgame-Perfect Behavior in Extensive Games," Working Papers, Brown University, Department of Economics 2003-02, Brown University, Department of Economics.
    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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