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Two equivalence results for two-person strict games

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  • Tang, Pingzhong
  • Lin, Fangzhen
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    Abstract

    A game is strict if for both players, different profiles have different payoffs. Two games are best response equivalent if their best response functions are the same. We prove that a two-person strict game has at most one pure Nash equilibrium if and only if it is best response equivalent to a strictly competitive game, and that it is best response equivalent to an ordinal potential game if and only if it is best response equivalent to a quasi-supermodular game.

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    File URL: http://www.sciencedirect.com/science/article/B6WFW-4YYGH1F-1/2/0032a616981430ddcafbc6b5fcbdde82
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    Bibliographic Info

    Article provided by Elsevier in its journal Games and Economic Behavior.

    Volume (Year): 71 (2011)
    Issue (Month): 2 (March)
    Pages: 479-486

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    Handle: RePEc:eee:gamebe:v:71:y:2011:i:2:p:479-486

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    Web page: http://www.elsevier.com/locate/inca/622836

    Related research

    Keywords: Strictly competitive games Ordinal potential games Quasi-supermodular games Best response equivalence Strict games;

    References

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    1. Echenique, Federico, 2004. "A characterization of strategic complementarities," Games and Economic Behavior, Elsevier, vol. 46(2), pages 325-347, February.
    2. Zhou Lin, 1994. "The Set of Nash Equilibria of a Supermodular Game Is a Complete Lattice," Games and Economic Behavior, Elsevier, vol. 7(2), pages 295-300, September.
    3. Martin J Osborne & Ariel Rubinstein, 2009. "A Course in Game Theory," Levine's Bibliography 814577000000000225, UCLA Department of Economics.
    4. Berger, Ulrich, 2007. "Two more classes of games with the continuous-time fictitious play property," Games and Economic Behavior, Elsevier, vol. 60(2), pages 247-261, August.
    5. Voorneveld, Mark, 2000. "Best-response potential games," Economics Letters, Elsevier, vol. 66(3), pages 289-295, March.
    6. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
    7. Nikolai S. Kukushkin & Satoru Takahashi & Tetsuo Yamamori, 2005. "Improvement dynamics in games with strategic complementarities," International Journal of Game Theory, Springer, vol. 33(2), pages 229-238, 06.
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