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Two equivalence results for two-person strict games

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  • Tang, Pingzhong
  • Lin, Fangzhen

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.

Suggested Citation

  • Tang, Pingzhong & Lin, Fangzhen, 2011. "Two equivalence results for two-person strict games," Games and Economic Behavior, Elsevier, vol. 71(2), pages 479-486, March.
  • Handle: RePEc:eee:gamebe:v:71:y:2011:i:2:p:479-486
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    References listed on IDEAS

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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.
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    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;Game Theory Society, vol. 33(2), pages 229-238, June.
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    Cited by:

    1. Kerber, Manfred & Lange, Christoph & Rowat, Colin, 2016. "An introduction to mechanized reasoning," Journal of Mathematical Economics, Elsevier, vol. 66(C), pages 26-39.

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