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The conditions in the existence results for discontinuous games by Reny and by Simon and Zame are incomparable

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  • Carmona, Guilherme
  • Podczeck, Konrad

Abstract

A natural way to relate the existence theorems of Reny (1999) and Simon and Zame (1990) would be to show the following: Each game with an endogenous sharing rule satisfying the assumptions of Simon and Zame (1990) is such that the payoff correspondence has a measurable selection inducing a normal-form game whose mixed extension satisfies the assumptions in Reny (1999). We present a result showing that this is not so in general, even when the assumptions in Reny (1999) are weakened to those in Barelli and Meneghel (2013).

Suggested Citation

  • Carmona, Guilherme & Podczeck, Konrad, 2018. "The conditions in the existence results for discontinuous games by Reny and by Simon and Zame are incomparable," Games and Economic Behavior, Elsevier, vol. 111(C), pages 16-19.
    • Handle: RePEc:eee:gamebe:v:111:y:2018:i:c:p:16-19
    DOI: 10.1016/j.geb.2018.05.008
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    References listed on IDEAS

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    1. Philippe Bich & Rida Laraki, 2017. "On the Existence of approximative Equilibria and Sharing Rule Solutions in Discontinuous Games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01396183, HAL.
    2. Paulo Barelli & Idione Meneghel, 2013. "A Note on the Equilibrium Existence Problem in Discontinuous Games," Econometrica, Econometric Society, vol. 81(2), pages 813-824, March.
    3. Simon, Leo K & Zame, William R, 1990. "Discontinuous Games and Endogenous Sharing Rules," Econometrica, Econometric Society, vol. 58(4), pages 861-872, July.
    4. Philippe Bich & Rida Laraki, 2017. "On the Existence of approximative Equilibria and Sharing Rule Solutions in Discontinuous Games," Post-Print hal-01396183, HAL.
    5. Matthew O. Jackson & Jeroen M. Swinkels, 2005. "Existence of Equilibrium in Single and Double Private Value Auctions," Econometrica, Econometric Society, vol. 73(1), pages 93-139, January.
    6. Bich, Philippe & Laraki, Rida, 2017. "On the existence of approximate equilibria and sharing rule solutions in discontinuous games," Theoretical Economics, Econometric Society, vol. 12(1), January.
    7. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
    8. Andrew McLennan & Paulo K. Monteiro & Rabee Tourky, 2011. "Games With Discontinuous Payoffs: A Strengthening of Reny's Existence Theorem," Econometrica, Econometric Society, vol. 79(5), pages 1643-1664, September.
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    Cited by:

    1. Allison, Blake A. & Bagh, Adib & Lepore, Jason J., 2022. "Invariant equilibria and classes of equivalent games," Games and Economic Behavior, Elsevier, vol. 132(C), pages 448-462.
    2. Scalzo, Vincenzo, 2020. "Doubly Strong Equilibrium," MPRA Paper 99329, University Library of Munich, Germany.

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    More about this item

    Keywords

    Games with an endogenous sharing rule; Discontinuous games; Existence of equilibrium;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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