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The nonatomic supermodular game

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  • Yang, Jian
  • Qi, Xiangtong

Abstract

We introduce the nonatomic supermodular game, where no playerʼs action has any discernible impact on other playersʼ payoffs and yet strategic complementarities prevail among all playersʼ types and actions. For both semi-anonymous and anonymous games, we show that monotone equilibria form nonempty complete lattices and among these equilibria, the largest and smallest members vary in monotone fashions with respect to certain game-changing parameters. Results here complement existing nonatomic-game works, which focused more on pure equilibria of anonymous games where opponentsʼ types are not influential. They are also applicable to price competition involving diverse cost/quality parameters, as well as a slew of other situations.

Suggested Citation

  • Yang, Jian & Qi, Xiangtong, 2013. "The nonatomic supermodular game," Games and Economic Behavior, Elsevier, vol. 82(C), pages 609-620.
    • Handle: RePEc:eee:gamebe:v:82:y:2013:i:c:p:609-620
    DOI: 10.1016/j.geb.2013.09.005
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    Cited by:

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    2. Rene Carmona & Francois Delarue & Daniel Lacker, 2016. "Mean field games of timing and models for bank runs," Papers 1606.03709, arXiv.org, revised Jan 2017.
    3. Sun, Xiang & Sun, Yeneng & Yu, Haomiao, 2020. "The individualistic foundation of equilibrium distribution," Journal of Economic Theory, Elsevier, vol. 189(C).
    4. Yang, Jian, 2018. "Game-theoretic modeling of players’ ambiguities on external factors," Journal of Mathematical Economics, Elsevier, vol. 75(C), pages 31-56.

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    More about this item

    Keywords

    Nonatomic game; Supermodular game; Strong set order; Stochastic dominance order; Complete lattice;
    All these keywords.

    JEL classification:

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

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