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The structure of Nash equilibria in Poisson games

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  • Meroni, Claudia
  • Pimienta, Carlos

Abstract

We show that many results on the structure and stability of equilibria in finite games extend to Poisson games. In particular, the set of Nash equilibria of a Poisson game consists of finitely many connected components and at least one of them contains a stable set (De Sinopoli et al., 2014). In a similar vein, we prove that the number of Nash equilibria in Poisson voting games under plurality, negative plurality, and (when there are at most three candidates) approval rule, as well as in Poisson coordination games, is generically finite. As in finite games, these results are obtained exploiting the geometric structure of the set of Nash equilibria which, in the case of Poisson games, is shown to be semianalytic.

Suggested Citation

  • Meroni, Claudia & Pimienta, Carlos, 2017. "The structure of Nash equilibria in Poisson games," Journal of Economic Theory, Elsevier, vol. 169(C), pages 128-144.
    • Handle: RePEc:eee:jetheo:v:169:y:2017:i:c:p:128-144
    DOI: 10.1016/j.jet.2017.02.003
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    Cited by:

    1. Hans Gersbach & Akaki Mamageishvili & Oriol Tejada, 2017. "Assessment Voting in Large Electorates," CER-ETH Economics working paper series 17/284, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich.
    2. Gersbach, Hans & Mamageishvili, Akaki & Tejada, Oriol, 2019. "The Effect of Handicaps on Turnout for Large Electorates: An Application to Assessment Voting," CEPR Discussion Papers 13921, C.E.P.R. Discussion Papers.
    3. Mamageishvili, Akaki & Tejada, Oriol, 2023. "Large elections and interim turnout," Games and Economic Behavior, Elsevier, vol. 137(C), pages 175-210.
    4. Gersbach, Hans & Mamageishvili, Akaki & Tejada, Oriol, 2021. "The effect of handicaps on turnout for large electorates with an application to assessment voting," Journal of Economic Theory, Elsevier, vol. 195(C).

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    More about this item

    Keywords

    Poisson games; Voting; Stable sets; Generic determinacy of equilibria; o-Minimal structures;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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