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Fictitious play in networks

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  • Ewerhart, Christian
  • Valkanova, Kremena

Abstract

This paper studies fictitious play in networks of noncooperative two-person games. We show that continuous-time fictitious play converges to the set of Nash equilibria if the overall n-person game is zero-sum. Moreover, the rate of convergence is 1/τ, regardless of the size of the network. In contrast, arbitrary n-person zero-sum games with bilinear payoff functions do not possess the continuous-time fictitious-play property. As extensions, we consider networks in which each bilateral game is either strategically zero-sum, a weighted potential game, or a two-by-two game. In those cases, convergence requires a condition on bilateral payoffs or, alternatively, that the network is acyclic. Our results hold also for the discrete-time variant of fictitious play, which implies, in particular, a generalization of Robinson's theorem to arbitrary zero-sum networks. Applications include security games, conflict networks, and decentralized wireless channel selection.

Suggested Citation

  • Ewerhart, Christian & Valkanova, Kremena, 2020. "Fictitious play in networks," Games and Economic Behavior, Elsevier, vol. 123(C), pages 182-206.
    • Handle: RePEc:eee:gamebe:v:123:y:2020:i:c:p:182-206
    DOI: 10.1016/j.geb.2020.06.006
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    1. Abheek Ghosh & Paul W. Goldberg, 2023. "Best-Response Dynamics in Lottery Contests," Papers 2305.10881, arXiv.org.
    2. Ewerhart, Christian, 2017. "The lottery contest is a best-response potential game," Economics Letters, Elsevier, vol. 155(C), pages 168-171.

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    More about this item

    Keywords

    Fictitious play; Networks; Zero-sum games; Conflicts; Potential games; Miyasawa's theorem; Robinson's theorem;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation

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