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A rank based mean field game in the strong formulation

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  • Erhan Bayraktar
  • Yuchong Zhang

Abstract

We discuss a natural game of competition and solve the corresponding mean field game with \emph{common noise} when agents' rewards are \emph{rank dependent}. We use this solution to provide an approximate Nash equilibrium for the finite player game and obtain the rate of convergence.

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  • Erhan Bayraktar & Yuchong Zhang, 2016. "A rank based mean field game in the strong formulation," Papers 1603.06312, arXiv.org, revised Oct 2016.
    • Handle: RePEc:arx:papers:1603.06312
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    References listed on IDEAS

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    1. Olivier Guéant & Pierre Louis Lions & Jean-Michel Lasry, 2011. "Mean Field Games and Applications," Post-Print hal-01393103, HAL.
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    Cited by:

    1. Marcel Nutz & Yuchong Zhang, 2019. "A Mean Field Competition," Management Science, INFORMS, vol. 44(4), pages 1245-1263, November.
    2. Marcel Nutz & Yuchong Zhang, 2017. "A Mean Field Competition," Papers 1708.01308, arXiv.org.
    3. Xiang Yu & Yuchong Zhang & Zhou Zhou, 2020. "Teamwise Mean Field Competitions," Papers 2006.14472, arXiv.org, revised May 2021.

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