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On non-uniqueness in mean field games

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  • Erhan Bayraktar
  • Xin Zhang

Abstract

We analyze an $N+1$-player game and the corresponding mean field game with state space $\{0,1\}$. The transition rate of $j$-th player is the sum of his control $\alpha^j$ plus a minimum jumping rate $\eta$. Instead of working under monotonicity conditions, here we consider an anti-monotone running cost. We show that the mean field game equation may have multiple solutions if $\eta

Suggested Citation

  • Erhan Bayraktar & Xin Zhang, 2019. "On non-uniqueness in mean field games," Papers 1908.06207, arXiv.org, revised Mar 2020.
    • Handle: RePEc:arx:papers:1908.06207
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    Cited by:

    1. Dianetti, Jodi & Ferrari, Giorgio & Fischer, Markus & Nendel, Max, 2022. "A Unifying Framework for Submodular Mean Field Games," Center for Mathematical Economics Working Papers 661, Center for Mathematical Economics, Bielefeld University.
    2. Alberto Bressan & Khai T. Nguyen, 2023. "Generic Properties of First-Order Mean Field Games," Dynamic Games and Applications, Springer, vol. 13(3), pages 750-782, September.
    3. Paolo Dai Pra & Elena Sartori & Marco Tolotti, 2023. "Polarization and Coherence in Mean Field Games Driven by Private and Social Utility," Journal of Optimization Theory and Applications, Springer, vol. 198(1), pages 49-85, July.
    4. Julio Backhoff-Veraguas & Xin Zhang, 2023. "Dynamic Cournot-Nash equilibrium: the non-potential case," Mathematics and Financial Economics, Springer, volume 17, number 1, June.

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