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A Consensus-based Algorithm for Non-convex Multiplayer Games

Author

Listed:
  • Enis Chenchene

    (University of Vienna)

  • Hui Huang

    (University of Graz)

  • Jinniao Qiu

    (University of Calgary)

Abstract

In this paper, we present a novel consensus-based zeroth-order algorithm tailored for non-convex multiplayer games. The proposed method leverages a metaheuristic approach using concepts from swarm intelligence to reliably identify global Nash equilibria. We utilize a group of interacting particles, each agreeing on a specific consensus point, asymptotically converging to the corresponding optimal strategy. This paradigm permits a passage to the mean-field limit, allowing us to establish convergence guarantees under appropriate assumptions regarding initialization and objective functions. Finally, we conduct a series of numerical experiments to unveil the dependency of the proposed method on its parameters and apply it to solve a nonlinear Cournot oligopoly game involving multiple goods.

Suggested Citation

  • Enis Chenchene & Hui Huang & Jinniao Qiu, 2025. "A Consensus-based Algorithm for Non-convex Multiplayer Games," Journal of Optimization Theory and Applications, Springer, vol. 206(2), pages 1-30, August.
    • Handle: RePEc:spr:joptap:v:206:y:2025:i:2:d:10.1007_s10957-025-02719-z
    DOI: 10.1007/s10957-025-02719-z
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    References listed on IDEAS

    as
    1. Chaitanya Gokhale & Arne Traulsen, 2014. "Evolutionary Multiplayer Games," Dynamic Games and Applications, Springer, vol. 4(4), pages 468-488, December.
    2. Kang Liu & Nadia Oudjane & Cheng Wan, 2023. "Approximate Nash Equilibria in Large Nonconvex Aggregative Games," Mathematics of Operations Research, INFORMS, vol. 48(3), pages 1791-1809, August.
    3. Bae, Hyeong-Ohk & Ha, Seung-Yeal & Kang, Myeongju & Lim, Hyuncheul & Min, Chanho & Yoo, Jane, 2022. "A constrained consensus based optimization algorithm and its application to finance," Applied Mathematics and Computation, Elsevier, vol. 416(C).
    Full references (including those not matched with items on IDEAS)

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