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Bosen Lian, Vrushabh S Donge, Wenqian Xue

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    This study introduces a distributed minmax strategy for multiplayer games, enabling players to find optimal control policies independently using reinforcement learning (RL). This approach enhances system stability and performance compared to traditional methods.

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    Area of Science:

    • Control Theory
    • Game Theory
    • Artificial Intelligence

    Background:

    • Multiplayer noncooperative games present challenges in decentralized control.
    • Standard control methods often require global information, limiting scalability.
    • Robustness and stability are critical in complex dynamic systems.

    Purpose of the Study:

    • To develop a distributed minmax strategy for multiplayer games.
    • To create reinforcement learning (RL) algorithms for solving these distributed strategies.
    • To analyze the stability and performance improvements of the proposed strategy.

    Main Methods:

    • Formulating a distributed minmax strategy where each player optimizes against worst-case opponents.
    • Solving distributed algebraic Riccati equations for individual control policies.
    • Employing model-based policy iteration and data-driven off-policy RL algorithms.

    Main Results:

    • Guaranteed existence of distributed minmax solutions.
    • Demonstrated L2 and asymptotic stability of the proposed policies.
    • Minmax control policies improve robust gain and phase margins over standard linear-quadratic regulator controllers.
    • Computational efficiency verified against nondistributed Nash solutions.

    Conclusions:

    • The proposed distributed minmax strategy offers a robust and stable control solution for multiplayer games.
    • Reinforcement learning effectively solves these distributed control problems.
    • This approach provides significant performance benefits in multiplayer systems.