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    This study introduces an off-policy reinforcement learning (RL) algorithm to solve complex N-player nonzero-sum (NZS) games with unknown dynamics. The method successfully finds Nash equilibria without needing system dynamics information.

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    Area of Science:

    • Control Theory
    • Game Theory
    • Artificial Intelligence

    Background:

    • N-player nonzero-sum (NZS) games present challenges due to complex dynamics and unknown system parameters.
    • Traditional policy iteration (PI) algorithms require complete knowledge of system dynamics, limiting their applicability.
    • Developing adaptive algorithms for dynamic games with unknown system characteristics is crucial.

    Purpose of the Study:

    • To establish an off-policy reinforcement learning (RL) algorithm for discrete-time N-player NZS games with completely unknown dynamics.
    • To derive and solve the N-coupled Hamilton-Jacobi (HJ) equation independent of system dynamics.
    • To prove the existence of Nash equilibrium for these games using the proposed method.

    Main Methods:

    • Derivation of N-coupled generalized algebraic Riccati equations (GARE).
    • Development of an off-policy RL method based on quadratic value functions, leading to the off-policy N-coupled HJ equation.
    • Decomposition of the N-coupled HJ equation using Kronecker product to separate unknown parameters from system data.
    • Application of least squares for calculating iterative value functions and control strategies.

    Main Results:

    • The N-coupled HJ equation is solved independently of system dynamics.
    • An N-tuple of iterative control and iterative value function are obtained.
    • The existence of Nash equilibrium is mathematically proven.
    • Simulation examples demonstrate the method's effectiveness for discrete-time unknown dynamics NZS games.

    Conclusions:

    • The proposed off-policy RL algorithm effectively solves discrete-time N-player NZS games with unknown dynamics.
    • The method provides a dynamic-independent approach to finding Nash equilibria.
    • The findings contribute to advancing RL and game theory applications in complex systems.