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Fully Distributed Nash Equilibrium Seeking: A Double-Layer Adaptive Approach.

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    New strategies help networked game players find Nash equilibrium efficiently. These methods use adaptive control to avoid large gains and global information, ensuring convergence even with diverse player dynamics.

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    Area of Science:

    • Control Theory
    • Game Theory
    • Networked Systems

    Background:

    • Distributed Nash equilibrium seeking is crucial for multi-agent systems.
    • Existing methods often require global information or suffer from large control gains.
    • Networked games present challenges due to communication graph structures (undirected/directed).

    Purpose of the Study:

    • To develop novel fully distributed strategies for Nash equilibrium seeking in networked games.
    • To ensure control gains remain bounded and independent of global information.
    • To extend the strategies for players with heterogeneous linear dynamics.

    Main Methods:

    • Gradient-based optimization algorithms.
    • Consensus algorithms.
    • Double-layer adaptive control laws with a damping term.

    Main Results:

    • Theoretical analysis proves convergence of players' actions to Nash equilibrium.
    • The proposed strategies effectively manage control gains, avoiding excessive values.
    • Demonstrated extension to players with heterogeneous linear dynamics.

    Conclusions:

    • The presented fully distributed strategies are effective for Nash equilibrium seeking in networked games.
    • The double-layer adaptive control approach successfully addresses limitations of existing methods.
    • The findings are validated through numerical examples, confirming practical applicability.