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    This study presents a new method for finding Nash equilibrium (NE) in N-player games with integrator agents over dynamic networks. The approach improves upon existing methods by not requiring specific network conditions or inequalities.

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    Area of Science:

    • Control Theory
    • Networked Systems
    • Game Theory

    Background:

    • Existing research on Nash equilibrium (NE) seeking in N-player games has focused on static, undirected networks.
    • These methods often impose strict conditions, such as inequalities involving Lipschitz constants and network Laplacian eigenvalues.

    Purpose of the Study:

    • To develop a more general and robust method for Nash equilibrium seeking in N-player games.
    • To address high-order integrator agents and jointly strongly connected networks, which are more dynamic and complex.
    • To relax existing analytical conditions and remove reliance on specific network properties.

    Main Methods:

    • Utilizing a novel approach to Nash equilibrium seeking that does not depend on the smallest nonzero eigenvalue of the network graph.
    • Designing control strategies for high-order integrator agents operating over jointly strongly connected networks.
    • Extending the method to accommodate additive disturbances in agent inputs.

    Main Results:

    • The proposed method achieves Nash equilibrium seeking over jointly strongly connected networks, a more general case than previously studied.
    • The results strictly encompass existing findings for static, undirected networks as special cases.
    • The method is shown to be robust to additive disturbances, further enhancing its applicability.

    Conclusions:

    • The developed Nash equilibrium seeking strategy offers a significant advancement for networked multi-agent systems.
    • This work provides a more flexible and broadly applicable framework for analyzing and controlling complex game-theoretic scenarios.
    • The findings are validated through two illustrative numerical examples.