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    Area of Science:

    • Game Theory
    • Optimization Algorithms
    • Computational Economics

    Background:

    • Noncooperative games with constraints are common in economics and engineering.
    • Finding generalized Nash equilibria (GNE) is computationally challenging.
    • Existing algorithms may lack guaranteed convergence or efficiency.

    Purpose of the Study:

    • To propose a novel adaptive neurodynamic algorithm (ANA) for seeking GNE in constrained noncooperative games.
    • To analyze the convergence properties of the proposed ANA under various monotonicity conditions.
    • To introduce a new ANA variant for approximating GNE using Tikhonov regularization.

    Main Methods:

    • Development of an adaptive neurodynamic algorithm (ANA) with trajectory-dependent penalty parameters.
    • Mathematical analysis of finite-time convergence to the action set.
    • Proof of exponential or polynomial convergence to GNE based on monotonicity conditions.
    • Application of Tikhonov regularization for approximating $\varepsilon $-GNE.

    Main Results:

    • The ANA ensures finite-time entry into the action set due to adaptive penalty terms.
    • Exponential convergence to GNE is proven for strongly monotone games.
    • Polynomial convergence to GNE is established for "generalized" strongly monotone games, a novel result.
    • Exponential convergence to $\varepsilon $-GNE is demonstrated for generally monotone games.

    Conclusions:

    • The proposed ANA is effective for finding GNE in constrained noncooperative games.
    • The algorithm offers improved convergence properties, including polynomial convergence for the first time.
    • The Tikhonov-regularized ANA provides a method for approximating GNE when exact solutions are difficult.
    • The algorithm's effectiveness is validated through examples like pollution and base station location games.