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    This study introduces a distributed approximate algorithm for finding Nash equilibria (NE) in aggregative games. The method uses inscribed polyhedrons to approximate constraints, enabling efficient computation of approximate NE with proven convergence.

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    Area of Science:

    • Game Theory
    • Distributed Computing
    • Optimization

    Background:

    • Nash equilibria (NE) are crucial in game theory for predicting outcomes.
    • Projection-based algorithms are common for solving games with local constraints.
    • Exact projections can be computationally challenging in practice.

    Purpose of the Study:

    • To design a distributed approximate algorithm for Nash equilibria in aggregative games.
    • To address the computational difficulty of exact projections in constraint sets.
    • To analyze the approximation accuracy and computational savings.

    Main Methods:

    • Approximating local set constraints using inscribed polyhedrons.
    • Developing a distributed algorithm to find approximate Nash equilibria (ϵ-NE).
    • Utilizing quadratic optimization with linear constraints for projections.

    Main Results:

    • Proving that the NE of the approximate game corresponds to the ϵ-NE of the original game.
    • Demonstrating the convergence of the proposed distributed algorithm.
    • Estimating approximation accuracy based on exponential convergence and analyzing computational costs.

    Conclusions:

    • The proposed distributed approximate algorithm effectively finds ϵ-NE in aggregative games.
    • Approximation via inscribed polyhedrons offers a practical alternative to exact projections.
    • The method provides insights into computational savings and accuracy trade-offs.