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A reversible chemical reaction represents a chemical process that proceeds in both forward (left to right) and reverse (right to left) directions. When the rates of the forward and reverse reactions are equal, the concentrations of the reactant and product species remain constant over time and the system is at equilibrium. A special double arrow is used to emphasize the reversible nature of the reaction. The relative concentrations of reactants and products in equilibrium systems vary greatly;...
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    Area of Science:

    • Control Theory
    • Game Theory
    • Distributed Optimization

    Background:

    • Investigating distributed Nash equilibrium (NE) searching problems with complex constraints.
    • Addressing scenarios where cost functions and feasible action sets are interdependent across all players.
    • Considering limitations where players only access information from their neighbors.

    Purpose of the Study:

    • To develop a distributed algorithm for solving Nash equilibrium problems with coupled constraints and limited communication.
    • To enable players to estimate others' actions using only local information.

    Main Methods:

    • A continuous-time distributed gradient-based projected algorithm is proposed.
    • A leader-following consensus algorithm is utilized for estimating neighboring players' actions.
    • The algorithm operates under nonlinear inequality and linear equation constraints.

    Main Results:

    • Players' actions are shown to asymptotically converge to a generalized Nash equilibrium.
    • The convergence is demonstrated under mild assumptions on cost functions and network topology.
    • Simulation examples validate the theoretical findings.

    Conclusions:

    • The proposed algorithm effectively solves distributed Nash equilibrium problems with coupled characteristics and limited information.
    • The leader-following consensus mechanism is crucial for achieving convergence in decentralized settings.
    • The findings have implications for distributed decision-making in networked systems.