Multilevel Distributed Fuzzy Optimum Policy Iteration Pareto-Nash Equilibrium Seeking of Multiagent Multiobjective General Sum Games

Seeking the Pareto-Nash equilibrium in multiagent, multiobjective general-sum games (MMGSG) poses a significant challenge, particularly in accurately capturing individual preferences and adhering to the fairness principle of the solution. To address this issue, this article introduces, for the first time, a multilevel distributed fuzzy optimum policy iteration (MDFOPI) method for identifying the Pareto-Nash equilibrium point in MMGSG. This approach is grounded in fuzzy optimal membership degrees, and employs fuzzy measures and $\lambda$-mean classification to construct the coupled multiobjective optimum matrix, utilizing the strategy space as the foundation. The Pareto-Nash equilibrium point is sought through the MDFOPI method, with the multiobjective optimal membership degree matrix used to organize the sampled data and integrate the results of multiobjective evaluations. This work rigorously proves the existence of Nash equilibria in MMGSG and establishes the convergence of the MDFOPI method to a fixed point, specifically a Pareto-Nash equilibrium point. The accuracy and practical applicability of the research findings are verified through simulation experiments.