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

Seeking the Pareto-Nash equilibrium in multi-agent, multi-objective 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 paper introduces, for the first time, a multi-level 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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\lambda$</tex-math></inline-formula>-mean classification to construct the coupled multi-objective optimum matrix, utilizing the strategy space as the foundation. The Pareto-Nash equilibrium point is sought through the MDFOPI method, with the multi-objective optimal membership degree matrix used to organize the sampled data and integrate the results of multi-objective 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.