Distributed Nash Equilibrium Seeking Algorithm Design for Multi-Cluster Games with High-Order Players

TL;DR

This paper proposes a distributed algorithm for multi-cluster games with high-order players, accounting for players' dynamics, and guarantees exponential convergence to the Nash equilibrium through stability analysis.

Contribution

It introduces a novel distributed gradient-based algorithm tailored for high-order player dynamics in multi-cluster games, with proven convergence properties.

Findings

Algorithm successfully converges to Nash equilibrium.

Numerical simulations confirm effectiveness and stability.

Handles high-order dynamics unlike existing methods.

Abstract

In this paper, a multi-cluster game with high-order players is investigated. Different from the well-known multi-cluster games, the dynamics of players are taken into account in our problem. Due to the high-order dynamics of players, existing algorithms for multi-cluster games cannot solve the problem. For purpose of seeking the Nash equilibrium of the game, we design a distributed algorithm based on gradient descent and state feedback, where a distributed estimator is embedded for the players to estimate the decisions of other players. Furthermore, we analyze the exponential convergence of the algorithm via variational analysis and Lyapunov stability theory. Finally, a numerical simulation verifies the effectiveness of our method.