Adaptive Approaches for Fully Distributed Nash Equilibrium Seeking in Networked Games

TL;DR

This paper introduces two adaptive, fully distributed strategies for Nash equilibrium seeking in networked games, ensuring global stability and adaptability to changing communication networks.

Contribution

It proposes novel node-based and edge-based adaptive control laws for distributed Nash equilibrium seeking, with proven stability and adaptability to switching networks.

Findings

Both strategies guarantee global asymptotic stability of the Nash equilibrium.

The edge-based method adapts to time-varying communication networks.

Numerical example confirms effectiveness of the proposed methods.

Abstract

This paper considers the design of fully distributed Nash equilibrium seeking strategies for multi-agent games. To develop fully distributed seeking strategies, two adaptive control laws, including a node-based control law and an edge-based control law, are proposed. In the node-based adaptive strategy, each player adjusts their own weight on their procurable consensus error dynamically. Moreover, in the edge-based algorithm, the fully distributed strategy is designed by adjusting the weights on the edges of the communication graph adaptively. By utilizing LaSalle's invariance principle, it is shown that the Nash equilibrium is globally asymptotically stable by both strategies given that the players' objective functions are twice-continuously differentiable, the partial derivatives of the players' objective functions with respect to their own actions are globally Lipschitz, the pseudo-gradient vector of the game is strongly monotone and the communication network is undirected and connected. In addition, we further show that the edge-based method can be easily adapted to accommodate time-varying communication conditions, in which the communication network is switching among a set of undirected and connected graphs. In the last, a numerical example is given to illustrate the effectiveness of the proposed methods.