Generalized Nash Equilibrium Seeking for Noncooperative Games With Heterogeneous Individual Dynamics

This article investigates the constrained noncooperative game problems where players with individual dynamics are subject to local strategy set constraints and global nonlinear inequality constraints. The cost function of each player depends on the strategies of all players and is only locally accessible to the player. With only the local information, players estimate all others' strategies and deal with coupled constraints by communicating with their neighbors in a graph. To avoid the usage of the graph's algebraic connectivity, a distributed control algorithm is proposed with adaptive parameters. With arbitrary initial strategies, the control algorithm guarantees the convergence of the strategies of all players to a generalized Nash equilibrium. Simulations illustrate the effectiveness of the proposed distributed control algorithms.

I. Introduction

With the development of cooperative control of multi-agent systems [1], [2], [3], [4], constrained noncooperative game problems have attracted considerable attention in recent years. Practical applications involve smart grids, noncooperative flow control, and so on [5], [6], [7]. In noncooperative game problems, the cost function of each player depends on the strategies of all players. Each player drives strategies independently to minimize its cost function. A Generalized Nash Equilibrium (GNE) that is a solution to constrained noncooperative games has been a hot research topic for decades. At GNEs, each player has no incentives to change its strategy to get a smaller cost function.