Distributed Nash Equilibrium Seeking by A Consensus Based Approach

In this paper, Nash equilibrium seeking among a network of players is considered. Different from most of the existing works on Nash equilibrium seeking, the players considered in this paper cannot observe their opponents' actions. Instead, the players are supposed to be capable of communicating with their neighbors on their estimated actions under an undirected and connected communication graph. By employing a dynamic consensus protocol, distributed Nash seeking strategies are proposed for general non-cooperative games and quadratic games, respectively. Singular perturbation is leveraged for the analysis of games with non-quadratic payoffs and a local convergence result is derived as multiple isolated Nash equilibria may coexist in the game. For quadratic games, it is shown that the proposed method enables the players' actions to converge to the Nash equilibrium globally. A numerical example is provided to verify the effectiveness of the proposed method.