Consensus‐based and extremum seeking methods for distributed generalized nash equilibrium

Abstract

AbstractThis article investigates the generalized Nash equilibrium (GNE) seeking for the game with equality constraints. Each player cannot directly access all the other player's actions and the gradients of all players' payoff functions are unknown. In these scenarios, an interesting question is under what distributed algorithm the GNE can be found. To address such games, we first design a two‐time‐scale distributed algorithm based on the extremum seeking method and consensus protocol. Then, by utilizing singular perturbation techniques and Lyapunov robust analysis, we show that the players' decisions can be regulated to an arbitrarily small neighborhood of the GNE. Moreover, we further consider the ideal case in which the gradients are known. In this case, the proposed strategy can be degenerated to a gradient‐based algorithm and the players' decisions exponentially converge to the GNE. Finally, two examples along with simulation results are used to illustrate the effectiveness of the proposed algorithms.