Distributed seeking of Nash equilibrium for non-cooperative game over general strongly connected digraphs

In this paper, a modified distributed Nash equilibrium seeking problem has been proposed. Different from most existing results, the payoff function of each player has been determined by its own and its neighbors' actions, which are more consistent with real situations. By making use of the gradient of the payoff functions and the communication between players, both continuous-time and discrete-time distributed Nash equilibrium seeking algorithms solving the modified problem for non-cooperative game over general strongly connected digraphs are proposed. Based on the Lyapunov method, it is shown that when players update their actions according to the proposed distributed seeking algorithms under the given condition, actions of players converge globally exponentially to Nash equilibrium. Numerical simulations are given to validate the proposed Nash equilibrium seeking strategy.