Nash Equilibrium Strategy in Stochastic Non-cooperative Games

Abstract

In this paper, we consider a stochastic noncooperative game where each player can communicate with others via an undirected communication graph. For games with nonlinear payoff function, we design a Nash equilibrium seeking strategy in the presence of noises in information flow. Based on the gradient descent approach and the consensus protocol, the convergence of the seeking strategy is presented. Due to the existence of noises, a neighborhood convergence rather than asymptotic convergence is obtained and the convergence error bound is analyzed. The boundary depends on the step size of gradient and the control gain in the consensus protocol. An example is given to illustrate the results.