Stochastic Nash equilibrium seeking for players with linear dynamics

In this paper, we will study the problem of stochastic Nash equilibrium seeking in an $N$-player non-cooperative game for players with general linear dynamics. Our focus is on minimizing the expectation value with respect to the distribution of uncertainties in players’ individual cost functions. We adopt two regularization approaches, the Tikhonov regularization scheme and the iterative proximal point method. These approaches provide an advantage over the standard stochastic approximation method by relaxing the requirement for strongly monotone cost functions to monotone ones. We examine distributed stochastic Nash equilibrium seeking for players with linear dynamics over a strongly connected graph. We provide an example involving energy systems to demonstrate the efficacy of our proposed algorithms.