  In this paper we propose a new operator splitting algorithm for distributed
Nash equilibrium seeking under stochastic uncertainty, featuring relaxation and
inertial effects. Our work is inspired by recent deterministic operator
splitting methods, designed for solving structured monotone inclusion problems.
The algorithm is derived from a forward-backward-forward scheme for solving
structured monotone inclusion problems featuring a Lipschitz continuous and
monotone game operator. To the best of our knowledge, this is the first
distributed (generalized) Nash equilibrium seeking algorithm featuring
acceleration techniques in stochastic Nash games without assuming cocoercivity.
Numerical examples illustrate the effect of inertia and relaxation on the
performance of our proposed algorithm.
