  We solve the stochastic generalized Nash equilibrium (SGNE) problem in merely
monotone games with expected value cost functions. Specifically, we present the
first distributed SGNE seeking algorithm for monotone games that requires one
proximal computation (e.g., one projection step) and one pseudogradient
evaluation per iteration. Our main contribution is to extend the relaxed
forward-backward operator splitting by Malitsky (Mathematical Programming,
2019) to the stochastic case and in turn to show almost sure convergence to a
SGNE when the expected value of the pseudogradient is approximated by the
average over a number of random samples.
