  We consider the stochastic generalized Nash equilibrium problem (SGNEP) with
joint feasibility constraints and expected-value cost functions. We propose a
distributed stochastic projected reflected gradient algorithm and show its
almost sure convergence when the pseudogradient mapping is monotone and the
solution is unique. The algorithm is based on monotone operator splitting
methods tailored for SGNEPs when the expected-value pseudogradient mapping is
approximated at each iteration via an increasing number of samples of the
random variable. Finally, we show that a preconditioned variant of our proposed
algorithm has convergence guarantees when the pseudogradient mapping is
cocoercive.
