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We consider the stochastic generalized Nash equilibrium problem (SGNEP) withjoint feasibility constraints and expected-value cost functions. We propose adistributed stochastic projected reflected gradient algorithm and show itsalmost sure convergence when the pseudogradient mapping is monotone and thesolution is unique. The algorithm is based on monotone operator splittingmethods tailored for SGNEPs when the expected-value pseudogradient mapping isapproximated at each iteration via an increasing number of samples of therandom variable. Finally, we show that a preconditioned variant of our proposedalgorithm has convergence guarantees when the pseudogradient mapping iscocoercive.

Distributed projected-reflected-gradient algorithms for stochastic generalized Nash equilibrium problems