A Distributed Douglas-Rachford Based Algorithm for Stochastic GNE Seeking with Partial Information

We consider the stochastic generalized Nash equilibrium problem (SGNEP) where a set of self-interested players, subject to certain global constraints, aim to optimize their local objectives that depend on their own decisions and the decisions of others and are influenced by some random factors. A distributed stochastic generalized Nash equilibrium seeking algorithm is proposed based on the Douglas-Rachford operator splitting scheme, which only requires local communications among neighbors. The proposed scheme significantly relaxes assumptions on co-coercivity and contractiveness in the existing literature, where the projected stochastic subgradient method is applied to provide approximate solutions to the augmented best-response subproblems for each player. Finally, we illustrate the validity of the proposed algorithm through a Nash-Cournot production game.