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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. 

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. 

We consider a class of multi-agent optimization problems, where each agent has a local objective function that depends on its own decision variables and the aggregate of others, and is willing to cooperate with other agents to minimize the sum of the local objectives. After associating each agent with an auxiliary variable and the related local estimates, we conduct primal decomposition to the globally coupled problem and reformulate it so that it can be solved distributedly. Based on the Douglas-Rachford method, an algorithm is proposed which ensures the exact convergence to a solution of the original problem. The proposed method enjoys desirable scalability by only requiring each agent to keep local estimates whose number grows linearly with the number of its neighbors. We illustrate our proposed algorithm by numerical simulations on a commodity distribution problem over a transport network. 

The aim of this paper is to find the distributed solution of the generalized Nash equilibrium problem (GNEP) for a group of players that can communicate with each other over a connected communication network. Each player tries to minimize a local objective function of its own that may depend on the other players’ decisions, and collectively all the players’ decisions are subject to some globally shared resource constraints. After reformulating the local optimization problems, we introduce the notion of network Lagrangian and recast the GNEP as the zero finding problem of a properly defined operator. Utilizing the Douglas-Rachford operator splitting method, a distributed algorithm is proposed that requires only local information exchanges between neighboring players in each iteration. The convergence of the proposed algorithm to an exact variational generalized Nash equilibrium is established under two different sets of assumptions. The effectiveness of the proposed algorithm is demonstrated using the example of a Nash-Cournot production game.