Distributed GNE Seeking under Global-Decision and Partial-Decision Information over Douglas-Rachford Splitting Method

This paper develops an algorithm for solving the generalized Nash equilibrium problem (GNEP) in non-cooperative games. The problem involves a set of players, each with a cost function that depends on their own decision as well as the decisions of other players. The goal is to find a decision vector that minimizes the cost for each player. Unlike most of the existing algorithms for GNEP, which require full information exchange among all players, this paper considers a more realistic scenario where players can only communicate with a subset of players through a connectivity graph. The proposed algorithm enables each player to estimate the decisions of other players and update their own and others' estimates through local communication with their neighbors. By introducing a network Lagrangian function and applying the Douglas-Rachford splitting method (DR), the GNEP is reformulated as a zero-finding problem. It is shown that the DR method can find the generalized Nash equilibrium (GNE) of the original problem under some mild conditions.