Distributed GNE Seeking Over Directed Graphs: A Scalar-State Variable Approach

This paper explores distributed generalized Nash equilibrium (GNE) seeking problems for non-cooperation games over weight-unbalanced directed graphs. To address this issue, a new distributed GNE seeking framework is developed, where a scalar-state variable is introduced for each player. The scalar-state variable is designed by using local out-degree information and limited communications among neighbors, to compensate for the unbalance of the directed graphs. In addition, with the help of the scalar-state variable, the Lagrange multiplier and projection operator are further developed over directed graphs for addressing additional local constraint sets and the coupling equality constraint simultaneously. It is theoretically shown that the convergence of GNE can be guaranteed. Finally, a practical simulation verifies the effectiveness of the proposed algorithm.