Distributed Primal-Dual Algorithm for Seeking Generalized Nash Equilibria in Aggregative Games

The paper proposes a distributed algorithm for finding generalized Nash equilibria (GNE) in aggregative games with globally coupled constraints. In such games, each player seeks to minimize its own local objective function, which is dependent on both its own decision and the aggregate of all players in the game. The objective is to find a solution where no player can unilaterally improve its outcome, which is known as a GNE. The proposed algorithm is distributed, meaning that each player only shares its local information with its neighbors over an undirected connected graph. To achieve this, the paper introduces a local estimation of the aggregate of overall player decisions for each player. The paper proves that the proposed algorithm can converge to a v-GNE with fixed step-sizes. Numerical studies are conducted to verify the convergence and effectiveness of the proposed algorithm. Overall, the paper presents a promising approach for finding GNE in aggregative games with globally coupled constraints in a distributed manner.