A Distributed Relaxed Inertial Projection Nash Equilibrium Seeking Algorithm

Nash equilibrium(NE) seeking is an important part in game theory. This paper is concerned with the NE seeking problem in a partial decision information setting, where each agent just can communicate decision strategy with its neighbors through a graph, although the cost function of each agent may depend on all agents. A new distributed relaxed-inertial projection algorithm is proposed, under the assumptions of strong-monotonicity and Lipschitz continuity of the pseudogradient mapping. By using the property of projection operator and the orthogonal decomposition on the consensus subspace, we prove that the proposed algorithm converges to the NE over an undirected and connected graph. Finally, a numerical example is presented to verify the effectiveness of the algorithm.