Aggregative Games on a Strongly Connected Digraphs

This paper considers the distributed Nash equilibrium seeking strategy for aggregative games. We consider the game to have no central-node and the aggregated information is not directly available to the players. Therefore, we consider a average consensus protocol is adopted to estimate the aggregate information. By introducing a surplus variable, the changing states of each player's integral terms are recorded in real-time. Combining the average consensus protocol with gradient descent method, we establish a distributed strategy for seeking Nash equilibrium in aggregative games under strongly connected nonequilibrium directed topologies and prove the algorithm's convergence. Finally, a numerical example is presented to validate the proposed algorithm.