A Linearly Convergent Distributed Nash Equilibrium Seeking Algorithm for Aggregative Games

This article considers distributed Nash equilibrium (NE) seeking of strongly monotone aggregative games over a multiagent network. Each player can only observe its own strategy while can exchange information with its neighbors via a communication graph. To solve the problem, we propose a distributed algorithm with multiple rounds of communication, where the players need constant rounds of communication with their neighbors at each iteration. We then prove that our algorithm converges to the (unique) NE with a linear convergence rate. We further study a single-round communication version of our algorithm, which can also achieve linear convergence rate with an additional condition related to the structure of the graph and the properties of the aggregative game. Finally, we provide numerical simulations to verify our results.