Distributed Nash equilibrium seeking of an aggregative game by a singular perturbed algorithm

This paper proposes a distributed singular perturbed algorithm for finding a Nash Equilibrium (NE) of an aggregative game, which is known as one class of a non-cooperative Nash game. A motivation model for this game is formulated in a distributed energy network consisting of players equipped with generators. We deal with the problem of operating each agent's generator at an optimal set value to minimize its objective function selfishly. The algorithm is designed in such a manner that each player estimates the sum of players' actions in an interconnected network based on information exchanged with its local neighbors in order to determine the optimal decision. The effectiveness of the proposed algorithm is demonstrated via a simulation.