Extremum-seeking Based Approach for Distributed Noncooperative N-coalition Games

This paper investigates the N-coalition game, which covers the generalized Nash equilibrium problems (GNEPs) and distributed optimization problems. To seek the Nash equilibrium of the N-coalition games, we firstly exploit a centralized algorithm. Under the full information, the algorithm can exponentially converge to the Nash equilibrium of the N-coalition games. Then, based on the extremum seeking (ES) approach, we extend the centralized algorithm to distributed counterpart. Different from the centralized algorithm, the explicit cost functions are not available in the distributed algorithm. The players not only can converge to a small neighborhood of the Nash equilibrium, but do not communicate with the other coalitions. Furthermore, in order to reduce the communication burden in intra-coalition, an event-triggered based distributed algorithm is proposed. By the algorithm, the players only communicate with their neighbors in intra-coalition at event-triggered time constants, and also can converge to a neighborhood of the Nash equilibrium of the N-coalition games. Finally, an example about Nash-Cournot game is given to illustrate the effectiveness of our algorithms.