Distributed Nash Equilibrium Seeking for Merely Monotone N-Coalition Noncooperative Games

This paper considers a distributed Nash equilibrium computation problem for merely monotone N-coalition noncooperative games. Different from most of exsiting works, the main challenge of this paper is that the game mappings of the considered N-coalition games only satisfy monotone conditions but not strictly/strongly monotone conditions, which further bring difficulties in the design of Nash equilibrium seeking strategy. Based on a regularization technique, the gradient search algorithm and a dynamic average consensus protocol, a distributed Nash equilirbrium seeking strategy is established. The proposed strategy is leveraged to achieve convergence towards the NE, with convergence properties towards the NE rigorously analyzed through Lyapunov stability analysis. The numerical simulation further illustrates the effectiveness of the strategy.