Seeking strategy design for distributed nonsmooth games and its application

Abstract

This paper investigates the nonsmooth noncooperative games (NGs) over unbalanced digraphs, where each player has a nondifferentiable payoff function. Meanwhile, these players are subject to local nonsmooth inequality constraints, local convex set constraints and coupled equality constraints. Due to the coexistence of nonsmooth payoff functions, unbalanced digraphs and constraints, existing generalized Nash equilibrium (GNE) seeking strategies are fail to address our problem. Based on subgradient descents, differential inclusions, projection and primal-dual methods, we develop a distributed seeking strategy. Besides, the convergence of the strategy is proved. Finally, the proposed method is applied to electricity market games (EMGs) of smart grids.