Distributed algorithm for nonsmooth multi-coalition games and its application in electricity markets

Abstract

In this paper, we study distributed nonsmooth multi-coalition games (MCGs), where the players are subject to local convex set constraints and coupled inequality constraints. Different from existing distributed MCGs, our problem involves nonsmooth payoff functions and constraints, relaxes the requirement for communication networks, and only relies on the strict monotonicity of pseudo-gradients. Due to the nonsmoothness of payoff functions and constraints, the weaker communication networks as well as the coexistence of cooperation and competition among players, existing generalized Nash equilibrium (GNE) seeking algorithms cannot solve the problem. Also, they pose obstacles to the algorithm design and analysis, mainly because of the non-global Lipschitz continuity of subgradients and the unconnectedness of subnetworks. To seek the variational GNE (vGNE) of the nonsmooth MCGs, we design a distributed subgradient-based algorithm. We prove that the algorithm converges to the exact vGNE of the nonsmooth MCGs from any initial states. Finally, our result is applied to the electricity market games (EMGs) of smart grids.