Distributed seeking for generalized Nash equilibria of monotone games via preconditioned proximal algorithms

Abstract

In this paper, we propose distributed algorithms to seek generalized Nash equilibrium (GNE) of monotone games with affine coupling constraints. Each player can only utilize its local objective function, local feasible set and a local block of the coupling constraint, and can only communicate with its neighbours. The games are assumed to have monotone pseudo-subdifferential without Lipschitz continuity restrictions. Center-free distributed GNE seeking algorithms are proposed for equality and inequality coupling constraints, respectively. In both algorithms, the complicated GNE seeking task is decomposed into a sequential NE computation of regularized subgames and a distributed update of multipliers and auxiliary variables, based on local data and local communication. Our double-layer GNE seeking algorithms only require that the strongly monotone subgames are inexactly solved using any of the available distributed NE seeking algorithms. We relate both GNE seeking algorithms to preconditioned proximal algorithms (PPA) for finding zeros of monotone operators. Applications and numerical simulations are given for illustration.