Edge-based distributed primal–dual algorithms for seeking generalized Nash equilibria

Abstract

This paper introduces two novel distributed algorithms aimed at finding the generalized Nash equilibria (GNE) in noncooperative games. To tackle this, we utilize the variational inequality framework, transforming the noncooperative game into the challenge of identifying the zeros of a sum of monotone operators. Within noncooperative games, the decisions made by individual players are interlinked via shared affine constraints. Our proposed approach involves two edge-based distributed algorithms, differentiated by their access to players’ actions, whether it is full-decision information or partial-decision information. We establish the parameter range and demonstrate the convergence of both algorithms, showcasing their efficacy under local constant step-sizes. Additionally, we validate the effectiveness and advantages of these algorithms through two numerical experiments.