Asynchronous Distributed Algorithms for Seeking Generalized Nash Equilibria Under Full and Partial-Decision Information

This paper investigates asynchronous algorithms for distributedly seeking generalized Nash equilibria with delayed information in multiagent networks. In the game model, a shared affine constraint couples all players' local decisions. Each player is assumed to only access its private objective function, private feasible set, and a local block matrix of the affine constraint. We first give an algorithm for the case when each agent is able to fully access all other players' decisions. By using auxiliary variables related to communication links and the edge Laplacian matrix, each player can carry on its iteration asynchronously with only private data and possibly delayed information from its neighbors. Then, we consider the case when agents cannot know all other players' decisions, called a partial-decision information case. We introduce a local estimation of the overall agents' decisions and incorporate consensus dynamics on these local estimations. The two algorithms do not need any centralized clock coordination, fully exploit the local computation resource, and remove the idle time due to waiting for the "slowest" agent. Both algorithms are developed by preconditioned forward-backward operator splitting, and their convergence is shown by relating them to asynchronous fixed-point iterations, under proper assumptions and fixed and nondiminishing step-size choices. Numerical studies verify the algorithms' convergence and efficiency.