Asynchronous distributed algorithm for seeking generalized Nash equilibria

In this paper, we propose an asynchronous distributed algorithm with delayed information for computing a generalized Nash equilibrium over multi-agent systems. We consider a game where all players' local decisions are coupled via a shared affine constraint. We assume each player can only access its local objective function, local constraint, and a local block matrix of the affine constraint. With the help of auxiliary edge variables and edge Laplacian matrix, each player can perform its local iteration in an asynchronous manner, using only local data and possibly delayed neighbour information, without any centralized clock coordination. Therefore, the algorithm fully exploits the local computation resource of each player, and reduces the idle time due to waiting for the "slowest" agent. The algorithm convergence is shown using asynchronous fixed-point iterations. Numerical studies verify its convergence.