  In this paper, we propose an asynchronous distributed algorithm for the
computation of generalized Nash equilibria in noncooperative games, where the
players interact via an undirected communication graph. Specifically, we extend
the paper "Asynchronous distributed algorithm for seeking generalized Nash
equilibria" by Yi and Pavel: we redesign the asynchronous update rule using
auxiliary variables over the nodes rather than over the edges. This key
modification renders the algorithm scalable for highly interconnected games.
The derived asynchronous algorithm is robust against delays in the
communication and it eliminates the idle times between computations, hence
modeling a more realistic interaction between players with different update
frequencies. We address the problem from an operator-theoretic perspective and
design the algorithm via a preconditioned forward-backward splitting. Finally,
we numerically simulate the algorithm for the Cournot competition in networked
markets.
