Approximate Nash Equilibria in Large Nonconvex Aggregative Games

This paper shows the existence of O(1/n(gamma))-Nash equilibria in n-player noncooperative sum-aggregative games in which the players' cost functions, depending only on their own action and the average of all players' actions, are lower semicontinuous in the former, whereas gamma-Holder continuous in the latter. Neither the action sets nor the cost functions need to be convex. For an important class of sum-aggregative games, which includes congestion games with gamma equal to one, a gradient-proximal algorithm is used to construct O(1/n)-Nash equilibria with at most O(n(3)) iterations. These results are applied to a numerical example concerning the demand-side management of an electricity system. The asymptotic performance of the algorithm when n tends to infinity is illustrated.