Distributed Computation of Nash Equilibria for Monotone Aggregative Games via Iterative Regularization

This work considers an aggregative game over time-varying graphs, where each player's cost function depends on its own strategy and the aggregate of its competitors' strategies. Though the aggregate is unknown to any given player, each player may interact with its neighbors to construct an estimate of the aggregate. We design a distributed iterative Tikhonov regularization method in which each player may independently choose its steplengths and regularization parameters while meeting some overall coordination requirements. Under a monotonicity assumption on the concatenated player-specific gradient map, we prove that the generated sequence converges to the least-norm Nash equilibrium (i.e., a Nash equilibrium with the smallest two-norm) and validate the proposed method on a networked Nash-Cournot equilibrium problem.