Networked Aggregative Games with Linear Convergence

TL;DR

This paper introduces a distributed algorithm for networked aggregative games that guarantees linear convergence to the unique Nash equilibrium under certain conditions, validated through theoretical analysis and numerical experiments.

Contribution

It proposes a novel distributed algorithm combining consensus and projection descent for NAGs with proven linear convergence under strong monotonicity.

Findings

Algorithm converges linearly to Nash equilibrium.

Proven convergence under strongly monotone pseudo-gradient.

Validated results through numerical experiments.

Abstract

This paper considers a networked aggregative game (NAG) where the players are distributed over a communication network. By only communicating with a subset of players, the goal of each player in the NAG is to minimize an individual cost function that depends on its own action and the aggregate of all the players' actions. To this end, we design a novel distributed algorithm that jointly exploits the ideas of the consensus algorithm and the conditional projection descent. Under strongly monotone assumption on the pseudo-gradient mapping, the proposed algorithm with fixed step-sizes is proved to converge linearly to the unique Nash equilibrium of the NAG. Then the theoretical results are validated by numerical experiments.