Distributed Algorithms for Aggregative Games on Graphs

TL;DR

This paper develops distributed algorithms for computing Nash equilibria in aggregative games over networks, ensuring convergence under standard conditions and demonstrating effectiveness through numerical simulations.

Contribution

It introduces novel distributed synchronous and asynchronous algorithms for aggregative games on graphs with convergence guarantees and extensions to more general aggregate functions.

Findings

Algorithms converge almost surely to the equilibrium.

Numerical results validate the effectiveness of the proposed schemes.

Extensions handle more complex aggregate functions.

Abstract

We consider a class of Nash games, termed as aggregative games, being played over a networked system. In an aggregative game, a player's objective is a function of the aggregate of all the players' decisions. Every player maintains an estimate of this aggregate, and the players exchange this information with their local neighbors over a connected network. We study distributed synchronous and asynchronous algorithms for information exchange and equilibrium computation over such a network. Under standard conditions, we establish the almost-sure convergence of the obtained sequences to the equilibrium point. We also consider extensions of our schemes to aggregative games where the players' objectives are coupled through a more general form of aggregate function. Finally, we present numerical results that demonstrate the performance of the proposed schemes.