Efficient Estimation of Equilibria in Large Aggregative Games with Coupling Constraints

TL;DR

This paper introduces a method to efficiently approximate equilibria in large aggregative games with coupling constraints by reducing the problem to a smaller auxiliary game, facilitating easier computation.

Contribution

It proposes a novel approach linking variational Nash equilibria to Wardrop equilibria in auxiliary population games for large aggregative games.

Findings

Approximate variational Nash equilibria using Wardrop equilibria.

Reduces computational complexity for large games.

Validated with a smart grid example.

Abstract

Aggregative games have many industrial applications, and computing an equilibrium in those games is challenging when the number of players is large. In the framework of atomic aggregative games with coupling constraints, we show that variational Nash equilibria of a large aggregative game can be approximated by a Wardrop equilibrium of an auxiliary population game of smaller dimension. Each population of this auxiliary game corresponds to a group of atomic players of the initial large game. This approach enables an efficient computation of an approximated equilibrium, as the variational inequality characterizing the Wardrop equilibrium is of smaller dimension than the initial one. This is illustrated on an example in the smart grid context.