Efficient Estimation of Equilibria of Large Congestion Games with Heterogeneous Players

TL;DR

This paper introduces a method to efficiently approximate equilibria in large, complex congestion games with heterogeneous players by reducing the problem to a smaller auxiliary population game, enabling faster computation.

Contribution

It proposes a novel approximation technique for variational Nash equilibria in large congestion games with heterogeneity and coupling constraints, improving computational efficiency.

Findings

Approximate equilibria can be computed efficiently in large games.

The method reduces the problem size via an auxiliary population game.

It handles heterogeneity and coupling constraints effectively.

Abstract

Computing an equilibrium in congestion games can be challenging when the number of players is large. Yet, it is a problem to be addressed in practice, for instance to forecast the state of the system and be able to control it. In this work, we analyze the case of generalized atomic congestion games, with coupling constraints, and with players that are heterogeneous through their action sets and their utility functions. We obtain an approximation of the variational Nash equilibria---a notion generalizing Nash equilibria in the presence of coupling constraints---of a large atomic congestion game by an equilibrium of an auxiliary population game, where each population corresponds to a group of atomic players of the initial game. Because the variational inequalities characterizing the equilibrium of the auxiliary game have smaller dimension than the original problem, this approach enables the fast computation of an estimation of equilibria in a large congestion game with thousands of heterogeneous players.