Nash and Wardrop equilibria in aggregative games with coupling constraints

TL;DR

This paper analyzes Nash and Wardrop equilibria in aggregative games with coupling constraints, providing bounds on their differences, proposing decentralized algorithms for equilibrium computation, and applying these concepts to electric vehicle charging and route choice problems.

Contribution

It introduces a novel analysis of the relationship between Nash and Wardrop equilibria in aggregative games and develops decentralized algorithms for constrained scenarios.

Findings

Bound the distance between Nash and Wardrop equilibria as population grows

Propose decentralized algorithms that converge to equilibria with coupling constraints

Apply the theoretical framework to electric vehicle charging and traffic routing

Abstract

We consider the framework of aggregative games, in which the cost function of each agent depends on his own strategy and on the average population strategy. As first contribution, we investigate the relations between the concepts of Nash and Wardrop equilibrium. By exploiting a characterization of the two equilibria as solutions of variational inequalities, we bound their distance with a decreasing function of the population size. As second contribution, we propose two decentralized algorithms that converge to such equilibria and are capable of coping with constraints coupling the strategies of different agents. Finally, we study the applications of charging of electric vehicles and of route choice on a road network.