Nash and Wardrop equilibria in aggregative games with coupling constraints
For game theory and multi-agent systems, it provides theoretical bounds and practical algorithms for equilibrium computation in large populations with coupling constraints.
The paper studies aggregative games with coupling constraints, bounding the distance between Nash and Wardrop equilibria as a decreasing function of population size, and proposes two decentralized algorithms that converge to these equilibria.
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.