Marginal cost pricing for Atomic Network Congestion Games

We study optimal tolls for network congestion games where players aim to route certain amount of traffic between various source destination pairs. We consider weighted atomic users, unsplittable traffic and arbitrary nondecreasing latency functions. Users are selfish and want to follow routes that minimize their respective latencies. We focus on pure Nash equilibria. A Nash equilibrium profile need not be system optimal and the system performance can be improved if users are asked to pay tolls for using edges. We assume propose a toll mechanism, which we call marginal cost pricing. Marginal cost pricing turns any system optimal profile into a Nash equilibrium of the priced game. Marginal costs can be calculated in a distributed fashion. Also, the priced game is a finite weighted potential game and thus selfish updates of users converge to a Nash equilibrium. In the special case of unweighted network congestion games on twoterminal series-parallel networks, any Nash equilibrium profile of the priced game is system optimal.