Tolls For Atomic Congestion Games

Abstract

In games where selfish players compete for resources, they often arrive at equilibria that are less desirable than the social optimum. To combat this inefficiency, it is common for some central authority to place tolls on the resources in order to guide these players to a more advantageous result. In this thesis, we consider the question of how to add tolls to atomic unsplittable congestion games in order to enforce a specific flow as the unique equilibrium. We consider this question in the context of both routing games and matroid congestion games. In the former case, we show that for the class of series-parallel graphs the nonatomic tolls suffice, and investigate examples for which nonatomic tolls fail. In the latter case, we show that the nonatomic tolls can also be used to impose flows in atomic laminar matroid games.