Optimal Cost-Sharing in General Resource Selection Games

Resource selection games provide a model for a diverse collection of applications where a set of resources is matched to a set of demands. Examples include routing in traffic and in telecommunication networks, service of requests on multiple parallel queues, and acquisition of services or goods with demand-dependent prices. In reality, demands are often submitted by selfish entities (players) and congestion on the resources results in negative externalities for their users. We consider a policy maker that can set a priori rules to minimize the inefficiency induced by selfish players. For example, these rules may assume the form of scheduling policies or pricing decisions. We explore the space of such rules abstracted as cost-sharing methods. We prescribe desirable properties that the cost-sharing method should possess and prove that, in this natural design space, the cost-sharing method induced by the Shapley value minimizes the worst-case inefficiency of equilibria.