Optimal Cost Sharing for Resource Selection Games

Joint use of resources with usage-dependent cost raises the question: who pays how much? We study cost sharing in resource selection games where the strategy spaces are either singletons or bases of a matroid defined on the ground set of resources. Our goal is to design cost sharing protocols so as to minimize the resulting price of anarchy and price of stability. We investigate three classes of protocols: basic protocols guarantee the existence of at least one pure Nash equilibrium; separable protocols additionally require that the resulting cost shares only depend on the set of players on a resource; uniform protocols are separable and require that the cost shares on a resource may not depend on the instance, that is, they remain the same even if new resources are added to or removed from the instance. We find optimal basic and separable protocols that guarantee the price of stability and price of anarchy to grow logarithmically in the number of players, except for the case of matroid games induced by separable protocols where the price of anarchy grows linearly with the number of players. For uniform protocols we show that the price of anarchy is unbounded even for singleton games.