Efficient Black-Box Reductions for Separable Cost Sharing

Abstract

In cost-sharing games with delays, a set of agents jointly uses a subset of resources. Each resource has a fixed cost that has to be shared by the players, and each agent has a nonshareable player-specific delay for each resource. A separable cost-sharing protocol determines cost shares that are budget-balanced, separable, and guarantee existence of pure Nash equilibria (PNE). We provide black-box reductions reducing the design of such a protocol to the design of an approximation algorithm for the underlying cost-minimization problem. In this way, we obtain separable cost-sharing protocols in matroid games, single-source connection games, and connection games on n-series-parallel graphs. All these reductions are efficiently computable - given an initial allocation profile, we obtain a cheaper profile and separable cost shares turning the profile into a PNE. Hence, in these domains, any approximation algorithm yields a separable cost-sharing protocol with price of stability bounded by the approximation factor.