More Powerful and Simpler Cost-Sharing Methods

We provide a new technique to derive group strategyproof mechanisms for the cost-sharing problem. Our technique is simpler and provably more powerful than the existing one based on so called crossmonotonic cost-sharing methods given by Moulin and Shenker [1997]. Indeed, our method yields the first polynomial-time mechanism for the Steiner tree game which is group strategyproof, budget balance and also meets other standard requirements (No Positive Transfer, Voluntary Participation and Consumer Sovereignty). A known result by Megiddo [1978] implies that this result cannot be achieved with cross-monotonic costsharing methods, even if using exponential-time mechanisms.