On Budget-Balanced Group-Strategyproof Cost-Sharing Mechanisms
A cost-sharing mechanism defines how to share the cost of a service among serviced customers. It solicits bids from potential customers and selects a subset of customers to serve and a price to charge each of them. The mechanism is group-strategyproof if no subset of customers can gain by lying about their values. There is a rich literature that designs group-strategyproof cost-sharing mechanisms using schemes that satisfy a property called cross-monotonicity. Unfortunately, Immorlica et al. showed that for many services, cross-monotonic schemes are provably not budget-balanced, i.e., they can recover only a fraction of the cost. While cross-monotonicity is a sufficient condition for designing group-strategyproof mechanisms, it is not necessary. Pountourakis and Vidali recently provided a complete characterization of group-strategyproof mechanisms. We construct a fully budget-balanced cost-sharing mechanism for the edge-cover problem that is not cross-monotonic and we apply their characterization to show that it is group-strategyproof. This improves upon the cross-monotonic approach which can recover only half the cost, and provides a proof-of-concept as to the usefulness of the complete characterization. This raises the question of whether all “natural” problems have budget-balanced group-strategyproof mechanisms. We answer this question in the negative by designing a set-cover instance in which no group-strategyproof mechanism can recover more than a (18/19)-fraction of the cost.
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- 2.Buchfuhrer, D., Schapira, M., Singer, Y.: Computation and incentives in combinatorial public projects. In: Parkes, D.C., Dellarocas, C., Tennenholtz, M. (eds.) ACM Conference on Electronic Commerce, pp. 33–42. ACM (2010)Google Scholar
- 5.Gupta, A., Könemann, J., Leonardi, S., Ravi, R., Schäfer, G.: An efficient cost-sharing mechanism for the prize-collecting steiner forest problem. In: Bansal, N., Pruhs, K., Stein, C. (eds.) SODA, pp. 1153–1162. SIAM (2007)Google Scholar
- 7.Jain, K., Vazirani, V.V.: Applications of approximation algorithms to cooperative games. In: STOC, pp. 364–372 (2001)Google Scholar
- 10.Moulin, H.: Incremental cost sharing: Characterization by coalition strategy-proofness. Social Choice and Welfare (16), 279–320 (1999)Google Scholar
- 12.Pál, M., Tardos, É.: Group strategyproof mechanisms via primal-dual algorithms. In: FOCS, pp. 584–593. IEEE Computer Society (2003)Google Scholar
- 13.Papadimitriou, C.H., Schapira, M., Singer, Y.: On the hardness of being truthful. In: FOCS, pp. 250–259. IEEE Computer Society (2008)Google Scholar