Abstract
Assuming strict consumer sovereignty (CS*), when can cost-sharing mechanisms simultaneously be group-strategyproof (GSP) and β-budget-balanced (β-BB)? Moulin mechanisms are GSP and 1-BB for submodular costs. We overcome the submodularity requirement and instead consider arbitrary—yet symmetric—costs:
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Already for 4 players, we show that symmetry of costs is not sufficient for the existence of a GSP and 1-BB mechanism. However, for only 3 players, we give a GSP and 1-BB mechanism.
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We introduce two-price cost-sharing forms (2P-CSFs) that define players’ cost shares and present a novel mechanism that is GSP given any such 2P-CSF. For subadditive costs, we give an algorithm to compute 2P-CSFs that are \({\ensuremath{\frac{\sqrt{17} + 1}{4}}}\)-BB (≈ 1.28). This result is then shown to be tight for 2P-CSFs. Yet, this is a significant improvement over 2-BB, which is the best Moulin mechanisms can achieve.
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We give applications to the minimum makespan scheduling problem.
A key feature of all our mechanisms is a preference order on the set of players. Higher cost shares are always payed by least preferred players.
This work was partially supported by the IST Program of the European Union under contract number IST-15964 (AEOLUS).
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References
Archer, A., Feigenbaum, J., Krishnamurthy, A., Sami, R.: Approximation and collusion in multicast cost sharing. Games and Economic Behaviour 47, 36–71 (2004)
Becchetti, L., Könemann, J., Leonardi, S., Pál, M.: Sharing the cost more efficiently: improved approximation for multicommodity rent-or-buy. In: Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 375–384. ACM Press, New York (2005)
Bleischwitz, Y., Monien, B.: Fair cost-sharing methods for scheduling jobs on parallel machines. In: Calamoneri, T., Finocchi, I., Italiano, G.F. (eds.) CIAC 2006. LNCS, vol. 3998, pp. 175–186. Springer, Heidelberg (2006)
Brenner, J., Schäfer, G.: Cost sharing methods for makespan and completion time scheduling. In: Thomas, W., Weil, P. (eds.) STACS 2007. LNCS, vol. 4393, Springer, Heidelberg (2007)
Graham, R.: Bounds on multiprocessing timing anomalies. SIAM Journal of Applied Mathematics 17(2), 416–429 (1969)
Gupta, A., Könemann, J., Leonardi, S., Ravi, R., Schäfer, G.: An efficient cost-sharing mechanism for the prize-collecting Steiner forest problem. In: Proceedings of the 18th Annual ACM-SIAM Symposium on Discrete Algorithms, ACM Press, New York (2007)
Gupta, A., Srinivasan, A., Tardos, E.: Cost-sharing mechanisms for network design. In: Jansen, K., Khanna, S., Rolim, J.D.P., Ron, D. (eds.) RANDOM 2004 and APPROX 2004. LNCS, vol. 3122, pp. 139–152. Springer, Heidelberg (2004)
Immorlica, N., Mahdian, M., Mirrokni, V.: Limitations of cross-monotonic cost sharing schemes. In: Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 602–611. ACM Press, New York (2005)
Könemann, J., Leonardi, S., Schäfer, G.: A group-strategyproof mechanism for Steiner forests. In: Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 612–619. ACM Press, New York (2005)
Könemann, J., Leonardi, S., Schäfer, G., van Zwam, S.: From primal-dual to cost shares and back: A stronger LP relaxation for the Steiner forest problem. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 930–942. Springer, Heidelberg (2005)
Leonardi, S., Schäfer, G.: Cross-monotonic cost-sharing methods for connected facility location games. In: Proceedings of the ACM Conference on Electronic Commerce, pp. 224–243. ACM Press, New York (2004)
Mehta, A., Roughgarden, T., Sundararajan, M.: Beyond Moulin mechanisms. In: The Proceedings of the 8th ACM Conference on Electronic Commerce, ACM Press, New York (to appear, 2007)
Moulin, H.: Incremental cost sharing: Characterization by coalition strategy-proofness. Social Choice and Welfare 16(2), 279–320 (1999)
Penna, P., Ventre, C.: The algorithmic structure of group strategyproof budget-balanced cost-sharing mechanisms. In: Durand, B., Thomas, W. (eds.) STACS 2006. LNCS, vol. 3884, pp. 337–348. Springer, Heidelberg (2006)
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Bleischwitz, Y., Monien, B., Schoppmann, F., Tiemann, K. (2007). The Power of Two Prices: Beyond Cross-Monotonicity. In: Kučera, L., Kučera, A. (eds) Mathematical Foundations of Computer Science 2007. MFCS 2007. Lecture Notes in Computer Science, vol 4708. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74456-6_58
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DOI: https://doi.org/10.1007/978-3-540-74456-6_58
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