Abstract
We develop for set cover games several general cost-sharing methods that are approximately budget-balanced, core, and/or group-strategyproof. We first study the cost sharing for a single set cover game, which does not have a budget-balanced core. We show that there is no cost allocation method that can always recover more than \(\frac{1}{ln n}\) of the total cost if we require the cost sharing being a core. Here n is the number of all players to be served. We give an efficient cost allocation method that always recovers \(\frac{1}{ln d_max}\) of the total cost, where d max is the maximum size of all sets. We then study the cost allocation scheme for all induced subgames. It is known that no cost sharing scheme can always recover more than \(\frac{1}{n}\) of the total cost for every subset of players. We give an efficient cost sharing scheme that always recovers at least \(\frac{1}{2n}\) of the total cost for every subset of players and furthermore, our scheme is cross-monotone. When the elements to be covered are selfish agents with privately known valuations, we present a strategyproof charging mechanism, under the assumption that all sets are simple sets, such that each element maximizes its profit when it reports its valuation truthfully; further, the total cost of the set cover is no more than ln d max times that of an optimal solution. When the sets are selfish agents with privately known costs, we present a strategyproof payment mechanism in which each set maximizes its profit when it reports its cost truthfully. We also show how to fairly share the payments to all sets among the elements.
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References
Chvátal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operation Research 4, 233–235 (1979)
Feige, U.: A threshold of for approximating set cover. JACM 45, 634–652 (1998)
SlavÃk, P.: Improved performance of the greedy algorithm for partial cover. Information Processing Letters 64, 251–254 (1997)
Immorlica, N., Mahdian, M., Mirrokni, V.S.: Limitations of cross-monotonic cost-sharing schemes. In: ACM SODA 2005 (2005) (to appear)
Marbach, P.: Priority service and max-min fairness. IEEE/ACM Transactions on Networking 11, 733–746 (2003)
Radunović, B., Boudec, J.Y.L.: A unified framework for max-min and min-max fairness with applications. In: Proceedings of 40th Annual Allerton Conference on Communication, Control, and Computing (2002)
Osborne, M.J., Rubinstein, A.: A course in game theory. The MIT Press, Cambridge (1994)
Moulin, H., Shenker, S.: Strategyproof sharing of submodular costs:budget balance versus efficiency. Economic Theory 18, 511–533 (2001)
Devanur, N., Mihail, M., Vazirani, V.: Strategyproof cost-sharing mechanisms for set cover and facility location games. In: ACM EC, pp. 108–114 (2003)
Pál, M., Tardos, E.: Group strategyproof mechanisms via primal-dual algorithms. In: IEEE FOCS, pp. 584–593 (2003)
Feigenbaum, J., Papadimitriou, C.H., Shenker, S.: Sharing the cost of multicast transmissions. Journal of Computer and System Sciences 63, 21–41 (2001)
Libman, L., Orda, A.: Atomic resource sharing in noncooperative networks. Telecommunication Systems 17, 385–409 (2001)
Shenker, S., Clark, D., Estrin, D., Herzog, S.: Pricing in computer networks: Reshaping the research agenda. ACM Computer Comm. Review 26, 19–43 (1996)
Feigenbaum, J., Krishnamurthy, A., Sami, R., Shenker, S.: Hardness results for multicast cost sharing. Theoretical Computer Science 304, 215–236 (2003)
Archer, A., Feigenbaum, J., Krishnamurthy, A., Sami, R., Shenker, S.: Approximation and collusion in multicast cost sharing. Games and Economic Behavior 47, 36–71 (2004)
Herzog, S., Shenker, S., Estrin, D.: Sharing the cost of multicast trees: An axiomatic analysis. IEEE/ACM Transactions on Networking 5, 847–860 (1997)
Li, X.Y., Sun, Z., Wang, W.: Cost sharing and strategyproof mechanisms for set cover games (2004), http://www.cs.iit.edu/~xli/publications-select.htm
Vickrey, W.: Counterspeculation, auctions and competitive sealed tenders. Journal of Finance 16, 8–37 (1961)
Clarke, E.H.: Multipart pricing of public goods. Public Choice 11, 17–33 (1971)
Groves, T.: Incentives in teams. Econometrica 41, 617–631 (1973)
Lehmann, D.J., Oćallaghan, L.I., Shoham, Y.: Truth revelation in approximately efficient combinatorial auctions. JACM 49, 577–602 (2002)
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Li, XY., Sun, Z., Wang, W. (2005). Cost Sharing and Strategyproof Mechanisms for Set Cover Games. In: Diekert, V., Durand, B. (eds) STACS 2005. STACS 2005. Lecture Notes in Computer Science, vol 3404. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31856-9_18
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DOI: https://doi.org/10.1007/978-3-540-31856-9_18
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