Abstract
In a cost-sharing problem, finitely many players have an unknown preference for some public excludable good (service), and the task is to determine which players to serve and how to distribute the incurred cost. Therefore, incentive-compatible mechanisms are sought that elicit truthful bids, charge prices that recover the cost, and are economically efficient in that they reasonably balance cost and valuations. A commonplace notion of incentive-compatibility in cost sharing is group-strategyproofness (GSP), meaning that not even coordinated deceit is profitable. However, GSP makes strong implications on players’ coordination abilities and is known to impose severe limitations on other goals in cost sharing. There is hence good reason to seek for a weaker axiom: In this work, we study the following question: Does relaxing GSP to resilience only against coalitions of bounded size yield a richer set of possible mechanisms? Surprisingly, the answer is essentially “no”: We prove that already a mechanism resilient to coalitions of size only two (“2-GSP”) is GSP, once we require that cost shares must only depend on the service allocation (and not directly on the bids). Moreover, we show that even without additional requirements, 2-GSP implies weak group-strategyproofness (WGSP). Consequently, our results give some justification that GSP may, after all, still be desirable in various scenarios. As another benefit, we believe that our characterizations will facilitate devising and understanding new GSP cost-sharing mechanisms. Finally, we relate our findings to other concepts of non-manipulability such as (outcome) non-bossiness [19] and weak utility non-bossiness [13].
This work was partially supported by the IST Program of the European Union under contract number IST-15964 (AEOLUS).
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References
Andelman, N., Feldman, M., Mansour, Y.: Strong price of anarchy. In: Proc. of the 18th SODA 2007, pp. 189–198. Society for Industrial and Applied Mathematics (2007)
Archer, A., Feigenbaum, J., Krishnamurthy, A., Sami, R., Shenker, S.: Approximation and collusion in multicast cost sharing. Games and Economic Behaviour 47(1), 36–71 (2004)
Bleischwitz, Y., Monien, B., Schoppmann, F.: To be or not to be (served). In: Deng, X., Graham, F.C. (eds.) WINE 2007. LNCS, vol. 4858, pp. 515–528. Springer, Heidelberg (2007)
Bleischwitz, Y., Monien, B., Schoppmann, F., Tiemann, K.: The power of two prices: Beyond cross-monotonicity. In: MFCS 2007. LNCS, vol. 4708, pp. 657–668. Springer, Heidelberg (2007)
Brenner, J., Schäfer, G.: Singleton acyclic mechanisms and their applications to scheduling problems. In: Monien, B., Schroeder, U.-P. (eds.) SAGT 2008. LNCS, vol. 4997, pp. 315–326. Springer, Heidelberg (2008)
Deb, R., Razzolini, L.: Voluntary cost sharing for an excludable public project. Mathematical Social Sciences 37(2), 123–138 (1999)
Deb, R., Razzolini, L.: Auction-like mechanisms for pricing excludable public goods. Journal of Economic Theory 88(2), 340–368 (1999)
Dobzinski, S., Mehta, A., Roughgarden, T., Sundararajan, M.: Is Shapley cost sharing optimal? In: Monien, B., Schroeder, U.-P. (eds.) SAGT 2008. LNCS, vol. 4997, pp. 327–336. Springer, Heidelberg (2008)
Green, J., Laffont, J.-J.: Characterizations of satisfactory mechanisms for the revelation of preferences for public goods. Econometrica 45(2), 427–438 (1977)
Immorlica, N., Mahdian, M., Mirrokni, V.S.: Limitations of cross-monotonic cost-sharing schemes. ACM Transactions on Algorithms 4(2), 1–25 (2008)
Mehta, A., Roughgarden, T., Sundararajan, M.: Beyond Moulin mechanisms. In: Proc. of the 8th EC 2007, pp. 1–10 (2007)
Moulin, H.: Incremental cost sharing: Characterization by coalition strategy-proofness. Social Choice and Welfare 16(2), 279–320 (1999)
Mutuswami, S.: Strategy proof mechanisms for cost sharing. Economics Discussion Papers 520, University of Essex, Department of Economics (2000)
Mutuswami, S.: Strategyproofness, non-bossiness and group strategyproofness in a cost sharing model. Economics Letters 89(1), 83–88 (2005)
Nisan, N.: Introduction to mechanisms design (for computer scientists). In: Algorithmic Game Theory, ch. 9. Cambridge University Press, Cambridge (2007)
Penna, P., Ventre, C.: More powerful and simpler cost-sharing methods. In: Persiano, G., Solis-Oba, R. (eds.) WAOA 2004. LNCS, vol. 3351, pp. 97–110. Springer, Heidelberg (2005)
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)
Roughgarden, T., Sundararajan, M.: New trade-offs in cost-sharing mechanisms. In: STOC 2006, pp. 79–88 (2006)
Satterthwaite, M., Sonnenschein, H.: Strategy-proof allocation mechanisms at differentiable points. Review of Economic Studies 48(4), 587–597 (1981)
Schummer, J.: Manipulation through bribes. Journal of Economic Theory 91(2), 180–198 (2000)
Serizawa, S.: Pairwise strategy-proofness and self-enforcing manipulation. Social Choice and Welfare 26(2), 305–331 (2006)
Shenker, S.: Some technical results on continuity, strategy-proofness, and related strategic concepts (1993), ftp://parcftp.parc.xerox.com/pub/net-research/str.ps
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Schoppmann, F. (2008). The Power of Small Coalitions in Cost Sharing. In: Papadimitriou, C., Zhang, S. (eds) Internet and Network Economics. WINE 2008. Lecture Notes in Computer Science, vol 5385. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92185-1_72
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DOI: https://doi.org/10.1007/978-3-540-92185-1_72
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