Is Shapley Cost Sharing Optimal?

  • Shahar Dobzinski
  • Aranyak Mehta
  • Tim Roughgarden
  • Mukund Sundararajan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4997)

Abstract

We study the best guarantees of efficiency approximation achievable by cost-sharing mechanisms. Our main result is the first quantitative lower bound that applies to all truthful cost-sharing mechanisms, including randomized mechanisms that are only truthful in expectation, and only β-budget-balanced in expectation. Our lower bound is optimal up to constant factors and applies even to the simple and central special case of the public excludable good problem. We also give a stronger lower bound for a subclass of deterministic cost-sharing mechanisms, which is driven by a new characterization of the Shapley value mechanism. Finally, we show a separation between the best-possible efficiency guarantees achievable by deterministic and randomized cost-sharing mechanisms.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Blumrosen, L., Nisan, N.: Combinatorial auctions. In: Nisan, N., Roughgarden, T., Tardos, E., Vazirani, V. (eds.) Algorithmic Game TheoryGoogle Scholar
  2. 2.
    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)CrossRefGoogle Scholar
  3. 3.
    Clarke, E.H.: Multipart pricing of public goods. Public Choice V11(1), 17–33 (1971)CrossRefGoogle Scholar
  4. 4.
    Deb, R., Razzolini, L.: Auction-like mechanisms for pricing excludable public goods. Journal of Economic Theory 88(2), 340–368 (1999), http://ideas.repec.org/a/eee/jetheo/v88y1999i2p340-368.html MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Deb, R., Razzolini, L.: Voluntary cost sharing for an excludable public project. Mathematical Social Sciences 37, 123–138 (1999)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Feigenbaum, J., Krishnamurthy, A., Sami, R., Shenker, S.: Hardness results for multicast cost sharing. Theoretical Computer Science 304, 215–236 (2003)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Green, J., Kohlberg, E., Laffont, J.J.: Partial equilibrium approach to the free rider problem. Journal of Public Economics 6, 375–394 (1976)CrossRefGoogle Scholar
  8. 8.
    Groves, T.: Incentives in teams. Econometrica 41(4), 617–631 (1973)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Immorlica, N., Mahdian, M., Mirrokni, V.S.: Limitations of cross-monotonic cost-sharing schemes. In: Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 602–611 (2005)Google Scholar
  10. 10.
    Lavi, R.: Computationally efficient approximation mechanisms. In: Nisan, N., Roughgarden, T., Tardos, E., Vazirani, V. (eds.) Algorithmic Game TheoryGoogle Scholar
  11. 11.
    Mehta, A., Roughgarden, T., Sundararajan, M.: Beyond Moulin mechanisms. In: EC 2007: Proceedings of the 8th ACM conference on Electronic commerce, pp. 1–10 (2007)Google Scholar
  12. 12.
    Mehta, A., Vazirani, V.V.: Randomized truthful auctions of digital goods are randomizations over truthful auctions. In: ACM Conference on Electronic Commerce, pp. 120–124 (2004)Google Scholar
  13. 13.
    Moulin, H.: Incremental cost sharing: Characterization by coalition strategy-proofness. Social Choice and Welfare 16, 279–320 (1999)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Moulin, H., Shenker, S.: Strategyproof sharing of submodular costs: Budget balance versus efficiency. Economic Theory 18, 511–533 (2001)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Nisan, N., Ronen, A.: Algorithmic mechanism design. In: STOC 1999 (1999)Google Scholar
  16. 16.
    Roberts, K.: The characterization of implementable choice rules. In: Laffont, J.J. (ed.) Aggregation and Revelation of Preferences, North-Holland, Amsterdam (1979)Google Scholar
  17. 17.
    Roughgarden, T., Sundararajan, M.: New trade-offs in cost-sharing mechanisms. In: Proceedings of the 38th Annual ACM Symposium on the Theory of Computing (STOC), pp. 79–88 (2006)Google Scholar
  18. 18.
    Vickrey, W.: Counterspeculation, auctions, and competitive sealed tenders. Journal of Finance 16(1), 8–37 (1961)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Shahar Dobzinski
    • 1
  • Aranyak Mehta
    • 2
  • Tim Roughgarden
    • 3
  • Mukund Sundararajan
    • 3
  1. 1.The School of Computer Science and EngineeringThe Hebrew University of JerusalemIsrael
  2. 2.Google, Inc.USA
  3. 3.Department of Computer ScienceStanford UniversityStanfordUSA

Personalised recommendations