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Strongly Polynomial-Time Truthful Mechanisms in One Shot

  • Paolo Penna
  • Guido Proietti
  • Peter Widmayer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4286)

Abstract

One of the main challenges in algorithmic mechanism design is to turn (existing) efficient algorithmic solutions into efficient truthful mechanisms. Building a truthful mechanism is indeed a difficult process since the underlying algorithm must obey certain “monotonicity” properties and suitable payment functions need to be computed (this task usually represents the bottleneck in the overall time complexity).

We provide a general technique for building truthful mechanisms that provide optimal solutions in strongly polynomial time. We show that the entire mechanism can be obtained if one is able to express/write a strongly polynomial-time algorithm (for the corresponding optimization problem) as a “suitable combination” of simpler algorithms. This approach applies to a wide class of mechanism design graph problems, where each selfish agent corresponds to a weighted edge in a graph (the weight of the edge is the cost of using that edge). Our technique can be applied to several optimization problems which prior results cannot handle (e.g., MIN-MAX optimization problems).

As an application, we design the first (strongly polynomial-time) truthful mechanism for the minimum diameter spanning tree problem, by obtaining it directly from an existing algorithm for solving this problem. For this non-utilitarian MIN-MAX problem, no truthful mechanism was known, even considering those running in exponential time (indeed, exact algorithms do not necessarily yield truthful mechanisms). Also, standard techniques for payment computations may result in a running time which is not polynomial in the size of the input graph. The overall running time of our mechanism, instead, is polynomial in the number n of nodes and m of edges, and it is only a factor O((n,n)) away from the best known canonical centralized algorithm.

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References

  1. 1.
    Agarwal, P.K., Sharir, M.: Davenport-Schinzel sequences and their geometric applications. Cambridge University Press, New York (1995)zbMATHGoogle Scholar
  2. 2.
    Archer, A., Tardos, É.: Truthful mechanisms for one-parameter agents. In: Proc. of 42nd FOCS, pp. 482–491 (2001)Google Scholar
  3. 3.
    Clarke, E.H.: Multipart Pricing of Public Goods. Public Choice, 17–33 (1971)Google Scholar
  4. 4.
    Feigenbaum, J., Shenker, S.: Distributed algorithmic mechanism design: Recent results and future directions. In: Proceedings of the 6th DIALM, pp. 1–13. ACM Press, New York (2002)CrossRefGoogle Scholar
  5. 5.
    Groves, T.: Incentive in Teams. Econometrica 41, 617–631 (1973)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Gualà, L., Proietti, G.: A truthful (2-2/k)-approximation mechanism for the Steiner tree problem with k terminals. In: Wang, L. (ed.) COCOON 2005. LNCS, vol. 3595, pp. 90–400. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  7. 7.
    Gualà, L., Proietti, G.: Efficient truthful mechanisms for the single-source shortest paths tree problem. In: Cunha, J.C., Medeiros, P.D. (eds.) Euro-Par 2005. LNCS, vol. 3648, pp. 941–951. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  8. 8.
    Hassin, R., Tamir, A.: On the minimum diameter spanning tree problem. Info. Proc. Lett. 53(2), 109–111 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Hershberger, J., Suri, S.: Vickrey prices and shortest paths: what is an edge worth? In: Proc. of the 42nd FOCS, pp. 252–259 (2001)Google Scholar
  10. 10.
    Kao, M.-Y., Li, X.-Y., Wang, W.: Towards truthful mechanisms for binary demand games: A general framework. In: Proc. of ACM EC, pp. 213–222 (2005)Google Scholar
  11. 11.
    Koutsoupias, E., Papadimitriou, C.H.: Worst-case equilibria. In: Meinel, C., Tison, S. (eds.) STACS 1999. LNCS, vol. 1563, pp. 404–413. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  12. 12.
    Mu’Alem, A., Nisan, N.: Truthful approximation mechanisms for restricted combinatorial auctions. In: Proc. of 18th AAAI, pp. 379–384 (2002)Google Scholar
  13. 13.
    Myerson, R.: Optimal auction design. Mathematics of Operations Research 6, 58–73 (1981)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Nardelli, E., Proietti, G., Widmayer, P.: Finding the most vital node of a shortest path. Theoretical Computer Science 296(1), 167–177 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Nisan, N., Ronen, A.: Algorithmic mechanism design. In: Proc. of the 31st STOC, pp. 129–140 (1999)Google Scholar
  16. 16.
    Papadimitriou, C.H.: Algorithms, games, and the Internet. In: Proc. of the 33rd STOC, pp. 749–753 (2001)Google Scholar
  17. 17.
    Penna, P., Proietti, G., Widmayer, P.: Strongly polynomial-time truthful mechanisms in one shot. Technical report, Università di Salerno (2006), Available at: http://ec.tcfs.it/Group/Selfish_Agents.html
  18. 18.
    Pettie, S., Ramachandran, V.: Computing shortest paths with comparisons and additions. In: Proc. of the 13th SODA, pp. 267–276 (2002)Google Scholar
  19. 19.
    Proietti, G., Widmayer, P.: A truthful mechanism for the non-utilitarian minimum radius spanning tree problem. In: Proc. of SPAA, pp. 195–202 (2005)Google Scholar
  20. 20.
    Tansel, B.C., Francis, R.L., Lowe, T.J.: Location on networks: a survey. Part I: The p-center and p-median problems. Management Sciences 29, 482–497 (1983)zbMATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Vickrey, W.: Counterspeculation, auctions and competitive sealed tenders. Journal of Finance 16, 8–37 (1961)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Paolo Penna
    • 1
  • Guido Proietti
    • 2
  • Peter Widmayer
    • 3
  1. 1.Dipartimento di Informatica ed Applicazioni “Renato M. Capocelli”Università di SalernoBaronissiItaly
  2. 2.Dipartimento di InformaticaUniversità di L’AquilaL’AquilaItaly
  3. 3.Institut für Theoretische InformatikETH Zürich, CAB H 15 Universitätstrasse 6ZürichSwitzerland

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