Online Mechanism Design (Randomized Rounding on the Fly)

  • Piotr Krysta
  • Berthold Vöcking
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7392)


We study incentive compatible mechanisms for combinatorial auctions (CAs) in an online model with sequentially arriving bidders, where the arrivals’ order is either random or adversarial. The bidders’ valuations are given by demand oracles. Previously known online mechanisms for CAs assume that each item is available at a certain multiplicity b > 1. Typically, one assumes b = Ω(logm), where m is the number of different items.

We present the first online mechanisms guaranteeing competitiveness for any multiplicity b ≥ 1. We introduce an online variant of oblivious randomized rounding enabling us to prove competitive ratios that are close to or even beat the best known offline approximation factors for various CAs settings. Our mechanisms are universally truthful, and they significantly improve on the previously known mechanisms.


Competitive Ratio Online Algorithm Approximation Factor Price Vector Valuation Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Awerbuch, B., Azar, Y., Meyerson, A.: Reducing truth-telling online mechanisms to online optimization. In: STOC, pp. 503–510 (2003)Google Scholar
  2. 2.
    Awerbuch, B., Azar, Y., Plotkin, S.A.: Throughput-competitive on-line routing. In: FOCS, pp. 32–40 (1993)Google Scholar
  3. 3.
    Babaioff, M., Immorlica, N., Kleinberg, R.: Matroids, secretary problems, and online mechanisms. In: SODA, pp. 434–443 (2007)Google Scholar
  4. 4.
    Bansal, N., Korula, N., Nagarajan, V., Srinivasan, A.: On k-Column Sparse Packing Programs. In: Eisenbrand, F., Shepherd, F.B. (eds.) IPCO 2010. LNCS, vol. 6080, pp. 369–382. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  5. 5.
    Bartal, Y., Gonen, R., Nisan, N.: Incentive compatible multi unit combinatorial auctions. In: The Proc. of the 9th TARK, pp. 72–87 (2003)Google Scholar
  6. 6.
    Blumrosen, L., Nisan, N.: Combinatorial auctions. In: Nisan, N., Roughgarden, T., Tardos, E., Vazirani, V. (eds.) Algorithmic Game Theory (2007)Google Scholar
  7. 7.
    Borodin, A., El-Yaniv, R.: Online computation and competitive analysis. Cambridge University Press (1998)Google Scholar
  8. 8.
    Buchbinder, N., Naor, J.: Online Primal-Dual Algorithms for Covering and Packing Problems. In: Brodal, G.S., Leonardi, S. (eds.) ESA 2005. LNCS, vol. 3669, pp. 689–701. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  9. 9.
    Buchbinder, N., Naor, J.: Improved bounds for online routing and packing via a primal-dual approach. In: FOCS, pp. 293–304 (2006)Google Scholar
  10. 10.
    Dobzinski, S.: Two Randomized Mechanisms for Combinatorial Auctions. In: Charikar, M., Jansen, K., Reingold, O., Rolim, J.D.P. (eds.) RANDOM 2007 and APPROX 2007. LNCS, vol. 4627, pp. 89–103. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  11. 11.
    Dobzinski, S., Fu, H., Kleinberg, R.: Truthfulness via proxies. CoRR, abs/1011.3232 (2010)Google Scholar
  12. 12.
    Dobzinski, S., Nisan, N., Schapira, M.: Truthful randomized mechanisms for combinatorial auctions. In: STOC, pp. 644–652 (2006)Google Scholar
  13. 13.
    Dynkin, E.B.: The optimum choice of the instant for stopping a markov process. Sov. Math Dokl. 4 (1963)Google Scholar
  14. 14.
    Feige, U.: On maximizing welfare when utility functions are subadditive. In: STOC, pp. 41–50 (2006)Google Scholar
  15. 15.
    Feige, U.: On maximizing welfare when utility functions are subadditive. SIAM J. Comput. 39(1), 122–142 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Kleinberg, R.D.: A multiple-choice secretary algorithm with applications to online auctions. In: SODA, pp. 630–631 (2005)Google Scholar
  17. 17.
    Korula, N., Pál, M.: Algorithms for Secretary Problems on Graphs and Hypergraphs. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) ICALP 2009, Part II. LNCS, vol. 5556, pp. 508–520. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  18. 18.
    Lavi, R., Swamy, C.: Truthful and near-optimal mechanism design via linear programming. In: Proc. of FOCS, pp. 595–604 (2005)Google Scholar
  19. 19.
    Lehmann, B., Lehmann, D.J., Nisan, N.: Combinatorial auctions with decreasing marginal utilities. In: ACM Conference on Electronic Commerce, pp. 18–28 (2001)Google Scholar
  20. 20.
    Nisan, N.: Introduction to mechanism design (for computer scientists). In: Nisan, N., Roughgarden, T., Tardos, E., Vazirani, V. (eds.) Algorithmic Game Theory (2007)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Piotr Krysta
    • 1
  • Berthold Vöcking
    • 2
  1. 1.Department of Computer ScienceUniversity of LiverpoolUK
  2. 2.Department of Computer ScienceRWTH Aachen UniversityGermany

Personalised recommendations