Auctions with Heterogeneous Items and Budget Limits

  • Paul Dütting
  • Monika Henzinger
  • Martin Starnberger
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7695)

Abstract

We study individual rational, Pareto optimal, and incentive compatible mechanisms for auctions with heterogeneous items and budget limits. For multi-dimensional valuations we show that there can be no deterministic mechanism with these properties for divisible items. We use this to show that there can also be no randomized mechanism that achieves this for either divisible or indivisible items. For single-dimensional valuations we show that there can be no deterministic mechanism with these properties for indivisible items, but that there is a randomized mechanism that achieves this for either divisible or indivisible items. The impossibility results hold for public budgets, while the mechanism allows private budgets, which is in both cases the harder variant to show. While all positive results are polynomial-time algorithms, all negative results hold independent of complexity considerations.

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References

  1. 1.
    Archer, A., Tardos, É.: Truthful mechanisms for one-parameter agents. In: Proc. of 42nd FOCS, pp. 482–491 (2001)Google Scholar
  2. 2.
    Ausubel, L.: An efficient ascending-bid auction for multiple objects. The American Economic Review 94(5), 1452–1475 (2004)CrossRefGoogle Scholar
  3. 3.
    Ausubel, L.: An efficient dynamic auction for heterogeneous commodities. The American Economic Review 96(3), 602–629 (2006)CrossRefGoogle Scholar
  4. 4.
    Bhattacharya, S., Conitzer, V., Munagala, K., Xia, L.: Incentive compatible budget elicitation in multi-unit auctions. In: Proc. of 21st SODA, pp. 554–572 (2010)Google Scholar
  5. 5.
    Bikhchandani, S., Lavi, R., Mu, A., Nisan, N., Sen, A.: Weak monotonicity characterizes deterministic dominant-strategy implementation. Econometrica 74(4), 1109–1132 (2006)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Colini-Baldeschi, R., Henzinger, M., Leonardi, S., Starnberger, M.: On multiple keyword sponsored search auctions with budgets. In: Czumaj, A., Mehlhorn, K., Pitts, A., Wattenhofer, R. (eds.) Automata, Languages, and Programming, Part II. LNCS, vol. 7392, pp. 1–12. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  7. 7.
    Dobzinski, S., Lavi, R., Nisan, N.: Multi-unit auctions with budget limits. Games and Economic Behavior 74(2), 486–503 (2012)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Fiat, A., Leonardi, S., Saia, J., Sankowski, P.: Single-valued combinatorial auctions with budgets. In: Proc. of 12th EC, pp. 223–232 (2011)Google Scholar
  9. 9.
    Goel, G., Mirrokni, V., Paes Leme, R.: Polyhedral clinching auctions and the adwords polytope. In: Proc. of 44th STOC, pp. 107–122 (2012)Google Scholar
  10. 10.
    Lavi, R., May, M.: A note on the incompatibility of strategy-proofness and pareto-optimality in quasi-linear settings with public budgets. In: Chen, N., Elkind, E., Koutsoupias, E. (eds.) Internet and Network Economics. LNCS, vol. 7090, p. 417. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  11. 11.
    Myerson, R.: Optimal auction design. Mathematics of Operations Research 6(1), 58–73 (1981)MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Paul Dütting
    • 1
  • Monika Henzinger
    • 2
  • Martin Starnberger
    • 2
  1. 1.École Polytechnique Fédérale de LausanneSwitzerland
  2. 2.Fakultät für InformatikUniversität WienAustria

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