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Efficiency-Revenue Trade-Offs in Auctions

  • Ilias Diakonikolas
  • Christos Papadimitriou
  • George Pierrakos
  • Yaron Singer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7392)

Abstract

When agents with independent priors bid for a single item, Myerson’s optimal auction maximizes expected revenue, whereas Vickrey’s second-price auction optimizes social welfare. We address the natural question of trade-offs between the two criteria, that is, auctions that optimize, say, revenue under the constraint that the welfare is above a given level. If one allows for randomized mechanisms, it is easy to see that there are polynomial-time mechanisms that achieve any point in the trade-off (the Pareto curve) between revenue and welfare. We investigate whether one can achieve the same guarantees using deterministic mechanisms. We provide a negative answer to this question by showing that this is a (weakly) NP-hard problem. On the positive side, we provide polynomial-time deterministic mechanisms that approximate with arbitrary precision any point of the trade-off between these two fundamental objectives for the case of two bidders, even when the valuations are correlated arbitrarily. The major problem left open by our work is whether there is such an algorithm for three or more bidders with independent valuation distributions.

Keywords

Multiobjective Optimization Multiobjective Optimization Problem Combinatorial Auction Pareto Point English Auction 
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.

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References

  1. 1.
    Abhishek, V., Hajek, B.E.: Efficiency loss in revenue optimal auctions. In: CDC (2010)Google Scholar
  2. 2.
    Aggarwal, G., Goel, G., Mehta, A.: Efficiency of (revenue-)optimal mechanisms. In: EC (2009)Google Scholar
  3. 3.
    Armstrong, M.: Optimal multi-object auctions. Review of Economic Studies 67(3), 455–481Google Scholar
  4. 4.
    Bulow, J., Klemperer, P.: Auctions versus negotiations. American Economic Review 86(1), 180–194 (1996)Google Scholar
  5. 5.
    Chekuri, C., Vondrak, J., Zenklusen, R.: Multi-budgeted matchings and matroid intersection via dependent rounding. In: SODA (2011)Google Scholar
  6. 6.
    Daskalakis, C., Diakonikolas, I., Yannakakis, M.: How good is the chord algorithm? In: SODA (2010)Google Scholar
  7. 7.
    Daskalakis, C., Pierrakos, G.: Simple, Optimal and Efficient Auctions. In: Chen, N., Elkind, E., Koutsoupias, E. (eds.) WINE 2011. LNCS, vol. 7090, pp. 109–121. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  8. 8.
    Diakonikolas, I.: Approximation of Multiobjective Optimization Problems. PhD thesis, Columbia University (2010)Google Scholar
  9. 9.
    Diakonikolas, I., Yannakakis, M.: Succinct Approximate Convex Pareto Curves. In: SODA (2008)Google Scholar
  10. 10.
    Diakonikolas, I., Yannakakis, M.: Small approximate pareto sets for biobjective shortest paths and other problems. SIAM J. Comput. 39, 1340–1371 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Dobzinski, S.: An impossibility result for truthful combinatorial auctions with submodular valuations. In: STOC (2011)Google Scholar
  12. 12.
    Dobzinski, S., Fu, H., Kleinberg, R.D.: Optimal auctions with correlated bidders are easy. In: STOC (2011)Google Scholar
  13. 13.
    Dughmi, S., Roughgarden, T., Yan, Q.: From convex optimization to randomized mechanisms: toward optimal combinatorial auctions. In: STOC (2011)Google Scholar
  14. 14.
    Ehrgott, M.: Multicriteria optimization. Springer (2005)Google Scholar
  15. 15.
    Galperin, H., Wigderson, A.: Succinct representations of graphs. Information and Control 56(3), 183–198 (1983)MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Grandoni, F., Krysta, P., Leonardi, S., Ventre, C.: Utilitarian mechanism design for multi-objective optimization. In: SODA (2010)Google Scholar
  17. 17.
    Grandoni, F., Ravi, R., Singh, M.: Iterative Rounding for Multi-Objective Optimization Problems. In: Fiat, A., Sanders, P. (eds.) ESA 2009. LNCS, vol. 5757, pp. 95–106. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  18. 18.
    Climacao, E.J.: Multicriteria Analysis. Springer (1997)Google Scholar
  19. 19.
    Likhodedov, A., Sandholm, T.: Mechanism for optimally trading off revenue and efficiency in multi-unit auctions. In: EC (2003)Google Scholar
  20. 20.
    Miettinen, K.M.: Nonlinear Multiobjective Optimization. Kluwer (1999)Google Scholar
  21. 21.
    Mulmuley, K., Vazirani, U.V., Vazirani, V.V.: Matching is as easy as matrix inversion. In: STOC (1987)Google Scholar
  22. 22.
    Myerson, R.B.: Optimal auction design. Mathematics of Operations Research 6, 58–73Google Scholar
  23. 23.
    Myerson, R.B., Satterthwaite, M.A.: Efficient mechanisms for bilateral trading. Journal of Economic Theory 29(2), 265–281 (1983)MathSciNetzbMATHCrossRefGoogle Scholar
  24. 24.
    Neeman, Z.: The effectiveness of english auctions. Games and Economic Behavior 43(2), 214–238 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  25. 25.
    Nisan, N., Roughgarden, T., Tardos, É., Vazirani, V.V.: Algorithmic Game Theory (2007)Google Scholar
  26. 26.
    Papadimitriou, C.H., Pierrakos, G.: On optimal single-item auctions. In: STOC (2011)Google Scholar
  27. 27.
    Papadimitriou, C.H., Yannakakis, M.: A note on succinct representations of graphs. Information and Control 71(3), 181–185 (1986)MathSciNetzbMATHCrossRefGoogle Scholar
  28. 28.
    Papadimitriou, C.H., Yannakakis, M.: On the approximability of trade-offs and optimal access of web sources. In: FOCS (2000)Google Scholar
  29. 29.
    Roughgarden, T., Sundararajan, M.: Is efficiency expensive? In: 3rd Workshop on Sponsored Search (2007)Google Scholar
  30. 30.
    Vassilvitskii, S., Yannakakis, M.: Efficiently computing succinct trade-off curves. Theoretical Computer Science 348, 334–356 (2005)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Ilias Diakonikolas
    • 1
  • Christos Papadimitriou
    • 1
  • George Pierrakos
    • 1
  • Yaron Singer
    • 2
  1. 1.EECSUC BerkeleyUSA
  2. 2.Google, Inc.USA

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