Efficiency Guarantees in Auctions with Budgets

  • Shahar Dobzinski
  • Renato Paes Leme
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8572)

Abstract

In settings where players have limited access to liquidity, represented in the form of budget constraints, efficiency maximization has proven to be a challenging goal. In particular, the social welfare cannot be approximated by a better factor than the number of players. Therefore, the literature has mainly resorted to Pareto-efficiency as a way to achieve efficiency in such settings. While successful in some important scenarios, in many settings it is known that either exactly one truthful auction that always outputs a Pareto-efficient solution, or that no truthful mechanism always outputs a Pareto-efficient outcome. Moreover, since Pareto-efficiency is a binary property (is either satisfied or not), it cannot be circumvented as usual by considering approximations. To overcome impossibilities in important setting such as multi-unit auctions with decreasing marginal values and private budgets, we propose a new notion of efficiency, which we call liquid welfare. This is the maximum amount of revenue an omniscient seller would be able to extract from a certain instance. For the aforementioned setting, we give a deterministic O(logn)-approximation for the liquid welfare in this setting.

We also study the liquid welfare in the traditional setting of additive values and public budgets. We present two different auctions that achieve a 2-approximation to the new objective. Moreover, we show that no truthful algorithm can guarantee an approximation factor better than 4/3 with respect to the liquid welfare.

Keywords

Europe Nash Geted Gonen 

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References

  1. 1.
    Aggarwal, G., Muthukrishnan, S., Pál, D., Pál, M.: General auction mechanism for search advertising. In: WWW, pp. 241–250 (2009)Google Scholar
  2. 2.
    Ausubel, L.M.: An efficient ascending-bid auction for multiple objects. American Economic Review 94 (1997)Google Scholar
  3. 3.
    Bartal, Y., Gonen, R., Nisan, N.: Incentive compatible multi unit combinatorial auctions. In: TARK, pp. 72–87 (2003)Google Scholar
  4. 4.
    Benoit, J.-P., Krishna, V.: Multiple-object auctions with budget constrained bidders. Review of Economic Studies 68(1), 155–179 (2001)CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Bhattacharya, S., Conitzer, V., Munagala, K., Xia, L.: Incentive compatible budget elicitation in multi-unit auctions. In: SODA, pp. 554–572 (2010)Google Scholar
  6. 6.
    Borgs, C., Chayes, J.T., Immorlica, N., Mahdian, M., Saberi, A.: Multi-unit auctions with budget-constrained bidders. In: ACM EC (2005)Google Scholar
  7. 7.
    Bulow, J., Levin, J., Milgrom, P.: Winning play in spectrum auctions. Working Paper 14765, National Bureau of Economic Research (March 2009)Google Scholar
  8. 8.
    Chawla, S., Malec, D.L., Malekian, A.: Bayesian mechanism design for budget-constrained agents. In: ACM EC, pp. 253–262 (2011)Google Scholar
  9. 9.
    Che, Y.-K., Gale, I.: Standard auctions with financially constrained bidders. Review of Economic Studies 65(1), 1–21 (1998)CrossRefMATHMathSciNetGoogle Scholar
  10. 10.
    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.) ICALP 2012, Part II. LNCS, vol. 7392, pp. 1–12. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  11. 11.
    Devanur, N.R., Ha, B.Q., Hartline, J.D.: Prior-free auctions for budgeted agents. In: EC (2013)Google Scholar
  12. 12.
    Dobzinski, S., Lavi, R., Nisan, N.: Multi-unit auctions with budget limits. Games and Economic Behavior 74(2), 486–503 (2012)CrossRefMATHMathSciNetGoogle Scholar
  13. 13.
    Dütting, P., Henzinger, M., Starnberger, M.: Auctions with heterogeneous items and budget limits. In: Goldberg, P.W. (ed.) WINE 2012. LNCS, vol. 7695, pp. 44–57. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  14. 14.
    Fiat, A., Leonardi, S., Saia, J., Sankowski, P.: Single valued combinatorial auctions with budgets. In: ACM EC, pp. 223–232 (2011)Google Scholar
  15. 15.
    Goel, G., Mirrokni, V.S., Paes Leme, R.: Polyhedral clinching auctions and the adwords polytope. In: STOC, pp. 107–122 (2012)Google Scholar
  16. 16.
    Goel, G., Mirrokni, V.S., Paes Leme, R.: Clinching auctions with online supply. In: SODA (2013)Google Scholar
  17. 17.
    Laffont, J.-J., Robert, J.: Optimal auction with financially constrained buyers. Economics Letters 52(2), 181–186 (1996)CrossRefMATHGoogle Scholar
  18. 18.
    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, pp. 417–417. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  19. 19.
    Malakhov, A., Vohra, R.V.: Optimal auctions for asymmetrically budget constrained bidders. Working paper (December 2005)Google Scholar
  20. 20.
    Maskin, E.S.: Auctions, development, and privatization: Efficient auctions with liquidity-constrained buyers. European Economic Review 44(4-6), 667–681 (2000)CrossRefGoogle Scholar
  21. 21.
    McAfee, R.P., McMillan, J.: Auctions and bidding. Journal of Economic Literature 25(2), 699–738 (1987)Google Scholar
  22. 22.
    Myerson, R.: Optimal auction design. Mathematics of Operations Research 6(1), 58–73 (1981)CrossRefMATHMathSciNetGoogle Scholar
  23. 23.
    Pai, M., Vohra, R.: Optimal auctions with financially constrained bidders. Working Paper (2008)Google Scholar
  24. 24.
    Syrgkanis, V., Tardos, É.: Composable and efficient mechanisms. In: STOC (2013)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Shahar Dobzinski
    • 1
  • Renato Paes Leme
    • 2
  1. 1.Weizmann InstituteIsrael
  2. 2.Google Research NYCUSA

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