Limits of Efficiency in Sequential Auctions

  • Michal Feldman
  • Brendan Lucier
  • Vasilis Syrgkanis
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8289)


We study the efficiency of sequential first-price item auctions at (subgame perfect) equilibrium. This auction format has recently attracted much attention, with previous work establishing positive results for unit-demand valuations and negative results for submodular valuations. This leaves a large gap in our understanding between these valuation classes. In this work we resolve this gap on the negative side. In particular, we show that even in the very restricted case in which each bidder has either an additive valuation or a unit-demand valuation, there exist instances in which the inefficiency at equilibrium grows linearly with the minimum of the number of items and the number of bidders. Moreover, these inefficient equilibria persist even under iterated elimination of weakly dominated strategies. Our main result implies linear inefficiency for many natural settings, including auctions with gross substitute valuations, capacitated valuations, budget-additive valuations, and additive valuations with hard budget constraints on the payments. For capacitated valuations, our results imply a lower bound that equals the maximum capacity of any bidder, which is tight following the upper-bound technique established by Paes Leme et al. [20].


Subgame Perfect Equilibrium Combinatorial Auction Price Setter Walrasian Equilibrium Optimal Welfare 
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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  1. 1.
    Ashenfelter, O.: How auctions work for wine and art. The Journal of Economic Perspectives 3(3), 23–36 (1989)CrossRefGoogle Scholar
  2. 2.
    Bae, J., Beigman, E., Berry, R., Honig, M.L., Vohra, R.: Sequential Bandwidth and Power Auctions for Distributed Spectrum Sharing. IEEE Journal on Selected Areas in Communications 26(7), 1193–1203 (2008)CrossRefGoogle Scholar
  3. 3.
    Bae, J., Beigman, E., Berry, R., Honig, M.L., Vohra, R.: On the efficiency of sequential auctions for spectrum sharing. In: 2009 International Conference on Game Theory for Networks, pp. 199–205 (May 2009)Google Scholar
  4. 4.
    Bhawalkar, K., Roughgarden, T.: Welfare guarantees for combinatorial auctions with item bidding. In: SODA (2011)Google Scholar
  5. 5.
    Bikhchandani, S.: Auctions of heterogeneous objects. Games and Economic Behavior 26(2), 193–220 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Blumrosen, L., Nisan, N.: Combinatorial Auctions. Camb. Univ. Press (2007)Google Scholar
  7. 7.
    Boutilier, C., Goldszmidt, M., Sabata, B.: Sequential Auctions for the Allocation of Resources with Complementarities. In: IJCAI 1999: Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence, pp. 527–534 (1999)Google Scholar
  8. 8.
    Christodoulou, G., Kovács, A., Schapira, M.: Bayesian combinatorial auctions. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part I. LNCS, vol. 5125, pp. 820–832. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  9. 9.
    Cohen, E., Feldman, M., Fiat, A., Kaplan, H., Olonetsky, S.: Truth, envy, and truthful market clearing bundle pricing. In: Chen, N., Elkind, E., Koutsoupias, E. (eds.) WINE 2011. LNCS, vol. 7090, pp. 97–108. Springer, Heidelberg (2011)Google Scholar
  10. 10.
    Rodriguez Gustavo, E.: Sequential auctions with multi-unit demands. The B.E. Journal of Theoretical Economics 9(1), 1–35 (2009)Google Scholar
  11. 11.
    Feldman, M., Fu, H., Gravin, N., Lucier, B.: Simultaneous auctions are (almost) efficient. In: STOC (2013)Google Scholar
  12. 12.
    Gale, I., Stegeman, M.: Sequential Auctions of Endogenously Valued Objects. Games and Economic Behavior 36(1), 74–103 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Gul, F., Stacchetti, E.: Walrasian equilibrium with gross substitutes. Journal of Economic Theory 87(1), 95–124 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Hassidim, A., Kaplan, H., Mansour, Y., Nisan, N.: Non-price equilibria in markets of discrete goods. In: EC 2011 (2011)Google Scholar
  15. 15.
    Huang, Z., Devanur, N.R., Malec, D.L.: Sequential auctions of identical items with budget-constrained bidders. CoRR, abs/1209.1698 (2012)Google Scholar
  16. 16.
    Lehmann, B., Lehmann, D., Nisan, N.: Combinatorial auctions with decreasing marginal utilities. In: EC 2001 (2001)Google Scholar
  17. 17.
    Preston McAfee, R.: Mechanism design by competing sellers. Econometrica 61(6), 1281–1312 (1993)CrossRefzbMATHGoogle Scholar
  18. 18.
    Milgrom, P.R., Weber, R.J.: A theory of auctions and competitive bidding II (1982)Google Scholar
  19. 19.
    Leme, R.P., Syrgkanis, V., Tardos, É.: The dining bidder problem: a la russe et a la francaise. SIGecom Exchanges 11(2) (2012)Google Scholar
  20. 20.
    Leme, R.P., Syrgkanis, V., Tardos, É.: Sequential auctions and externalities. In: SODA (2012)Google Scholar
  21. 21.
    Syrgkanis, V., Tardos, E.: Bayesian sequential auctions. In: EC (2012)Google Scholar
  22. 22.
    Syrgkanis, V., Tardos, E.: Composable and efficient mechanisms. In: STOC (2013)Google Scholar
  23. 23.
    Weber, R.J.: Multiple-object auctions. Discussion Paper 496, Kellog Graduate School of Management, Northwestern University (1981)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Michal Feldman
    • 1
  • Brendan Lucier
    • 2
  • Vasilis Syrgkanis
    • 3
  1. 1.Hebrew UnivsersityIsrael
  2. 2.Microsoft ResearchUSA
  3. 3.Dept of Computer ScienceCornell UniversityUSA

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