Liquid Welfare Maximization in Auctions with Multiple Items

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10504)


Liquid welfare is an alternative efficiency measure for auctions with budget constrained agents. Previous studies focused on auctions of a single (type of) good. In this paper, we initiate the study of general multi-item auctions, obtaining a truthful budget feasible auction with constant approximation ratio of liquid welfare under the assumption of large market.

Our main technique is random sampling. Previously, random sampling was usually used in the setting of single-parameter auctions. When it comes to multi-dimensional settings, this technique meets a number of obstacles and difficulties. In this work, we develop a series of analysis tools and frameworks to overcome these. These tools and frameworks are quite general and they may find applications in other scenarios.


Auction Feasible Budget Alternative Efficiency Measures Multi-item Setting Random Sampling Mechanism 
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.


  1. 1.
    Abrams, Z.: Revenue maximization when bidders have budgets. In: Proceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithm, pp. 1074–1082. Society for Industrial and Applied Mathematics (2006)Google Scholar
  2. 2.
    Anari, N., Goel, G., Nikzad, A.: Mechanism design for crowdsourcing: an optimal 1-1/e competitive budget-feasible mechanism for large markets. In: 2014 IEEE 55th Annual Symposium on Foundations of Computer Science (FOCS), pp. 266–275. IEEE (2014)Google Scholar
  3. 3.
    Azar, Y., Feldman, M., Gravin, M., Roytman, A.: Liquid price of anarchy. arXiv preprint arXiv:1511.01132 (2015)
  4. 4.
    Balcan, M.-F., Blum, A., Hartline, J.D., Mansour, Y.: Mechanism design via machine learning. In 46th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2005, pp. 605–614. IEEE (2005)Google Scholar
  5. 5.
    Balcan, M.-F., Blum, A., Hartline, J.D., Mansour, Y.: Reducing mechanism design to algorithm design via machine learning. J. Comput. Syst. Sci. 74(8), 1245–1270 (2008)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Balcan, M.-F., Devanur, N., Hartline, J.D., Talwar, K.: Random sampling auctions for limited supply. Manuscript (2007, submitted)Google Scholar
  7. 7.
    Bei, X., Chen, N., Gravin, N., Lu, P.: Budget feasible mechanism design: from prior-free to Bayesian. In: STOC, pp. 449–458 (2012)Google Scholar
  8. 8.
    Borgs, C., Chayes, J.T., Immorlica, N., Mahdian, M., Saberi, A.: Multi-unit auctions with budget-constrained bidders. In: EC, pp. 44–51 (2005)Google Scholar
  9. 9.
    Caragiannis, I., Voudouris, A.A.: Welfare guarantees for proportional allocations. Theory Comput. Syst. 59(4), 581–599 (2016)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Chawla, S., Malec, D.L., Malekian, A.: Bayesian mechanism design for budget-constrained agents. In: EC, pp. 253–262 (2011)Google Scholar
  11. 11.
    Chen, N., Gravin, N., Lu, P.: On the approximability of budget feasible mechanisms. In: SODA, pp. 685–699 (2011)Google Scholar
  12. 12.
    Chen, N., Gravin, N., Lu, P.: Truthful generalized assignments via stable matching. Math. Oper. Res. 39(3), 722–736 (2013)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Christodoulou, G., Sgouritsa, A., Tang, B.: On the efficiency of the proportional allocation mechanism for divisible resources. Theory Comput. Syst. 59(4), 600–618 (2016)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Devanur, N.R., Ha, B.Q., Hartline, D.: Prior-free auctions for budgeted agents. In: EC, pp. 287–304 (2013)Google Scholar
  15. 15.
    Dobzinski, S., Lavi, R., Nisan, N.: Multi-unit auctions with budget limits. Games Econ. Behav. 74(2), 486–503 (2012)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Dobzinski, S., Leme, R.P.: Efficiency guarantees in auctions with budgets. In: Esparza, J., Fraigniaud, P., Husfeldt, T., Koutsoupias, E. (eds.) ICALP 2014. LNCS, vol. 8572, pp. 392–404. Springer, Heidelberg (2014). doi: 10.1007/978-3-662-43948-7_33CrossRefGoogle Scholar
  17. 17.
    Dobzinski, S., Papadimitriou, C.H., Singer, Y.: Mechanisms for complement-free procurement. In: EC, pp. 273–282 (2011)Google Scholar
  18. 18.
    Dughmi, S., Eden, A., Feldman, M., Fiat, A., Leonardi, S.: Lottery pricing equilibria. In: Proceedings of the 2016 ACM Conference on Economics and Computation, pp. 401–418. ACM (2016)Google Scholar
  19. 19.
    Eden, A., Feldman, M., Vardi, A.: Truthful secretaries with budgets. arXiv preprint arXiv:1504.03625 (2015)
  20. 20.
    Feldman, M., Fiat, A., Leonardi, S., Sankowski, P.: Revenue maximizing envy-free multi-unit auctions with budgets. In: EC, pp. 532–549 (2012)Google Scholar
  21. 21.
    Feldman, M., Immorlica, M., Lucier, B., Roughgarden, T., Syrgkanis, V.: The price of anarchy in large games. In: Proceedings of the 48th Annual ACM SIGACT Symposium on Theory of Computing, pp. 963–976. ACM (2016)Google Scholar
  22. 22.
    Fiat, A., Leonardi, S., Saia, J., Sankowski, P.: Single valued combinatorial auctions with budgets. In: EC, pp. 223–232 (2011)Google Scholar
  23. 23.
    Goldberg, A.V., Hartline, J.D., Karlin, A.R., Saks, M., Wright, A.: Competitive auctions. Games Econ. Behav. 55(2), 242–269 (2006)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Gravin, N., Lu, P.: Competitive auctions for markets with positive externalities. In: Fomin, F.V., Freivalds, R., Kwiatkowska, M., Peleg, D. (eds.) ICALP 2013. LNCS, vol. 7966, pp. 569–580. Springer, Heidelberg (2013). doi: 10.1007/978-3-642-39212-2_50CrossRefGoogle Scholar
  25. 25.
    Lu, P., Xiao, T.: Improved efficiency guarantees in auctions with budgets. In: Proceedings of the Sixteenth ACM Conference on Economics and Computation, pp. 397–413. ACM (2015)Google Scholar
  26. 26.
    Singer, Y.: Budget feasible mechanisms. In: FOCS, pp. 765–774 (2010)Google Scholar
  27. 27.
    Syrgkanis, V., Tardos, É.: Composable and efficient mechanisms. In: STOC, pp. 211–220 (2013)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.ITCSShanghai University of Finance and EconomicsShanghaiChina
  2. 2.Department of Computer ScienceShanghai Jiaotong UniversityShanghaiChina

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