Skip to main content

Liquid Welfare Maximization in Auctions with Multiple Items

  • Conference paper
  • First Online:
Algorithmic Game Theory (SAGT 2017)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 10504))

Included in the following conference series:

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

References

  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. 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. Azar, Y., Feldman, M., Gravin, M., Roytman, A.: Liquid price of anarchy. arXiv preprint arXiv:1511.01132 (2015)

  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. 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)

    Article  MathSciNet  Google Scholar 

  6. Balcan, M.-F., Devanur, N., Hartline, J.D., Talwar, K.: Random sampling auctions for limited supply. Manuscript (2007, submitted)

    Google Scholar 

  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. 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. Caragiannis, I., Voudouris, A.A.: Welfare guarantees for proportional allocations. Theory Comput. Syst. 59(4), 581–599 (2016)

    Article  MathSciNet  Google Scholar 

  10. Chawla, S., Malec, D.L., Malekian, A.: Bayesian mechanism design for budget-constrained agents. In: EC, pp. 253–262 (2011)

    Google Scholar 

  11. Chen, N., Gravin, N., Lu, P.: On the approximability of budget feasible mechanisms. In: SODA, pp. 685–699 (2011)

    Google Scholar 

  12. Chen, N., Gravin, N., Lu, P.: Truthful generalized assignments via stable matching. Math. Oper. Res. 39(3), 722–736 (2013)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  14. Devanur, N.R., Ha, B.Q., Hartline, D.: Prior-free auctions for budgeted agents. In: EC, pp. 287–304 (2013)

    Google Scholar 

  15. Dobzinski, S., Lavi, R., Nisan, N.: Multi-unit auctions with budget limits. Games Econ. Behav. 74(2), 486–503 (2012)

    Article  MathSciNet  Google Scholar 

  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_33

    Chapter  Google Scholar 

  17. Dobzinski, S., Papadimitriou, C.H., Singer, Y.: Mechanisms for complement-free procurement. In: EC, pp. 273–282 (2011)

    Google Scholar 

  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. Eden, A., Feldman, M., Vardi, A.: Truthful secretaries with budgets. arXiv preprint arXiv:1504.03625 (2015)

  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. 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. Fiat, A., Leonardi, S., Saia, J., Sankowski, P.: Single valued combinatorial auctions with budgets. In: EC, pp. 223–232 (2011)

    Google Scholar 

  23. Goldberg, A.V., Hartline, J.D., Karlin, A.R., Saks, M., Wright, A.: Competitive auctions. Games Econ. Behav. 55(2), 242–269 (2006)

    Article  MathSciNet  Google Scholar 

  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_50

    Chapter  Google Scholar 

  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. Singer, Y.: Budget feasible mechanisms. In: FOCS, pp. 765–774 (2010)

    Google Scholar 

  27. Syrgkanis, V., Tardos, É.: Composable and efficient mechanisms. In: STOC, pp. 211–220 (2013)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Pinyan Lu .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Lu, P., Xiao, T. (2017). Liquid Welfare Maximization in Auctions with Multiple Items. In: Bilò, V., Flammini, M. (eds) Algorithmic Game Theory. SAGT 2017. Lecture Notes in Computer Science(), vol 10504. Springer, Cham. https://doi.org/10.1007/978-3-319-66700-3_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-66700-3_4

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-66699-0

  • Online ISBN: 978-3-319-66700-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics