Skip to main content
Springer Nature Link
Log in

Envy-Free Revenue Approximation for Asymmetric Buyers with Budgets

  • Conference paper
  • First Online:
Algorithmic Game Theory (SAGT 2016)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 9928))

Included in the following conference series:

Abstract

We study the computation of revenue-maximizing envy-free outcomes in a monopoly market with budgeted buyers. Departing from previous works, we focus on buyers with asymmetric combinatorial valuation functions over subsets of items. We first establish a hardness result showing that, even with two identical additive buyers, the problem is inapproximable. In an attempt to identify tractable families of the problem’s instances, we introduce the notion of budget compatible buyers, placing a restriction on the budget of each buyer in terms of his valuation function. Under this assumption, we establish approximation upper bounds for buyers with submodular valuations over preference subsets as well as for buyers with identical subadditive valuation functions. Finally, we also analyze an algorithm for arbitrary additive valuation functions, which yields a constant factor approximation for a constant number of buyers. We conclude with several intriguing open questions regarding budgeted buyers with asymmetric valuation functions.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Balcan, M.F., Blum, A.: Approximation algorithms and online mechanisms for item pricing. Theory Comput. 3(1), 179–195 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  2. Briest, P.: Uniform budgets and the envy-free pricing problem. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part I. LNCS, vol. 5125, pp. 808–819. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  3. Briest, P., Krysta, P.: Single-minded unlimited supply pricing on sparse instances. In: Proceedings of the 17th ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 1093–1102 (2006)

    Google Scholar 

  4. Chen, N., Deng, X.: Envy-free pricing in multi-item markets. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds.) ICALP 2010. LNCS, vol. 6199, pp. 418–429. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  5. Cheung, M., Swamy, C.: Approximation algorithms for single-minded envy-free profit-maximization problems with limited supply. In: Proceedings of the 49th IEEE Symposium on Foundations of Computer Science (FOCS), pp. 35–44 (2008)

    Google Scholar 

  6. Colini-Baldeschi, R., Leonardi, S., Sankowski, P., Zhang, Q.: Revenue maximizing envy-free fixed-price auctions with budgets. In: Liu, T.-Y., Qi, Q., Ye, Y. (eds.) WINE 2014. LNCS, vol. 8877, pp. 233–246. Springer, Heidelberg (2014)

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  8. Dobzinski, S., Nisan, N., Schapira, M.: Approximation algorithms for combinatorial auctions with complement-free bidders. Math. Oper. Res. 35(1), 1–13 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  9. Feldman, M., Fiat, A., Leonardi, S., Sankowski, P.: Revenue maximizing envy-free multi-unit auctions with budgets. In: Proceedings of the 13th ACM Conference on Electronic Commerce (EC), pp. 532–549 (2012)

    Google Scholar 

  10. Fiat, A., Leonardi, S., Saia, J., Sankowski, P.: Single valued combinatorial auctions with budgets. In: Proceedings of the 12th ACM Conference on Electronic Commerce (EC), pp. 223–232 (2011)

    Google Scholar 

  11. Fiat, A., Wingarten, A.: Envy, multi envy, and revenue maximization. In: Leonardi, S. (ed.) WINE 2009. LNCS, vol. 5929, pp. 498–504. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  12. Foley, D.: Resource allocation and the public sector. Yale Econ. Essays 7, 45–98 (1967)

    Google Scholar 

  13. Goel, G., Mirrokni, V.S., Paes Leme, R.: Polyhedral clinching auctions and the adwords polytope. J. ACM 62(3), 18 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  14. Gul, F., Stacchetti, E.: Walrasian equilibrium with gross substitutes. J. Econ. Theory 87(1), 95–124 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  15. Guruswami, V., Hartline, J.D., Karlin, A.R., Kempe, D., Kenyon, C., McSherry, F.: On profit-maximizing envy-free pricing. In: Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 1164–1173 (2005)

    Google Scholar 

  16. Hartline, J., Yan, Q.: Envy, truth, and profit. In: Proceedings of the 12th ACM Conference on Electronic Commerce (EC), pp. 243–252 (2011)

    Google Scholar 

  17. Lehmann, B., Lehmann, D.J., Nisan, N.: Combinatorial auctions with decreasing marginal utilities. Games Econ. Behav. 55(2), 270–296 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  18. Lehmann, D.J., O’Callaghan, L., Shoham, Y.: Truth revelation in approximately efficient combinatorial auctions. J. ACM 49(5), 577–602 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  19. Monaco, G., Sankowski, P., Zhang, Q.: Revenue maximization envy-free pricing for homogeneous resources. In: Proceedings of the 24th International Joint Conference on Artificial Intelligence (IJCAI), pp. 90–96 (2015)

    Google Scholar 

  20. Varian, H.: Equity, envy and efficiency. J. Econ. Theory 9, 63–91 (1974)

    Article  MathSciNet  Google Scholar 

  21. Woeginger, G.H., Yu, Z.: On the equal-subset-sum problem. Inf. Process. Lett. 42(6), 299–302 (1992)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Informatics, Athens University of Economics and Business, Athens, Greece

    Evangelos Markakis

  2. Department of Digital Systems, University of Piraeus, Piraeus, Greece

    Orestis Telelis

Authors
  1. Evangelos Markakis
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Orestis Telelis
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Orestis Telelis .

Editor information

Editors and Affiliations

  1. University of Liverpool, Liverpool, United Kingdom

    Martin Gairing

  2. University of Liverpool, Liverpool, United Kingdom

    Rahul Savani

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Markakis, E., Telelis, O. (2016). Envy-Free Revenue Approximation for Asymmetric Buyers with Budgets. In: Gairing, M., Savani, R. (eds) Algorithmic Game Theory. SAGT 2016. Lecture Notes in Computer Science(), vol 9928. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53354-3_20

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-53354-3_20

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-53353-6

  • Online ISBN: 978-3-662-53354-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation