Skip to main content

On Strategy-Proof Allocation without Payments or Priors

  • Conference paper
Internet and Network Economics (WINE 2011)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 7090))

Included in the following conference series:

Abstract

In this paper we study the problem of allocating divisible items to agents without payments. We assume no prior knowledge about the agents. The utility of an agent is additive. The social welfare of a mechanism is defined as the overall utility of all agents. This model is first defined by Guo and Conitzer [7]. Here we are interested in strategy-proof mechanisms that have a good competitive ratio, that is, those that are able to achieve social welfare close to the maximal social welfare in all cases. First, for the setting of n agents and m items, we prove that there is no (1/m + ε)-competitive strategy-proof mechanism, for any ε > 0. And, no mechanism can achieve a competitive ratio better than \(4/\sqrt{n}\), when \(m \ge \sqrt{n}\). Next we study the setting of two agents and m items, which is also the focus of [7]. We prove that the competitive ratio of any swap-dictatorial mechanism is no greater than \(1/2 + 1/\sqrt{\left\lbrack\log{m}\right\rbrack }\). Then we give a characterization result: for the case of 2 items, if the mechanism is strategy-proof, symmetric and second order continuously differentiable, then it is always swap-dictatorial. In the end we consider a setting where an agent’s valuation of each item is bounded by C/m, where C is an arbitrary constant. We show a mechanism that is (1/2 + ε(C))-competitive, where ε(C) > 0.

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

Access this chapter

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
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Alon, N., Feldman, M., Procaccia, A.D., Tennenholtz, M.: Strategyproof approximation of the minimax on networks. Mathematics of Operations Research 35(3), 513–526 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  2. Budish, É.: The combinatorial assignment problem: Approximate competitive equilibrium from equal incomes (2009) Working Paper

    Google Scholar 

  3. Clarke, E.H.: Multipart pricing of public goods. Public choice 11(1), 17–33 (1971)

    Article  Google Scholar 

  4. Dekel, O., Fischer, F., Procaccia, A.D.: Incentive compatible regression learning. In: Proceedings of the Nineteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 884–893 (2008)

    Google Scholar 

  5. Partial derivative. In: Hazewinkel, M. (ed.) Encyclopaedia of Mathematics. Springer, Heidelberg (2001)

    Google Scholar 

  6. Groves, T.: Incentives in teams. Econometrica: Journal of the Econometric Society, 617–631 (1973)

    Google Scholar 

  7. Guo, M., Conitzer, V.: Strategy-proof allocation of multiple items between two agents without payments or priors. In: Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems: International Foundation for Autonomous Agents and Multiagent Systems, vol. 1, pp. 881–888 (2010)

    Google Scholar 

  8. Johari, R.: The price of anarchy and the design of scalable resource allocation mechanisms. In: Nisan, N., Roughgarden, T., Tardos, É., Vazirani, V. (eds.) Algorithmic Game Theory, ch. 21. Cambridge Univ. Pr. (2007)

    Google Scholar 

  9. Lu, P., Sun, X., Wang, Y., Zhu, Z.A.: Asymptotically optimal strategy-proof mechanisms for two-facility games. In: Proceedings of the 11th ACM Conference on Electronic Commerce, pp. 315–324. ACM (2010)

    Google Scholar 

  10. Meir, R., Procaccia, A.D., Rosenschein, J.S.: Strategyproof classification under constant hypotheses: A tale of two functions. In: Proceedings of the 23rd AAAI Conference on Artificial Intelligence (AAAI), pp. 126–131 (2008)

    Google Scholar 

  11. Meir, R., Procaccia, A.D., Rosenschein, J.S.: On the limits of dictatorial classification. In: Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems International Foundation for Autonomous Agents and Multiagent Systems, vol. 1, pp. 609–616 (2010)

    Google Scholar 

  12. Meir, R., Procaccia, A.D., Rosenschein, J.S.: Strategyproof classification under constant hypotheses: A tale of two functions. In: Fox, D., Gomes, C.P. (eds.) AAAI, pp. 126–131. AAAI Press (2008)

    Google Scholar 

  13. Pápai, S.: Strategyproof and nonbossy multiple assignments. Journal of Public Economic Theory 3(3), 257–271 (2001)

    Article  Google Scholar 

  14. Procaccia, A.D., Tennenholtz, M.: Approximate mechanism design without money. In: Proceedings of the tenth ACM Conference on Electronic Commerce, pp. 177–186. ACM (2009)

    Google Scholar 

  15. Schummer, J., Vohra, R.V.: Mechanism design without money. In: Nisan, N., Roughgarden, T., Tardos, É., Vazirani, V. (eds.) Algorithmic Game Theory, ch. 10, Cambridge Univ. Pr. (2007)

    Google Scholar 

  16. Vickrey, W.: Counterspeculation, auctions, and competitive sealed tenders. The Journal of finance 16(1), 8–37 (1961)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Han, L., Su, C., Tang, L., Zhang, H. (2011). On Strategy-Proof Allocation without Payments or Priors. In: Chen, N., Elkind, E., Koutsoupias, E. (eds) Internet and Network Economics. WINE 2011. Lecture Notes in Computer Science, vol 7090. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25510-6_16

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-25510-6_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25509-0

  • Online ISBN: 978-3-642-25510-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics