On Strategy-Proof Allocation without Payments or Priors

  • Li Han
  • Chunzhi Su
  • Linpeng Tang
  • Hongyang Zhang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7090)

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.

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References

  1. 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)CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    Budish, É.: The combinatorial assignment problem: Approximate competitive equilibrium from equal incomes (2009) Working PaperGoogle Scholar
  3. 3.
    Clarke, E.H.: Multipart pricing of public goods. Public choice 11(1), 17–33 (1971)CrossRefGoogle Scholar
  4. 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. 5.
    Partial derivative. In: Hazewinkel, M. (ed.) Encyclopaedia of Mathematics. Springer, Heidelberg (2001)Google Scholar
  6. 6.
    Groves, T.: Incentives in teams. Econometrica: Journal of the Econometric Society, 617–631 (1973)Google Scholar
  7. 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. 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. 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. 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. 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. 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. 13.
    Pápai, S.: Strategyproof and nonbossy multiple assignments. Journal of Public Economic Theory 3(3), 257–271 (2001)CrossRefGoogle Scholar
  14. 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. 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. 16.
    Vickrey, W.: Counterspeculation, auctions, and competitive sealed tenders. The Journal of finance 16(1), 8–37 (1961)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Li Han
    • 1
  • Chunzhi Su
    • 1
  • Linpeng Tang
    • 1
  • Hongyang Zhang
    • 1
  1. 1.Shanghai Jiao Tong UniversityChina

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