Social Welfare in One-Sided Matchings: Random Priority and Beyond

  • Aris Filos-Ratsikas
  • Søren Kristoffer Stiil Frederiksen
  • Jie Zhang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8768)


We study the problem of approximate social welfare maximization (without money) in one-sided matching problems when agents have unrestricted cardinal preferences over a finite set of items. Random priority is a very well-known truthful-in-expectation mechanism for the problem. We prove that the approximation ratio of random priority is Θ(n− 1/2) while no truthful-in-expectation mechanism can achieve an approximation ratio better than O(n− 1/2), where n is the number of agents and items. Furthermore, we prove that the approximation ratio of all ordinal (not necessarily truthful-in-expectation) mechanisms is upper bounded by O(n− 1/2), indicating that random priority is asymptotically the best truthful-in-expectation mechanism and the best ordinal mechanism for the problem.


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  1. 1.
    Abdulkadiroglu, A., Sönmez, T.: Matching Markets: Theory and Practice. In: Advances in Economics and Econometrics (Tenth World Congress), pp. 3–47 (2013)Google Scholar
  2. 2.
    Adamczyk, M., Piotr, S., Zhang, Q.: Efficiency of Truthful and Symmetric Mechanisms in One-sided Matching. In: Proceedings of the 7th Symposium of Algorithmic Game Theory (to appear, 2014)Google Scholar
  3. 3.
    Anshelevich, E., Das, S.: Matching, cardinal utility, and social welfare. ACM SIGECom Exchanges 9(1), 4 (2010)CrossRefGoogle Scholar
  4. 4.
    Barbera, S.: Strategy-proof Social Choice. In: Arrow, K.J., Sen, A.K., Suzumura, K. (eds.) Handbook of Social Choice and Welfare, vol. 2, ch. 25, North-Holland, Amsterdam (2010)Google Scholar
  5. 5.
    Bhalgat, A., Chakrabarty, D., Khanna, S.: Social Welfare in One-Sided Matching Markets without Money. In: Goldberg, L.A., Jansen, K., Ravi, R., Rolim, J.D.P. (eds.) RANDOM 2011 and APPROX 2011. LNCS, vol. 6845, pp. 87–98. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  6. 6.
    Bogomolnaia, A., Moulin, H.: A New Solution to the Random Assignment Problem. Journal of Economic Theory 100, 295–328 (2001)CrossRefMATHMathSciNetGoogle Scholar
  7. 7.
    Boutilier, C., Caragiannis, I., Haber, S., Lu, T., Procaccia, A.D., Sheffet, O.: Optimal social choice functions: a utilitarian view. In: Proceedings of the 13th ACM Conference on Electronic Commerce, pp. 197–214. ACM (2012)Google Scholar
  8. 8.
    Chakrabarty, D., Swamy, C.: Welfare maximization and truthfulness in mechanism design with ordinal preferences. In: Proceedings of the 5th Conference on Innovations in Theoretical Computer Science, pp. 105–120 (2014)Google Scholar
  9. 9.
    Dughmi, S., Ghosh, A.: Truthful assignment without money. In: ACM Conference on Electronic Commerce, pp. 325–334 (2010)Google Scholar
  10. 10.
    Feige, U., Tennenholtz, M.: Responsive lotteries. In: Algorithmic Game Theory, pp. 150–161. Springer (2010)Google Scholar
  11. 11.
    Filos-Ratsikas, A., Miltersen, P.B.: Truthful approximations to range voting. CoRR, abs/1307.1766 (2013)Google Scholar
  12. 12.
    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, vol. 1, pp. 881–888 (2010)Google Scholar
  13. 13.
    Hylland, A., Zeckhauser, R.: The Efficient Allocation of Individuals to Positions. The Journal of Political Economy 87(2), 293–314 (1979)CrossRefGoogle Scholar
  14. 14.
    Mennle, T., Seuken, S.: An axiomatic approach to characterizing and relaxing strategyproofness of one-sided matching mechanisms. In: Proceedings of the 15th ACM Conference on Economics and Computation, pp. 37–38 (2014)Google Scholar
  15. 15.
    Procaccia, A.D.: Can Approximation Circumvent Gibbard-Satterthwaite? In: Proceedings of the Twenty-Fourth AAAI Conference on Artificial Intelligence. AAAI Press (2010)Google Scholar
  16. 16.
    Procaccia, A.D., Tennenholtz, M.: Approximate mechanism design without money. In: Proceedings of the 10th ACM Conference on Electronic Commerce, pp. 177–186. ACM (2009)Google Scholar
  17. 17.
    Sönmez, T., Ünver, U.: Matching, allocation and exchange of discrete resources. Handbook of Social Economics 1A, 781–852 (2011)CrossRefGoogle Scholar
  18. 18.
    Svensson, L.-G.: Strategy-proof allocation of indivisble goods. Social Choice and Welfare 16(4), 557–567 (1999)CrossRefMATHMathSciNetGoogle Scholar
  19. 19.
    Zhou, L.: On a Conjecture by Gale about One-Sided Matching Problems. Journal of Economic Theory 52, 123–135 (1990)CrossRefMATHMathSciNetGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Aris Filos-Ratsikas
    • 1
  • Søren Kristoffer Stiil Frederiksen
    • 1
  • Jie Zhang
    • 2
  1. 1.Department of Computer ScienceAarhus UniversityDenmark
  2. 2.Department of Computer ScienceUniversity of OxfordUK

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