Skip to main content
SpringerLink
Log in

Social Welfare in One-Sided Matching Mechanisms

  • Conference paper
  • First Online:
Autonomous Agents and Multiagent Systems (AAMAS 2016)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10002))

Included in the following conference series:

Abstract

We study the Price of Anarchy of mechanisms for the well-known problem of one-sided matching, or house allocation, with respect to the social welfare objective. We consider both ordinal mechanisms, where agents submit preference lists over the items, and cardinal mechanisms, where agents may submit numerical values for the items being allocated. We present a general lower bound of \(\varOmega (\sqrt{n})\) on the Price of Anarchy, which applies to all mechanisms. We show that two well-known mechanisms, Probabilistic Serial, and Random Priority, achieve a matching upper bound. We extend our lower bound to the Price of Stability of a large class of mechanisms that satisfy a common proportionality property, and show stronger bounds on the Price of Anarchy of all deterministic mechanisms.

George Christodoulou, Paul W. Goldberg and Jinshan Zhang were supported by the EPSRC grant EP/K01000X/1. Paul W. Goldberg was supported by COST Action IC1205. Aris Filos-Ratsikas and Jie Zhang were supported by the ERC Advanced Grant 321171 (ALGAME). Aris Filos-Ratsikas and Søren K.S. Frederiksen acknowledge support from the Danish National Research Foundation and The National Science Foundation of China (under the grant 61061130540) for the Sino-Danish Center for the Theory of Interactive Computation, within which part of this work was performed and support from the Center for Research in Foundations of Electronic Markets (CFEM), supported by the Danish Strategic Research Council.

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

Access this chapter

Log in via an institution
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 EPUB and 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

References

  1. Abdulkadiroğlu, A., Sönmez, T., Markets, M.: Theory and practice. In: Advances in Economics and Econometrics (Tenth World Congress), pp. 3–47 (2013)

    Google Scholar 

  2. Adamczyk, M., Sankowski, P., Zhang, Q.: Efficiency of truthful and symmetric mechanisms in one-sided matching. In: Lavi, R. (ed.) SAGT 2014. LNCS, vol. 8768, pp. 13–24. Springer, Heidelberg (2014). doi:10.1007/978-3-662-44803-8_2

    Google Scholar 

  3. Anshelevich, E., Dasgupta, A., Kleinberg, J., Tardos, E., Wexler, T., Roughgarden, T.: The price of stability for network design with fair cost allocation. SIAM J. Comput. 38(4), 1602–1623 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  4. Aziz, H., Brandt, F., Brill, M.: The computational complexity of random serial dictatorship. Econ. Lett. 121(3), 341–345 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  5. Aziz, H., Gaspers, S., Mackenzie, S., Mattei, N., Narodytska, N., Walsh, T.: Equilibria under the probabilistic serial rule. arXiv preprint arXiv:1502.04888 (2015)

  6. Aziz, H., Gaspers, S., Mackenzie, S., Mattei, N., Narodytska, N., Walsh, T.: Manipulating the probabilistic serial rule. In: Proceedings of the 2015 International Conference on Autonomous Agents and Multiagent Systems, pp. 1451–1459. International Foundation for Autonomous Agents and Multiagent Systems (2015)

    Google Scholar 

  7. Aziz, H., Gaspers, S., Mattei, N., Narodytska, N., Walsh, T.: Strategic aspects of the probabilistic serial rule for the allocation of goods. arXiv preprint arXiv: 1401.6523 (2014)

  8. 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.) APPROX/RANDOM 2011. LNCS, vol. 6845, pp. 87–98. Springer, Heidelberg (2011). doi:10.1007/978-3-642-22935-0_8

    Chapter  Google Scholar 

  9. Bogomolnaia, A., Moulin, H.: A new solution to the random assignment problem. J. Econ. Theory 100, 295–328 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  10. Brams, S.J., Feldman, M., Lai, J.K., Morgenstern, J., Procaccia, A.D.: On maxsum fair cake divisions. In: AAAI (2012)

    Google Scholar 

  11. Caragiannis, I., Kaklamanis, C., Kanellopoulos, P., Kyropoulou, M.: The efficiency of fair division. Theory Comput. Syst. 50(4), 589–610 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  12. 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 

  13. Christodoulou, G., Kovács, A., Schapira, M.: Bayesian combinatorial auctions. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008. LNCS, vol. 5125, pp. 820–832. Springer, Heidelberg (2008). doi:10.1007/978-3-540-70575-8_67

    Chapter  Google Scholar 

  14. Ekici, O., Kesten, O.: On the ordinal nash equilibria of the probabilistic serial mechanism. Technical report, working paper, Tepper School of Business, Carnegie Mellon University (2010)

    Google Scholar 

  15. Filos-Ratsikas, A., Frederiksen, S.K.S., Zhang, J.: Social welfare in one-sided matchings: random priority and beyond. In: Lavi, R. (ed.) SAGT 2014. LNCS, vol. 8768, pp. 1–12. Springer, Heidelberg (2014). doi:10.1007/978-3-662-44803-8_1

    Google Scholar 

  16. 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 

  17. Hashimoto, T., Hirata, D., Kesten, O., Kurino, M., Utku Ünver, M.: Two axiomatic approaches to the probabilistic serial mechanism. Theor. Econ. 9(1), 253–277 (2014)

    Article  MathSciNet  Google Scholar 

  18. Hylland, A., Zeckhauser, R.: The efficient allocation of individuals to positions. J. Polit. Econ. 87(2), 293–314 (1979)

    Article  MATH  Google Scholar 

  19. Katta, A.-K., Sethuraman, J.: A solution to the random assignment problem on the full preference domain. J. Econ. Theory 131(1), 231–250 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  20. Kesten, O: Probabilistic serial and top trading cycles from equal division for the random assignment problem. Technical report, mimeo (2006)

    Google Scholar 

  21. Kojima, F., Manea, M.: Incentives in the probabilistic serial mechanism. J. Econ. Theory 145(1), 106–123 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  22. Koutsoupias, E., Papadimitriou, C.: Worst-case equilibria. In: Meinel, C., Tison, S. (eds.) STACS 1999. LNCS, vol. 1563, pp. 404–413. Springer, Heidelberg (1999). doi:10.1007/3-540-49116-3_38

    Chapter  Google Scholar 

  23. Krysta, P., Manlove, D., Rastegari, B., Zhang, J.: Size versus truthfulness in the house allocation problem. In: Proceedings of the 15th ACM Conference on Economics and Computation, pp. 453–470. ACM (2014)

    Google Scholar 

  24. 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 

  25. Roughgarden, T.: Intrinsic robustness of the price of anarchy. In: Proceedings of the Forty-First Annual ACM Symposium on Theory of Computing, pp. 513–522. ACM (2009)

    Google Scholar 

  26. Syrgkanis, V., Tardos, E.: Composable and efficient mechanisms. In: STOC 2013: Proceedings of the 45th Symposium on Theory of Computing, November 2013

    Google Scholar 

  27. Von Neumann, J., Morgenstern, O.: Theory of games and economic behavior (60th Anniversary Commemorative Edition). Princeton University Press, Princeton (2007)

    Book  Google Scholar 

  28. Zhou, L.: On a conjecture by gale about one-sided matching problems. J. Econ. Theory 52, 123–135 (1990)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The authors would like to thank Piotr Krysta for useful discussion.

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Liverpool, Liverpool, UK

    George Christodoulou & Jinshan Zhang

  2. Department of Computer Science, University of Oxford, Oxford, UK

    Aris Filos-Ratsikas, Paul W. Goldberg & Jie Zhang

  3. Department of Computer Science, Aarhus University, Aarhus, Denmark

    Søren Kristoffer Stiil Frederiksen

Authors
  1. George Christodoulou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Aris Filos-Ratsikas
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Søren Kristoffer Stiil Frederiksen
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Paul W. Goldberg
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Jie Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Jinshan Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jie Zhang .

Editor information

Editors and Affiliations

  1. Campus de la UAB, IIIA-CSIC , Bellaterra, Spain

    Nardine Osman

  2. Campus de la UAB, IIIA-CSIC , Bellaterra, Spain

    Carles Sierra

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing AG

About this paper

Cite this paper

Christodoulou, G., Filos-Ratsikas, A., Frederiksen, S.K.S., Goldberg, P.W., Zhang, J., Zhang, J. (2016). Social Welfare in One-Sided Matching Mechanisms. In: Osman, N., Sierra, C. (eds) Autonomous Agents and Multiagent Systems. AAMAS 2016. Lecture Notes in Computer Science(), vol 10002. Springer, Cham. https://doi.org/10.1007/978-3-319-46882-2_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-46882-2_3

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-46881-5

  • Online ISBN: 978-3-319-46882-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation