Skip to main content
SpringerLink
Log in

Anarchy, stability, and utopia: creating better matchings

  • Published:
Autonomous Agents and Multi-Agent Systems Aims and scope Submit manuscript

Abstract

Historically, the analysis of matching has centered on designing algorithms to produce stable matchings as well as on analyzing the incentive compatibility of matching mechanisms. Less attention has been paid to questions related to the social welfare of stable matchings in cardinal utility models. We examine the loss in social welfare that arises from requiring matchings to be stable, the natural equilibrium concept under individual rationality. While this loss can be arbitrarily bad under general preferences, when there is some structure to the underlying graph corresponding to natural conditions on preferences, we prove worst case bounds on the price of anarchy. Surprisingly, under simple distributions of utilities, the average case loss turns out to be significantly smaller than the worst-case analysis would suggest. Furthermore, we derive conditions for the existence of approximately stable matchings that are also close to socially optimal, demonstrating that adding small switching costs can make socially (near-)optimal matchings stable. Our analysis leads to several concomitant results of interest on the convergence of decentralized partner-switching algorithms, and on the impact of heterogeneity of tastes on social welfare.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Abdulkadiroglu A., Che Y.K., Yasuda Y. (2011) Resolving conflicting preferences in school choice: The Boston mechanism reconsidered. American Economic Review 101(1): 399–410

    Article  Google Scholar 

  2. Abdulkadiroglu A., Pathak P. A., Roth A. E. (2005) The New York City high school match. American Economic Review 95(2): 364–367

    Article  Google Scholar 

  3. Abdulkadiroglu A., Pathak P. A., Roth A. E. (2009) Strategy-proofness versus efficiency in matching with indifferences: Redesigning the NYC high school match. American Economic Review 99(5): 1954–1978

    Article  Google Scholar 

  4. Abdulkadiroglu A., Pathak P. A., Roth A. E., Sonmez T. (2005) The Boston public school match. American Economic Review Papers and Proceedings 95(2): 368–371

    Article  Google Scholar 

  5. Abraham, D. J., Blum, A., & Sandholm, T. (2007). Clearing algorithms for barter exchange markets: Enabling nationwide kidney exchanges. In Proceedings of the 8th ACM Conference on Electronic commerce (pp. 295–304). New York: ACM.

  6. Ackermann, H., Goldberg, P. W., Mirrokni, V. S., Roglin, H., & Vocking, B. (2008). Uncoordinated two-sided markets. In Proceedings of the 9th ACM Conference on Electronic Commerce (EC) (pp. 256–263). New York: ACM.

  7. Anshelevich, E., Dasgupta, A., Kleinberg, J., Tardos, E., Wexler, T., & Roughgarden, T. (2004). The price of stability for network design with fair cost allocation. In Proc. FOCS, Washington, DC (pp. 295–304).

  8. Anshelevich, E., Dasgupta, A., Tardos, E., & Wexler, T. (2003). Near-optimal network design with selfish agents. In Proceedings STOC (pp. 511–520). New York: ACM.

  9. Barabasi A. L., Albert R. (1999) Emergence of scaling in random networks. Science 286(5439): 509–512

    Article  MathSciNet  Google Scholar 

  10. Becker G. S. (1983) A treatise on the family. Family Process 22(1): 127

    Google Scholar 

  11. Christodoulou G., Koutsoupias E. (2005) On the price of anarchy and stability of correlated equilibria of linear congestion games. Lecture Notes in Computer Science 3669: 59

    Article  MathSciNet  Google Scholar 

  12. Das, S., & Kamenica, E. (2005). Two-sided bandits and the dating market. In Proc. IJCAI, Edinburgh, UK, Aug 2005 (pp. 947–952).

  13. Dawande M., Kumar S., Mookerjee V., Sriskandarajah C. (2008) Maximum commonality problems: Applications and analysis. Management Science 54(1): 194

    Article  Google Scholar 

  14. Dubins, L. E., & Freedman, D. A. (1981). Machiavelli and the Gale–Shapley algorithm. The American Mathematical Monthly, 88(7), 485–494.

    Article  MathSciNet  MATH  Google Scholar 

  15. Gale D., Shapley L. S. (1962) College admissions and the stability of marriage. The American Mathematical Monthly 69(1): 9–15

    Article  MathSciNet  MATH  Google Scholar 

  16. Gale, D., & Sotomayor, M. (1985). Ms. Machiavelli and the stable matching problem. The American Mathematical Monthly, 92, 261–268.

    Article  MathSciNet  MATH  Google Scholar 

  17. Goemans M. X., Li L., Mirrokni V. S., Thottan M. (2006) Market sharing games applied to content distribution in ad hoc networks. IEEE Journal on Selected Areas in Communications 24(5): 1020–1033

    Article  Google Scholar 

  18. Held P. J., Kahan B. D., Hunsicker L. G., Liska D., Wolfe R. A., Port F. K. et al (1994) The impact of HLA mismatches on the survival of first cadaveric kidney transplants. The New England journal of medicine 331(12): 765

    Article  Google Scholar 

  19. Immorlica, N., & Mahdian, M. (2005). Marriage, honesty, and stability. In Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms (pp. 53–62). New York: ACM.

  20. Irving R. W., Leather P., Gusfield D. (1987) An efficient algorithm for the “optimal” stable marriage. Journal of the ACM 34(3): 532–543

    Article  MathSciNet  Google Scholar 

  21. Jovanovic B. (1979) Job matching and the theory of turnover. The Journal of Political Economy 87(5): 972

    Article  MathSciNet  Google Scholar 

  22. Mirrokni, V. S. (2005). Approximation algorithms for distributed and selfish agents. PhD thesis, Massachusetts Institute Of Technology.

  23. Mongell S., Roth A. E. (1991) Sorority rush as a two-sided matching mechanism. American Economic Review 81(3): 441–464

    Google Scholar 

  24. Roth A. E., Peranson E. (1999) The redesign of the matching market for American physicians: Some engineering aspects of economic design. American Economic Review 89(4): 748–780

    Article  Google Scholar 

  25. Roth A. E., Sönmez T., Ünver M. U. (2004) Kidney exchange. Quarterly Journal of Economics 119(2): 457–488

    Article  MATH  Google Scholar 

  26. Roth A. E., Sönmez T., Ünver M. U. (2005) A kidney exchange clearinghouse in New England. American Economic Review 95(2): 376–380

    Article  Google Scholar 

  27. Roth A. E., Sotomayor M. (1990) Two-sided matching: A study in game-theoretic modeling and analysis. Econometric society monograph series. Cambridge University Press, Cambridge, UK

    Google Scholar 

  28. Roth A. E., Vande Vate J. H. (1990) Random paths to stability in two-sided matching. Econometrica 58(6): 1475–1480

    Article  MathSciNet  MATH  Google Scholar 

  29. Roth A. E., Xing X. (1994) Jumping the gun: Imperfections and institutions related to the timing of market transactions. The American Economic Review 84(4): 992–1044

    Google Scholar 

  30. Schulz, A. S., & Moses, N. S. (2003). On the performance of user equilibria in traffic networks. In Proceedings of the 14th Annual ACM-SIAM Symposium on Discrete Algorithms (pp. 86–87). New York: ACM.

  31. Segev D. L., Gentry S. E., Warren D. S., Reeb B., Montgomery R. A. (2005) Kidney paired donation and optimizing the use of live donor organs. Journal of the American Medical Association 293(15): 1883

    Article  Google Scholar 

  32. Su X., Zenios S. A. (2005) Patient choice in kidney allocation: A sequential stochastic assignment model. Operations Research 53(3): 443–455

    Article  MathSciNet  MATH  Google Scholar 

  33. Thaler R. H., Sunstein C. R. (2008) Nudge. Yale University Press, New Haven, CT

    Google Scholar 

  34. Watts D. J., Strogatz S. H. (1998) Collective dynamics of ’small-world’ networks. Nature 393(6684): 440–442

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Rensselaer Polytechnic Institute, Troy, NY, USA

    Elliot Anshelevich, Sanmay Das & Yonatan Naamad

Authors
  1. Elliot Anshelevich
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sanmay Das
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yonatan Naamad
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sanmay Das.

Additional information

A preliminary version of this article appeared in SAGT 2009. This work was supported in part by NSF grants CCF-0914782, CNS-1017932, and IIS-0952918. Naamad is now at Princeton University.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Anshelevich, E., Das, S. & Naamad, Y. Anarchy, stability, and utopia: creating better matchings. Auton Agent Multi-Agent Syst 26, 120–140 (2013). https://doi.org/10.1007/s10458-011-9184-3

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10458-011-9184-3

Keywords

Search

Navigation