Peer Effects and Stability in Matching Markets

  • Elizabeth Bodine-Baron
  • Christina Lee
  • Anthony Chong
  • Babak Hassibi
  • Adam Wierman
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6982)

Abstract

Many-to-one matching markets exist in numerous different forms, such as college admissions, matching medical interns to hospitals for residencies, assigning housing to college students, and the classic firms and workers market. In all these markets, externalities such as complementarities and peer effects severely complicate the preference ordering of each agent. Further, research has shown that externalities lead to serious problems for market stability and for developing efficient algorithms to find stable matchings. In this paper we make the observation that peer effects are often the result of underlying social connections, and we explore a formulation of the many-to-one matching market where peer effects are derived from an underlying social network. The key feature of our model is that it captures peer effects and complementarities using utility functions, rather than traditional preference ordering. With this model and considering a weaker notion of stability, namely two-sided exchange stability, we prove that stable matchings always exist and characterize the set of stable matchings in terms of social welfare. To characterize the efficiency of matching markets with externalities, we provide general bounds on how far the welfare of the worst-case stable matching can be from the welfare of the optimal matching, and find that the structure of the social network (e.g. how well clustered the network is) plays a large role.

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References

  1. 1.
    Alcalde, J.: Exchange-proofness or divorce-proofness? stability in one-sided matching markets. Rev. Econ. Design 1, 275–287 (1994)CrossRefGoogle Scholar
  2. 2.
    Anshelevich, E., Das, S., Naamad, Y.: Anarchy, stability, and utopia: Creating better matchings. In: Mavronicolas, M., Papadopoulou, V.G. (eds.) SAGT 2009. LNCS, vol. 5814, pp. 159–170. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  3. 3.
    Baccara, M., Imrohoroglu, A., Wilson, A., Yariv, L.: A field study on matching with network externalities, Working paper (2009)Google Scholar
  4. 4.
    Bajari, P., Fox, J.: Measuring the efficiency of an fcc spectrum auction. Working Paper 11671, National Bureau of Economic Research (2009)Google Scholar
  5. 5.
    Bodine-Baron, E., Lee, C., Chong, A., Hassibi, B.: A Wierman. Matching with friends: stability and peer effects in housing assignment, working paper, available on arxiv (2011)Google Scholar
  6. 6.
    Bogomolnaia, A., Jackson, M.: The stability of hedonic coalition structures. Games Econ. Behav. 38(2), 201–230 (2002)MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Brânzei, S., Larson, K.: Coalitional affinity games and the stability gap. In: IJCAI, pp. 1319–1320 (2009)Google Scholar
  8. 8.
    Cechlarova, K., Manlove, D.: On the complexity of exchange-stable roommates. DAM 116(3), 279–287 (2002)MATHGoogle Scholar
  9. 9.
    Cechlarova, K., Manlove, D.: The exchange-stable marriage problem. DAM 152(1-3), 109–122 (2005)MathSciNetMATHGoogle Scholar
  10. 10.
    Dutta, B., Masso, J.: Stability of matchings when individuals have preferences over colleagues. J. Econ. Theory 75(2), 464–475 (1997)MathSciNetMATHCrossRefGoogle Scholar
  11. 11.
    Echenique, F., Yenmez, M.: A solution to matching with preferences over colleagues. Games Econ. Behav. 59(1), 46–71 (2007)MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    Fox, J.: Estimating matching games with transfers, Working paper (2010)Google Scholar
  13. 13.
    Gale, D., Shapley, L.S.: College admissions and the stability of marriage. AMM 69(1), 9–15 (1962)MathSciNetMATHGoogle Scholar
  14. 14.
    Hafalir, I.E.: Stability of marriage with externalities. Int. J. Game Theory 37, 353–370 (2008)MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    Irving, R.: Stable matching problems with exchange restrictions. J. Comb. Opt. 16, 344–360 (2008)MathSciNetMATHCrossRefGoogle Scholar
  16. 16.
    Jackson, M.: Social and Economic Networks. Princeton University Press, Princeton (2008)MATHGoogle Scholar
  17. 17.
    Kannan, R., Vempala, S., Vetta, A.: On clusterings: Good, bad and spectral. J. ACM 51(3), 497–515 (2004)MathSciNetMATHCrossRefGoogle Scholar
  18. 18.
    Klaus, B., Klijn, F.: Stable matchings and preferences of couples. J. Econ. Theory 121, 75–106 (2005)MathSciNetMATHCrossRefGoogle Scholar
  19. 19.
    Klaus, B., Klijn, F.: Paths to stability for matching markets with couples. Games Econ. Behav. 58, 154–171 (2007)MathSciNetMATHCrossRefGoogle Scholar
  20. 20.
    Kojima, F., Pathak, P.: Incentives and stability in large two-sided matching markets. Amer. Econ. Rev. 99(3), 608–627 (2009)CrossRefGoogle Scholar
  21. 21.
    Ostrovsky, M.: Stability in supply chain networks. Amer. Econ. Rev. 98(3), 897–923 (2008)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Pycia, M.: Many-to-one matching with complementarities and peer effects, Working paper (2007)Google Scholar
  23. 23.
    Radicchi, F., Castellano, C., Cecconi, F., Loreto, V., Parisi, D.: Defining and identifying communities in networks. PNAS 101(9), 2658–2663 (2004)CrossRefGoogle Scholar
  24. 24.
    Revilla, P.: Many-to-one matching when colleagues matter, Working paper (2004)Google Scholar
  25. 25.
    Ronn, E.: Np-complete stable matching problems. J. Alg. 11, 285–304 (1990)MathSciNetMATHCrossRefGoogle Scholar
  26. 26.
    Roth, A.E.: The evolution of the labor market for medical interns and residents: A case study in game theory. J. of Polit. Econ. 92, 991–1016 (1984)CrossRefGoogle Scholar
  27. 27.
    Roth, A.E., Rothblum, U.G., Vande Vate, J.H.: Stable matchings, optimal assignments and linear programming. MOR 18(4), 803–828 (1993)MathSciNetMATHCrossRefGoogle Scholar
  28. 28.
    Roth, A.E., Sotomayor, M.: Two-sided matching: A study in game-theoretic modeling and analysis. Cambridge University Press, Cambridge (1990)MATHGoogle Scholar
  29. 29.
    Roth, A.E., Vande Vate, J.H.: Random paths to stability in two-sided matching. Econometrica 58, 1475–1480 (1990)MathSciNetMATHCrossRefGoogle Scholar
  30. 30.
    Sasaki, H., Toda, M.: Two-sided matching problems with externalities. J. Econ. Theory 70(1), 93–108 (1996)MathSciNetMATHCrossRefGoogle Scholar
  31. 31.
    Shi, J., Malik, J.: Normalized cuts and image segmentation. IEEE Trans. of Pattern Analysis and Machine Intelligence 22(8), 888–905 (2000)CrossRefGoogle Scholar
  32. 32.
    Wasserman, S., Faust, K.: Social Network Analysis: Methods and Applications. Cambridge University Press, Cambridge (1994)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Elizabeth Bodine-Baron
    • 1
  • Christina Lee
    • 1
  • Anthony Chong
    • 1
  • Babak Hassibi
    • 1
  • Adam Wierman
    • 1
  1. 1.California Institute of TechnologyPasadenaUSA

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