New Directions of Study in Matching with Constraints

  • Fuhito KojimaEmail author
Part of the Studies in Economic Design book series (DESI)


This piece surveys a recent body of studies in “matching with constraints.” It discusses relationship with traditional matching theory and new applications, and concludes with some open questions.


  1. Abdulkadiroğlu, A. (2005). College admissions with affirmative action. International Journal of Game Theory, 33(4), 535–549.CrossRefGoogle Scholar
  2. Abdulkadiroğlu, A., & Sönmez, T. (2003). School choice: A mechanism design approach. American Economic Review, 93, 729–747.CrossRefGoogle Scholar
  3. Ashlagi, I., Braverman, M., & Hassidim, A. (2014). Stability in large matching markets with complementarities. Operations Research, 62, 713–732.CrossRefGoogle Scholar
  4. Delacrétaz, D., Kominers, S. D., & Teytelboym, A. (2016). Refugee resettlement, working paper.Google Scholar
  5. Ehlers, L., Hafalir, I. E., Yenmez, M. B., & Yildirim, M. A. (2014). School choice with controlled choice constraints: Hard bounds versus soft bounds. Journal of Economic Theory, 153, 648–683.CrossRefGoogle Scholar
  6. Fragiadakis, D., & Troyan, P. (2017). Improving matching under hard distributional constraints. Theoretical Economics, 12, 863–908.CrossRefGoogle Scholar
  7. Goto, M., Kojima, F., Kurata, R., Tamura, A., & Yokoo, M. (2017). Designing matching mechanisms under general distributional constraints. American Economic Journal: Microeconomics, 9, 226–262.Google Scholar
  8. Hafalir, I. E., Yenmez, M. B., & Yildirim, M. A. (2013). Effective affirmative action in school choice. Theoretical Economics, 8(2), 325–363.CrossRefGoogle Scholar
  9. Kamada, Y., & Kojima, F. (2015). Efficient matching under distributional constraints: Theory and applications. American Economic Review, 105(1), 67–99.CrossRefGoogle Scholar
  10. Kamada, Y., & Kojima, F. (2017). Stability concepts in matching with distributional constraints. Journal of Economic theory, 168, 107–142.CrossRefGoogle Scholar
  11. Kamada, Y., & Kojima, F. (2018a). Stability and strategy-proofness for matching with constraints: A necessary and sufficient condition. Theoretical Economics, 13, 761–793.Google Scholar
  12. Kamada, Y., & Kojima, F. (2018b). Fair matching under constraints: Theory and applications, working paper.Google Scholar
  13. Kasuya, Y. (2016). Anti-bullying school choice mechanism design, working paper.Google Scholar
  14. Klaus, B., & Klijn, F. (2005). Stable matchings and preferences of couples. Journal of Economic Theory, 121, 75–106.CrossRefGoogle Scholar
  15. Kojima, F. (2012). School choice: Impossibilities for affirmative action. Games and Economic Behavior, 75(2), 685–693.CrossRefGoogle Scholar
  16. Kojima, F., Pathak, P. A., & Roth, A. E. (2013). Matching with couples: Stability and incentives in large markets. Quarterly Journal of Economics, 128, 1585–1632.CrossRefGoogle Scholar
  17. Kojima, F., Tamura, A., & Yokoo, M. (2018). Designing matching mechanisms under constraints: An approach from discrete convex analysis. Journal of Economic Theory, 176, 803–833.Google Scholar
  18. McDermid, E. J., & Manlove, D. (2009). Keeping partners together: Algorithmic results for the hospitals/resident problem with couples. Journal of Combinatorial Optimization, 19, 279–303.CrossRefGoogle Scholar
  19. Okumura, Y. (2018). School choice with general constraints: A market design approach for nursery school waiting lists problem in Japan,” forthcoming. Japanese Economic Review.Google Scholar
  20. Roth, A. E. (1984). The evolution of the labor market for medical interns and residents: A case study in game theory. Journal of Political Economy, 92, 991–1016.CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Stanford UniversityStanfordUSA

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