Engineering Design of Matching Markets

  • Péter BiróEmail author
Part of the Studies in Economic Design book series (DESI)


Two-sided matching markets under preferences can be described by the stable matching model of Gale and Shapley, proposed for college admissions. Their deferred-acceptance algorithm always produces a student-optimal stable matching in linear time, and it is strategy-proof for the students. Mainly due to these desirable properties, this algorithm has been widely used in many applications across the world, including school choice, college admission, and resident allocation. Yet, having one extra custom feature can turn the corresponding problem intractable in a computational sense, the existence of a fair solution may not be guaranteed any more, and the strategic issues cannot be avoided either. One well-known example for such a market design challenge was the introduction of joint applications by couples in the US resident allocation program. In the 1990s Roth and Peranson managed to successfully resolve the case by taking an engineering approach, and constructing a Gale-Shapley based heuristic algorithm. In this writing we elaborate on this engineering concept by describing further examples for real-life design challenges in matching markets, the related computational and strategic issues, and the possible solution techniques from optimization and game theoretical points of view.



The author acknowledges the support of the Hungarian Academy of Sciences under its Momentum Programme (LP2016-3/2018) and Cooperation of Excellences Grant (KEP-6/2018), and the Hungarian Scientific Research Fund, OTKA, Grant No.\ K128611.


  1. Abdulkadiroglu, A., & Sönmez, T. (2003). School choice: A mechanism design approach. American Economic Review, 93(3), 729–747.CrossRefGoogle Scholar
  2. Abdulkadiroglu, A., Pathak, P. A., & Roth, A. E. (2005a). The New York city high school match. American Economic Review, Papers and Proceedings, 95(2), 364–367.CrossRefGoogle Scholar
  3. Abdulkadiroglu, A., Pathak, P. A., & Roth, A. E. (2005b). Boston public school match. American Economic Review, Papers and Proceedings, 95(2), 368–371.CrossRefGoogle Scholar
  4. 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.CrossRefGoogle Scholar
  5. Abdulkadiroglu, A., Che, Y. K., Pathak, P. A., Roth, A. E., & Tercieux, O. (2017). Minimizing Justified Envy in School Choice: The Design of New Orleans’ OneApp (No. w23265). National Bureau of Economic Research.Google Scholar
  6. Ágoston, K. Cs., Biró, P., & McBride, I. (2016). Integer programming methods for special college admissions problems. Journal of Combinatorial Optimization, 32(4), 1371–1399.Google Scholar
  7. Ágoston, K Cs, Biró, P., & Szántó, R. (2018). Stable project allocation under distributional constraints. Operations Research Perspectives, 5, 59–68.CrossRefGoogle Scholar
  8. Ashlagi, I., & Gonczarowski, Y. A. (2016). Stable matching mechanisms are not obviously strategy-proof. arXiv:1511.00452.
  9. Ashlagi, I., & Shi, P. (2015). Optimal allocation without money: An engineering approach. Management Science, 62(4), 1078–1097.CrossRefGoogle Scholar
  10. Azevedo, E. M., & Budish, E. (2013). Strategy-proofness in the large. The Review of Economic Studies, 86(1), 81–116.Google Scholar
  11. Biró, P. (2017). Applications of matching models under preferences. In U. Endriss (Ed.), Trends in Computational Social Choice, Chapter 18 (pp. 345–373). AI Access.Google Scholar
  12. Biró, P., & Gudmondsson, J. (2018). Complexity of finding pareto-efficient allocations of highest welfare. Working paper.Google Scholar
  13. Biró, P., & Kiselgof, S. (2015). College admissions with stable score limits. Central European Journal of Operations Research, 23(4), 727–741.CrossRefGoogle Scholar
  14. Biró, P., & Klijn, F. (2013). Matching with couples: A multidisciplinary survey. International Game Theory Review, 15(02), 1340008.CrossRefGoogle Scholar
  15. Biró, P., Manlove, D. F., & Rizzi, R. (2009). Maximum weight cycle packing in directed graphs, with application to the kidney exchange programs. Discrete Mathematics, Algorithms and Applications, 1(4), 499–517.CrossRefGoogle Scholar
  16. Biró, P., Fleiner, T., Irving, R. W., & Manlove, D. F. (2010). The College admissions problem with lower and common quotas. Theoretical Computer Science, 411, 3136–3153.CrossRefGoogle Scholar
  17. Biró, P., Irving, R. W., & Schlotter, I. (2011). Stable matching with couples: An empirical study. ACM Journal of Experimental Algorithmics, 16, 1–2.Google Scholar
  18. Biró, P., McBride, I., & Manlove, D. F. (2014). The hospitals/residents problem with couples: Complexity and integer programming models. In Proceedings of SEA 2014: The 13th International Symposium on Experimental Algorithms, 8504 (pp. 10–21). LNCS, Springer.Google Scholar
  19. Budish, E., & Kessler, J. (2015). Experiments as a Bridge from Market Design Theory to Market Design Practice: Changing the Course Allocation Mechanism at Wharton. Working paper.Google Scholar
  20. Chen, Y., & Sönmez, T. (2006). School choice: An experimental study. Journal of Economic Theory, 127(1), 202–231.CrossRefGoogle Scholar
  21. Echenique, F., & Yenmez, M. B. (2015). How to control controlled school choice. American Economic Review, 105(8), 2679–2694.CrossRefGoogle Scholar
  22. Gale, D., & Shapley, L. S. (1962). College admissions and the stability of marriage. American Mathematical Monthly, 69, 9–15.CrossRefGoogle Scholar
  23. Gusfield, D., & Irving, R. W. (1989). The Stable Marriage Problem: Structure and Algorithms. MIT press.Google Scholar
  24. Irving, R. W., & Manlove, D. F. (2009). Finding large stable matchings. ACM Journal of Experimental Algorithmics, 14, Section 1, Article 2, 30.Google Scholar
  25. Kojima, F., & Pathak, P. A. (2009). Incentives and stability in large two-sided matching markets. American Economic Review, 99(3), 608–627.CrossRefGoogle Scholar
  26. Kojima, F., Pathak, P. A., & Roth, A. E. (2013). Matching with couples: Stability and incentives in large markets. The Quarterly Journal of Economics, 128(4), 1585–1632.CrossRefGoogle Scholar
  27. Kwanashie, A., & Manlove, D. F. (2014). An integer programming approach to the hospitals/residents problem with ties. In Operations Research Proceedings 2013 (pp. 263–269). Springer.Google Scholar
  28. Li, S. (2017). Obviously Strategy-proof mechanisms. American Economic Review, 107(11), 3257–3287.CrossRefGoogle Scholar
  29. Manlove, D. F. (2013). Algorithms of Matching Under Preferences. World Scientific.Google Scholar
  30. Manlove, D. F., & O’Malley, G. (2012). Paired and altruistic kidney donation in the UK: Algorithms and experimentation. In proceeding of SEA 2012, 7276, (pp. 271–282). LNCS.Google Scholar
  31. Manlove, D. F., Irving, R. W., Iwama, K., Miyazaki, S., & Morita, Y. (2002). Hard variants of stable marriage. Theoretical Computer Science, 276(1–2), 261–279.CrossRefGoogle Scholar
  32. Marx, D., & Schlotter, I. (2011). Stable assignment with couples: parameterized complexity and local search. Discrete Optimization, 8, 25–40.CrossRefGoogle Scholar
  33. Mcdermid, E. (2009). A 3/2 approximation algorithm for general stable marriage. In Proceedings of ICALP ’09: The 36th International Colloquium on Automata, Languages and Programming, 5555 (pp. 689–700). LNCS, (Springer).Google Scholar
  34. Morrill, T. (2015). Making just school assignments. Games and Economic Behavior, 92, 18–27.CrossRefGoogle Scholar
  35. Pathak, P. A., & Sönmez, T. (2013). School admissions reform in Chicago and England: Comparing mechanisms by their vulnerability to manipulation. American Economic Review, 103(1), 80–106.CrossRefGoogle Scholar
  36. Rees-Jones, A. (2018). Suboptimal behavior in strategy-proof mechanisms: Evidence from the residency match. Games and Economic Behavior, 108, 317–330.CrossRefGoogle Scholar
  37. Ronn, E. (1990). NP-complete stable matching problems. Journal of Algorithms, 11, 285–304.CrossRefGoogle Scholar
  38. Roth, A. E. (1982). The Economics of matching: Stability and incentives. Mathematics of Operations Research, 7, 617–628.CrossRefGoogle Scholar
  39. 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
  40. Roth, A. E. (1991). A Natural experiment in the organization of entry level labor markets: Regional markets for new physicians and surgeons in the U.K. American Economic Review, 81, 415–440.Google Scholar
  41. Roth, A. E. (2002). The economist as engineer: Game theory, experimentation, and computation as tools for design economics. Econometrica, 70(4), 1341–1378.CrossRefGoogle Scholar
  42. Roth, A. E. (2008). Deferred acceptance algorithms: History, theory, practice, and open questions. International Journal of Game Theory, 36, 537–569.CrossRefGoogle Scholar
  43. Roth, A. E. (2015). Who Gets What and Why: The New Economics of Matchmaking and Market Design. Eamon Dolan.Google Scholar
  44. 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.CrossRefGoogle Scholar
  45. Roth, A. E., & Sotomayor, M. O. (1990). Two-Sided Matching: A Study in Game Theoretic Modelling and Analysis. Cambridge University Press.Google Scholar
  46. Roth, A. E., Sönmez, T., & Utku Ünver, M. (2005). A kidney exchange clearinghouse in New England. American Economic Review, 95(2), 376–380.CrossRefGoogle Scholar
  47. Veski, A., Biró, P., Pöder, K., & Lauri, T. (2017). Efficiency and fair access in kindergarten allocation policy design. Journal of Mechanism and Institutional Design, 2(1), 57–104.CrossRefGoogle Scholar
  48. Website of the Matching in Practice network.
  49. Yanagisawa, H. (2007). Approximation algorithms for stable marriage problems. Ph.D. thesis, Kyoto University, School of Informatics.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute of Economics, Hungarian Academy of SciencesBudapestHungary

Personalised recommendations