Approximate Efficiency in Matching Markets

  • Nicole ImmorlicaEmail author
  • Brendan Lucier
  • Glen Weyl
  • Joshua Mollner
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10660)


We propose a measure of approximate ex-ante Pareto efficiency in matching markets. According to this measure, a lottery over matchings is \(\gamma \)-approximately efficient if there is no alternate lottery in which each agent’s ex-ante expected utility increases by an \(\gamma \) factor. A mechanism is \(\gamma \)-approximately efficient if every lottery produced in equilibrium is \(\gamma \)-approximately efficient. We argue this is the natural extension of approximate efficiency in transferable-utility settings to our nontransferable-utility setting. Using this notion, we are able to quantify the intuited efficiency improvement of the so-called Boston mechanism and the recently-proposed choice-augmented deferred acceptance mechanism over the random serial dictatorship mechanism. Furthermore, we provide the first formal statement and analysis of the Raffle mechanism, which is conceptually simpler than the Boston mechanism and has a comparable efficiency guarantee.



We are grateful to Eric Budish, Peng Shi and especially Christina Lee for useful comments. All errors are our own.


  1. 1.
    Abdulkadiroğlu, A., Che, Y.-K., Yasuda, Y.: Resolving conflicting preferences in school choice: the “Boston mechanism”? Reconsidered. Am. Econ. Rev. 101(1), 399–410 (2011)CrossRefGoogle Scholar
  2. 2.
    Abdulkadiroğlu, A., Che, Y.-K., Yasuda, Y.: Expanding “choice” in school choice. Am. Econ. J.: Microeconomics 7(1), 1–42 (2015)Google Scholar
  3. 3.
    Abraham, D., Irving, R., Kavitha, T., Mehlhorn, K.: Popular matchings. SIAM J. Comput. 37, 1030–1045 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Anshelevich, E., Postl, J.: Randomized social choice functions under metric preferences. J. Artif. Intell. Res. 58, 797–827 (2017)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Azevedo, E., Budish, E.: Strategy-proofness in the large (2015).
  6. 6.
    Babaioff, M., Immorlica, N., Lucier, B., Weinberg, S.M.: A simple and approximately optimal mechanism for an additive buyer. In: 2014 IEEE 55th Annual Symposium on Foundations of Computer Science (FOCS), pp. 21–30. IEEE (2014)Google Scholar
  7. 7.
    Bansal, N., Sviridenko, M.: The Santa Claus problem. In: ACM Symposium on Theory of Computing (STOC) (2006)Google Scholar
  8. 8.
    Bogomolnaia, A., Moulin, H.: A new solution to the random assignment problem. J. Econ. Theory 100(2), 295–328 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Boutilier, C., Caragiannis, I., Haber, S., Lu, T., Procaccia, A., Sheffet, O.: Optimal social choice functions: a utilitarian view. Artif. Intell. 227, 190–213 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Branzei, S., Gkatzelis, V., Mehta, R.: Nash social welfare approximation for strategic agents. In: Proceedings of the 2017 ACM Conference on Economics and Computation, EC 2017 (2017)Google Scholar
  11. 11.
    Budish, E.: The combinatorial assignment problem: approximate competitive equilibrium from equal incomes. J. Polit. Econ. 119(6), 1061–1103 (2011)CrossRefGoogle Scholar
  12. 12.
    Budish, E., Che, Y.-K., Kojima, F., Milgrom, P.: Designing random allocation mechanisms: theory and applications. Am. Econ. Rev. 103(2), 585–623 (2013)CrossRefGoogle Scholar
  13. 13.
    Budish, E., Kessler, J.B.: Bringing real market participants’ real preferences into the lab: an experiment that changed the course allocation mechanism at Wharton (2016).
  14. 14.
    Caragiannis, I., Kurokawa, D., Moulin, H., Procaccia, A.D., Shah, N., Wang, J.: The unreasonable fairness of maximum Nash welfare. In: ACM Conference on Economics and Computation (2016)Google Scholar
  15. 15.
    Chade, H., Smith, L.: Simultaneous search. Econometrica 74(5), 1293–1307 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Chakrabarty, D., Swamy, C.: Welfare maximization and truthfulness in mechanism design with ordinal preferences. In: Innovations in Theoretical Computer Science (ITCS) (2014)Google Scholar
  17. 17.
    Che, Y.-K., Kojima, F.: Asymptotic equivalence of probabilistic serial and random priority mechanisms. Econometrica 78(5), 1625–1672 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Christodoulou, G., Kovács, A., Schapira, M.: Bayesian combinatorial auctions. J. ACM 63(2), 11 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Featherstone, C.R., Niederle, M.: Boston versus deferred acceptance in an interim setting: an experimental investigation. Games Econ. Behav. 100, 353–375 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Feige, U., Feldman, M., Immorlica, N., Izsak, R., Lucier, B., Syrgkanis, V.: A unifying hierarchy of valuations with complements and substitutes. In: Proceedings of the 29th AAAI Conference on Artificial Intelligence, pp. 872–878 (2015)Google Scholar
  21. 21.
    Feldman, M., Fu, H., Gravin, N., Lucier, B.: Simultaneous auctions are (almost) efficient. In: Proceedings of the 45th ACM Symposium on Theory of Computing, pp. 201–210 (2013)Google Scholar
  22. 22.
    Feldman, M., Immorlica, N., Lucier, B., Roughgarden, T., Syrgkanis, V.: The price of anarchy in large games. In: Proceedings of the 48th ACM Symposium on Theory of Computing, pp. 963–976 (2016)Google Scholar
  23. 23.
    Hart, S., Nisan, N.: Approximate revenue maximization with multiple items. In: Proceedings of the 13th ACM Conference on Electronic Commerce, EC 2012, pp. 656–656 (2012)Google Scholar
  24. 24.
    Hartline, J.D., Roughgarden, T.: Simple versus optimal mechanisms. In: Proceedings of the 10th ACM Conference on Electronic Commerce, pp. 225–234 (2009)Google Scholar
  25. 25.
    Hassidim, A., Kaplan, H., Mansour, Y., Nisan, N.: Non-price equilibria in markets of discrete goods. In: Proceedings of the 12th ACM Conference on Electronic Commerce, pp. 295–296 (2011)Google Scholar
  26. 26.
    Hassidim, A., Romm, A., Shorrer, R.I.: ‘strategic’ behavior in a strategy-proof environment (2016).
  27. 27.
    Hylland, A., Zeckhauser, R.: The efficient allocation of individuals to positions. J. Polit. Econ. 87(2), 293–314 (1979)CrossRefzbMATHGoogle Scholar
  28. 28.
    Papadimitriou, C.H., Yannakakis, M.: On the approximability of trade-offs and optimal access of web sources. In: Proceedings of the 41st Annual Symposium on Foundations of Computer Science, FOCS 2000 (2000)Google Scholar
  29. 29.
    Pycia, M.: The cost of ordinality, June 2014Google Scholar
  30. 30.
    Rawls, J.: A Theory of Justice. Cambridge, Belknap (1971)Google Scholar
  31. 31.
    Donald John Roberts and Andrew Postelwaite: The incentives for price-taking behavior in large exchange economies. Econometrica 44(1), 115–127 (1976)MathSciNetCrossRefGoogle Scholar
  32. 32.
    Shapley, L., Shubik, M.: Trade using one commodity as a means of payment. J. Polit. Econ. 85(5), 937–968 (1977)CrossRefGoogle Scholar
  33. 33.
    Syrgkanis, V., Tardos, E.: Composable and efficient mechanisms. In: Proceedings of the 45th ACM Symposium on Theory of Computing, pp. 211–220 (2013)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Nicole Immorlica
    • 1
    Email author
  • Brendan Lucier
    • 1
  • Glen Weyl
    • 1
  • Joshua Mollner
    • 2
  1. 1.Microsoft ResearchNew EnglandUSA
  2. 2.Kellogg School of Management, Northwestern UniversityEvanstonUSA

Personalised recommendations