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Deferred Acceptance Algorithms: History, Theory, Practice, and Open Questions

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Alvin E. Roth

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Abstract

The deferred acceptance algorithm proposed by Gale and Shapley (1962) has had a profound influence on market design, both directly, by being adapted into practical matching mechanisms, and, indirectly, by raising new theoretical questions. Deferred acceptance algorithms are at the basis of a number of labor market clearinghouses around the world, and have recently been implemented in school choice systems in Boston and New York City. In addition, the study of markets that have failed in ways that can be fixed with centralized mechanisms has led to a deeper understanding of some of the tasks a marketplace needs to accomplish to perform well. In particular, marketplaces work well when they provide thickness to the market, help it deal with the congestion that thickness can bring, and make it safe for participants to act effectively on their preferences. Centralized clearinghouses organized around the deferred acceptance algorithm can have these properties, and this has sometimes allowed failed markets to be reorganized.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 13225.

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Date of creation: Jul 2007
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Handle: RePEc:nbr:nberwo:13225

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Find related papers by JEL classification:
C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
N01 - Economic History - - General - - - Development of the Discipline: Historiographical; Sources and Methods

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  1. Li, Hao & Rosen, Sherwin, 1998. "Unraveling in Matching Markets," American Economic Review, American Economic Association, vol. 88(3), pages 371-87, June. [Downloadable!] (restricted)
  2. Roth, Alvin E, 1986. "On the Allocation of Residents to Rural Hospitals: A General Property of Two-Sided Matching Markets," Econometrica, Econometric Society, vol. 54(2), pages 425-27, March. [Downloadable!] (restricted)
  3. Szilvia Papai, 2000. "Strategyproof Assignment by Hierarchical Exchange," Econometrica, Econometric Society, vol. 68(6), pages 1403-1434, November.
  4. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March. [Downloadable!] (restricted)
  5. Alvin E. Roth & Tayfun Sonmez & M. Utku Ünver, 2007. "Efficient Kidney Exchange: Coincidence of Wants in Markets with Compatibility-Based Preferences," American Economic Review, American Economic Association, vol. 97(3), pages 828-851, June. [Downloadable!]
  6. Roth, Alvin E & Xing, Xiaolin, 1997. "Turnaround Time and Bottlenecks in Market Clearing: Decentralized Matching in the Market for Clinical Psychologists," Journal of Political Economy, University of Chicago Press, vol. 105(2), pages 284-329, April.
  7. Roth, Alvin E & Vande Vate, John H, 1990. "Random Paths to Stability in Two-Sided Matching," Econometrica, Econometric Society, vol. 58(6), pages 1475-80, November. [Downloadable!] (restricted)
  8. Atila Abdulkadiroğlu & Parag A. Pathak & Alvin E. Roth, 2005. "The New York City High School Match," American Economic Review, American Economic Association, vol. 95(2), pages 364-367, May. [Downloadable!]
  9. Sonmez, Tayfun & Utku Unver, M., 2005. "House allocation with existing tenants: an equivalence," Games and Economic Behavior, Elsevier, vol. 52(1), pages 153-185, July. [Downloadable!] (restricted)
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  10. Federico Echenique & Jorge Oviedo, 2004. "A Theory of Stability in Many-to-many Matching Markets," Game Theory and Information 0401002, EconWPA. [Downloadable!]
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  11. Roth, Alvin E., 1985. "The college admissions problem is not equivalent to the marriage problem," Journal of Economic Theory, Elsevier, vol. 36(2), pages 277-288, August. [Downloadable!] (restricted)
  12. Atila Abdulkadiroglu & Parag A. Pathak & Alvin E. Roth & Tayfun Sönmez, 2006. "Changing the Boston School Choice Mechanism," Boston College Working Papers in Economics 639, Boston College Department of Economics. [Downloadable!]
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  13. Echenique, Federico & Oviedo, Jorge, 2004. "Core many-to-one matchings by fixed-point methods," Journal of Economic Theory, Elsevier, vol. 115(2), pages 358-376, April. [Downloadable!] (restricted)
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  14. Fuhito Kojima, 2007. "Matching and Price Competition: Comment," American Economic Review, American Economic Association, vol. 97(3), pages 1027-1031, June. [Downloadable!]
  15. Roth, Alvin E. & Sotomayor, Marilda, 1992. "Two-sided matching," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 16, pages 485-541 Elsevier. [Downloadable!] (restricted)
  16. Chung, Kim-Sau, 2000. "On the Existence of Stable Roommate Matchings," Games and Economic Behavior, Elsevier, vol. 33(2), pages 206-230, November. [Downloadable!] (restricted)
  17. Alvin E. Roth & Tayfun Sonmez & M. Utku Unver, 2003. "Kidney Exchange," NBER Working Papers 10002, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  18. Christopher Avery & Christine Jolls & Richard Posner & Alvin E. Roth, 2007. "The New Market for Federal Judicial Law Clerks," NBER Working Papers 13213, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  19. John H. Kagel & Alvin E. Roth, 2000. "The Dynamics Of Reorganization In Matching Markets: A Laboratory Experiment Motivated By A Natural Experiment," The Quarterly Journal of Economics, MIT Press, vol. 115(1), pages 201-235, February. [Downloadable!] (restricted)
  20. Roth, Alvin E. & Sotomayor, Marilda, 1988. "Interior points in the core of two-sided matching markets," Journal of Economic Theory, Elsevier, vol. 45(1), pages 85-101, June. [Downloadable!] (restricted)
  21. Ettore Damiano, 2005. "Unravelling of Dynamic Sorting," Review of Economic Studies, Blackwell Publishing, vol. 72(4), pages 1057-1076, October. [Downloadable!] (restricted)
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  22. Atila Abdulkadiroğlu & Parag A. Pathak & Alvin E. Roth & Tayfun Sonmez, 2005. "The Boston Public School Match," American Economic Review, American Economic Association, vol. 95(2), pages 368-371, May. [Downloadable!]
  23. Sonmez, Tayfun, 1997. "Manipulation via Capacities in Two-Sided Matching Markets," Journal of Economic Theory, Elsevier, vol. 77(1), pages 197-204, November. [Downloadable!] (restricted)
  24. Alkan, Ahmet, 1988. "Nonexistence of stable threesome matchings," Mathematical Social Sciences, Elsevier, vol. 16(2), pages 207-209, October. [Downloadable!] (restricted)
  25. Echenique, Federico & Yenmez, M. Bumin, 2007. "A solution to matching with preferences over colleagues," Games and Economic Behavior, Elsevier, vol. 59(1), pages 46-71, April. [Downloadable!] (restricted)
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  26. Klaus, Bettina & Klijn, Flip, 2005. "Stable matchings and preferences of couples," Journal of Economic Theory, Elsevier, vol. 121(1), pages 75-106, March. [Downloadable!] (restricted)
  27. Roth, Alvin E & Xing, Xiaolin, 1994. "Jumping the Gun: Imperfections and Institutions Related to the Timing of Market Transactions," American Economic Review, American Economic Association, vol. 84(4), pages 992-1044, September. [Downloadable!] (restricted)
  28. Ehlers, Lars & Klaus, Bettina, 2006. "Efficient priority rules," Games and Economic Behavior, Elsevier, vol. 55(2), pages 372-384, May. [Downloadable!] (restricted)
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  29. Martinez, Ruth & Masso, Jordi & Neme, Alejandro & Oviedo, Jorge, 2004. "An algorithm to compute the full set of many-to-many stable matchings," Mathematical Social Sciences, Elsevier, vol. 47(2), pages 187-210, March. [Downloadable!] (restricted)
  30. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November. [Downloadable!] (restricted)
  31. Sotomayor, Marilda, 2007. "Connecting the cooperative and competitive structures of the multiple-partners assignment game," Journal of Economic Theory, Elsevier, vol. 134(1), pages 155-174, May. [Downloadable!] (restricted)
  32. Haluk I. Ergin, 2002. "Efficient Resource Allocation on the Basis of Priorities," Econometrica, Econometric Society, vol. 70(6), pages 2489-2497, November. [Downloadable!] (restricted)
  33. Balinski, Michel & Sonmez, Tayfun, 1999. "A Tale of Two Mechanisms: Student Placement," Journal of Economic Theory, Elsevier, vol. 84(1), pages 73-94, January. [Downloadable!] (restricted)
  34. Muriel Niederle, 2007. "Competitive Wages in a Match with Ordered Contracts," American Economic Review, American Economic Association, vol. 97(5), pages 1957-1969, December. [Downloadable!]
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  35. Ergin, Haluk & Sonmez, Tayfun, 2006. "Games of school choice under the Boston mechanism," Journal of Public Economics, Elsevier, vol. 90(1-2), pages 215-237, January. [Downloadable!] (restricted)
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  36. Abdulkadiroglu, Atila & Sonmez, Tayfun, 1999. "House Allocation with Existing Tenants," Journal of Economic Theory, Elsevier, vol. 88(2), pages 233-260, October. [Downloadable!] (restricted)
  37. Crawford, Vincent P & Knoer, Elsie Marie, 1981. "Job Matching with Heterogeneous Firms and Workers," Econometrica, Econometric Society, vol. 49(2), pages 437-50, March. [Downloadable!] (restricted)
  38. Alvin E. Roth & Tayfun Sonmez & M. Utku Ünver, 2005. "A Kidney Exchange Clearinghouse in New England," American Economic Review, American Economic Association, vol. 95(2), pages 376-380, May. [Downloadable!]
  39. Muriel Niederle & Alvin E. Roth, 2007. "The Effects of a Centralized Clearinghouse on Job Placement, Wages, and Hiring Practices," NBER Working Papers 13529, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  40. Parag A. Pathak & Tayfun Sonmez, 2008. "Leveling the Playing Field: Sincere and Sophisticated Players in the Boston Mechanism," American Economic Review, American Economic Association, vol. 98(4), pages 1636-52, September. [Downloadable!]
  41. Adachi, Hiroyuki, 2000. "On a characterization of stable matchings," Economics Letters, Elsevier, vol. 68(1), pages 43-49, July. [Downloadable!] (restricted)
  42. Demange, Gabrielle & Gale, David, 1985. "The Strategy Structure of Two-sided Matching Markets," Econometrica, Econometric Society, vol. 53(4), pages 873-88, July. [Downloadable!] (restricted)
  43. Roth, Alvin E & Sotomayor, Marilda, 1989. "The College Admissions Problem Revisited," Econometrica, Econometric Society, vol. 57(3), pages 559-70, May. [Downloadable!] (restricted)
  44. Kamecke, Ulrich, 1998. "Wage Formation in a Centralized Matching Market," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(1), pages 33-53, February.
  45. Muriel Niederle & Alvin E. Roth, 2005. "The Gastroenterology Fellowship Market: Should There Be a Match?," American Economic Review, American Economic Association, vol. 95(2), pages 372-375, May. [Downloadable!]
  46. Muriel Niederle & Alvin E. Roth, 2003. "Unraveling Reduces Mobility in a Labor Market: Gastroenterology with and without a Centralized Match," Journal of Political Economy, University of Chicago Press, vol. 111(6), pages 1342-1352, December. [Downloadable!] (restricted)
  47. C. Nicholas McKinney & Muriel Niederle & Alvin E. Roth, 2005. "The Collapse of a Medical Labor Clearinghouse (and Why Such Failures Are Rare)," American Economic Review, American Economic Association, vol. 95(3), pages 878-889, June. [Downloadable!]
  48. Hao Li & Wing Suen, 2000. "Risk Sharing, Sorting, and Early Contracting," Journal of Political Economy, University of Chicago Press, vol. 108(5), pages 1058-1087, October. [Downloadable!] (restricted)
  49. Atila Abdulkadiroglu & Parag A Pathak & Alvin E Roth, 2008. "Strategy-proofness vs. Efficiency in Matching with Indifferences: Redisigning the NYC High School Match," Levine's Bibliography 122247000000002108, UCLA Department of Economics. [Downloadable!]
  50. Roth, Alvin E, 1991. "A Natural Experiment in the Organization of Entry-Level Labor Markets: Regional Markets for New Physicians and Surgeons in the United Kingdom," American Economic Review, American Economic Association, vol. 81(3), pages 415-40, June. [Downloadable!] (restricted)
  51. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September. [Downloadable!]
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  52. Roth, Alvin E., 1982. "Incentive compatibility in a market with indivisible goods," Economics Letters, Elsevier, vol. 9(2), pages 127-132. [Downloadable!] (restricted)
  53. Sotomayor, Marilda, 1996. "A Non-constructive Elementary Proof of the Existence of Stable Marriages," Games and Economic Behavior, Elsevier, vol. 13(1), pages 135-137, March. [Downloadable!] (restricted)
  54. Michael Ostrovsky, 2008. "Stability in Supply Chain Networks," American Economic Review, American Economic Association, vol. 98(3), pages 897-923, June. [Downloadable!]
  55. Sonmez, Tayfun, 1999. "Can Pre-arranged Matches Be Avoided in Two-Sided Matching Markets?," Journal of Economic Theory, Elsevier, vol. 86(1), pages 148-156, May. [Downloadable!] (restricted)
  56. Alvin E. Roth & Elliott Peranson, 1999. "The Redesign of the Matching Market for American Physicians: Some Engineering Aspects of Economic Design," NBER Working Papers 6963, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  57. Sotomayor, Marilda, 2000. "Existence of stable outcomes and the lattice property for a unified matching market," Mathematical Social Sciences, Elsevier, vol. 39(2), pages 119-132, March. [Downloadable!] (restricted)
  58. Hao Li & Wing Suen, 2004. "Self-Fulfilling Early-Contracting Rush," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 45(1), pages 301-324, 02. [Downloadable!] (restricted)
  59. Demange, Gabrielle & Gale, David & Sotomayor, Marilda, 1986. "Multi-Item Auctions," Journal of Political Economy, University of Chicago Press, vol. 94(4), pages 863-72, August. [Downloadable!] (restricted)
  60. Jeremy Bulow & Jonathan Levin, 2006. "Matching and Price Competition," American Economic Review, American Economic Association, vol. 96(3), pages 652-668, June. [Downloadable!]
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  61. Roth, Alvin E, 1984. "The Evolution of the Labor Market for Medical Interns and Residents: A Case Study in Game Theory," Journal of Political Economy, University of Chicago Press, vol. 92(6), pages 991-1016, December. [Downloadable!] (restricted)
  62. Kesten, Onur, 2006. "On two competing mechanisms for priority-based allocation problems," Journal of Economic Theory, Elsevier, vol. 127(1), pages 155-171, March. [Downloadable!] (restricted)
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. James W. Boudreau, 2008. "Preference Structure and Random Paths to Stability in Matching Markets," Working papers 2008-29, University of Connecticut, Department of Economics. [Downloadable!]
    Other versions:
  2. Michael Schwarz & M. Bumin Yenmez, 2009. "Median Stable Matching," NBER Working Papers 14689, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  3. Eric Weese, 2008. "Political Mergers as Coalition Formation: Evidence from Japanese Municipal Amalgamations," Global COE Hi-Stat Discussion Paper Series gd08-017, Institute of Economic Research, Hitotsubashi University. [Downloadable!]
  4. Alexey Kushnir, 2009. "Matching Markets with Signals," Working Papers 2009.39, Fondazione Eni Enrico Mattei. [Downloadable!]
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