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Matching With Couples: A Multidisciplinary Survey

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  • PÉTER BIRÓ

    ()
    (Institute of Economics, Hungarian Academy of Sciences, Budaörsi út 45, Budapest, H-1112, Hungary)

  • FLIP KLIJN

    ()
    (Institute for Economic Analysis (CSIC) and Barcelona GSE, Campus UAB, 08193 Bellaterra (Barcelona), Spain)

Abstract

This survey deals with two-sided matching markets where one set of agents (workers/residents) has to be matched with another set of agents (firms/hospitals). We first give a short overview of a selection of classical results. Then, we review recent contributions to a complex and representative case of matching with complementarities, namely matching markets with couples. We discuss contributions from computer scientists, economists, and game theorists.

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Bibliographic Info

Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Game Theory Review.

Volume (Year): 15 (2013)
Issue (Month): 02 ()
Pages: 1340008-1-1340008-18

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Handle: RePEc:wsi:igtrxx:v:15:y:2013:i:02:p:1340008-1-1340008-18

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Related research

Keywords: Matching; couples; stability; computational complexity; incentive compatibility; restricted domains; large markets; 03D15; 68-02; 68Q17; 68Q25; 68R10; 68U10; 90B10; 90C27; 90C59; 91-02; 91-08; 91A06; 91A80; 91B10; 91B68;

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References

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  1. Herbert E. Scarf, 1965. "The Core of an N Person Game," Cowles Foundation Discussion Papers 182R, Cowles Foundation for Research in Economics, Yale University.
  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.
  3. Bettina Klaus & Flip Klijn, 2005. "Corrigendum: Stable Matchings and Preferences of Couples," UFAE and IAE Working Papers 653.05, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  4. 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.
  5. Florian M. Biermann, 2011. "A Measure to compare Matchings in Marriage Markets," Discussion Paper Series dp575, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  6. 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.
  7. Bettina Klaus & Flip Klijn, 2002. "Some things couples always wanted to know about stable matchings (but were afraid to ask)," UFAE and IAE Working Papers 552.02, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC), revised 01 Oct 2005.
  8. 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.
  9. Paul Milgrom, 2003. "Matching with Contracts," Working Papers 03003, Stanford University, Department of Economics.
  10. Klaus, Bettina & Klijn, Flip, 2005. "Stable matchings and preferences of couples," Journal of Economic Theory, Elsevier, vol. 121(1), pages 75-106, March.
  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.
  12. Alvin Roth, 2008. "Deferred acceptance algorithms: history, theory, practice, and open questions," International Journal of Game Theory, Springer, vol. 36(3), pages 537-569, March.
  13. Klijn, Flip & Masso, Jordi, 2003. "Weak stability and a bargaining set for the marriage model," Games and Economic Behavior, Elsevier, vol. 42(1), pages 91-100, January.
  14. Sonmez, Tayfun, 1997. "Manipulation via Capacities in Two-Sided Matching Markets," Journal of Economic Theory, Elsevier, vol. 77(1), pages 197-204, November.
  15. Tayfun Sönmez & M. Utku Ünver, 2009. "Matching, Allocation, and Exchange of Discrete Resources," Boston College Working Papers in Economics 717, Boston College Department of Economics.
  16. repec:ebl:ecbull:v:3:y:2004:i:45:p:1-11 is not listed on IDEAS
  17. Fuhito Kojima & M. Ünver, 2008. "Random paths to pairwise stability in many-to-many matching problems: a study on market equilibration," International Journal of Game Theory, Springer, vol. 36(3), pages 473-488, March.
  18. Dutta, B. & Masso, J., 1996. "Stability of Matchings when Individuals Have Preferences Over Colleagues," UFAE and IAE Working Papers 325.96, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  19. Fuhito Kojima & Parag A. Pathak & Alvin E. Roth, 2010. "Matching with Couples: Stability and Incentives in Large Markets," NBER Working Papers 16028, National Bureau of Economic Research, Inc.
  20. Bettina Klaus & Flip Klijn, 2004. "Paths to Stability for Matching Markets with Couples," Working Papers 156, Barcelona Graduate School of Economics.
  21. Roth, Alvin E., 1982. "Incentive compatibility in a market with indivisible goods," Economics Letters, Elsevier, vol. 9(2), pages 127-132.
  22. Fuhito Kojima & Peter Troyan, 2011. "Matching And Market Design: An Introduction To Selected Topics," The Japanese Economic Review, Japanese Economic Association, vol. 62(1), pages 82-98, 03.
  23. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
  24. Peter Biro & Tamas Fleiner & Rob Irving, 2013. "Matching Couples with Scarf's Algorithm," IEHAS Discussion Papers 1330, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.
  25. Klaus, Bettina & Klijn, Flip & Nakamura, Toshifumi, 2009. "Corrigendum to "Stable matchings and preferences of couples" [J. Econ. Theory 121 (1) (2005) 75-106]," Journal of Economic Theory, Elsevier, vol. 144(5), pages 2227-2233, September.
  26. Fuhito Kojima & Parag A. Pathak, 2009. "Incentives and Stability in Large Two-Sided Matching Markets," American Economic Review, American Economic Association, vol. 99(3), pages 608-27, June.
  27. Hatfield, John William & Kojima, Fuhito, 2010. "Substitutes and stability for matching with contracts," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1704-1723, September.
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Citations

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Cited by:
  1. Peter Biro & Tamas Fleiner, 2012. "Fractional solutions for capacitated NTU-games, with applications to stable matchings," IEHAS Discussion Papers 1234, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.
  2. Peter Biro & Tamas Fleiner & Rob Irving, 2013. "Matching Couples with Scarf's Algorithm," IEHAS Discussion Papers 1330, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.
  3. Peter Biro & Sofya Kiselgof, 2013. "College admissions with stable score-limits," IEHAS Discussion Papers 1306, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.

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