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Matching with Contracts

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Paul Milgrom

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Abstract

March 2003

We introduce a two-sided matching model with contracts that subsumes and extends the Gale-Shapley matching model, the Kelso-Crawford labor market model and the Ausubel-Milgrom package auction model. We identify the maximal set of preferences over contracts for which a stable match exists and the narrower set of preferences for which an analog of Roth’s “rural hospitals” result holds. Using the extended model, we characterize the dynamics of re-matching following a retirement and explore doctors’ incentives to report truthfully.

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Paper provided by Stanford University, Department of Economics in its series Working Papers with number 03003.

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Date of creation: Mar 2003
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Handle: RePEc:wop:stanec:03003

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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. Bulow, Jeremy I. & Levin, Jonathan, 2003. "Matching and Price Competition," Research Papers 1818, Stanford University, Graduate School of Business. [Downloadable!]
    Other versions:
  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. Adachi, Hiroyuki, 2000. "On a characterization of stable matchings," Economics Letters, Elsevier, vol. 68(1), pages 43-49, July. [Downloadable!] (restricted)
  4. 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)
  5. Gul, Faruk & Stacchetti, Ennio, 2000. "The English Auction with Differentiated Commodities," Journal of Economic Theory, Elsevier, vol. 92(1), pages 66-95, May. [Downloadable!] (restricted)
  6. Lawrence M. Ausubel & Peter Cramton & Paul Milgrom, 2004. "The Clock-Proxy Auction: A Practical Combinatorial Auction Design," Papers of Peter Cramton 04mit5, University of Maryland, Department of Economics - Peter Cramton, revised 2004. [Downloadable!]
  7. 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!]
  8. Peter Cramton & Yoav Shoham & Richard Steinberg, 2004. "Combinatorial Auctions," Papers of Peter Cramton 04mit, University of Maryland, Department of Economics - Peter Cramton, revised 2004. [Downloadable!]
  9. Alkan, Ahmet & Gale, David, 2003. "Stable schedule matching under revealed preference," Journal of Economic Theory, Elsevier, vol. 112(2), pages 289-306, October. [Downloadable!] (restricted)
  10. Paul R. Milgrom, 1985. "Auction Theory," Cowles Foundation Discussion Papers 779, Cowles Foundation, Yale University. [Downloadable!]
  11. Atila Abdulkadiroglu & Tayfun Smez, 2003. "School Choice: A Mechanism Design Approach," Discussion Papers 0203-18, Columbia University, Department of Economics. [Downloadable!]
  12. 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)
  13. 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)
  14. Lawrence M. Ausubel & Paul R. Milgrom, 2002. "Ascending Auctions with Package Bidding," The B.E. Journal of Theoretical Economics, Berkeley Electronic Press, vol. 0(1). [Downloadable!]
  15. Brewer, Paul J. & Plott, Charles R., 1996. "A binary conflict ascending price (BICAP) mechanism for the decentralized allocation of the right to use railroad tracks," International Journal of Industrial Organization, Elsevier, vol. 14(6), pages 857-886, October. [Downloadable!] (restricted)
  16. 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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  17. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July. [Downloadable!] (restricted)
  18. Atila Abdulkadiroglu, 2003. "College admissions with affirmative action," Discussion Papers 0203-19, Columbia University, Department of Economics. [Downloadable!]
  19. Paul Milgrom, 2000. "Putting Auction Theory to Work: The Simultaneous Ascending Auction," Journal of Political Economy, University of Chicago Press, vol. 108(2), pages 245-272, April. [Downloadable!] (restricted)
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  20. Atila Abdulkadiroglu & Tayfun Sonmez, 2003. "School Choice: A Mechanism Design Approach," American Economic Review, American Economic Association, vol. 93(3), pages 729-747, June. [Downloadable!]
  21. Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, vol. 52(1), pages 47-57, January. [Downloadable!] (restricted)
  22. Martinez, Ruth & Masso, Jordi & Neme, Alejandro & Oviedo, Jorge, 2000. "Single Agents and the Set of Many-to-One Stable Matchings," Journal of Economic Theory, Elsevier, vol. 91(1), pages 91-105, March. [Downloadable!] (restricted)
  23. 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!]
  24. 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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  25. 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)
  26. 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)
  27. 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)
  28. Blum, Yosef & Roth, Alvin E. & Rothblum, Uriel G., 1997. "Vacancy Chains and Equilibration in Senior-Level Labor Markets," Journal of Economic Theory, Elsevier, vol. 76(2), pages 362-411, October. [Downloadable!] (restricted)
  29. Lawrence M. Ausubel & Paul Milgrom, 2002. "Ascending Auctions with Package Bidding," Working Papers 02004, Stanford University, Department of Economics. [Downloadable!]
  30. 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)
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