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Core Many-to-one Matchings by Fixed-point Methods

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Author Info
Federico Echenique (Caltech)
Jorge Oviedo (Universidad de San Luis)

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Abstract

We characterize the core many-to-one matchings as fixed points of a map. Our characterization gives an algorithm for finding core allocations; the algorithm is efficient and simple to implement. Our characterization does not require substitutable preferences, so it is separate from the structure needed for the non-emptiness of the core. When preferences are substitutable, our characterization gives a simple proof of the lattice structure of core matchings, and it gives a method for computing the join and meet of two core matchings.

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Publisher Info
Paper provided by EconWPA in its series Game Theory and Information with number 0302001.

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Length: 30 pages
Date of creation: 13 Feb 2003
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Handle: RePEc:wpa:wuwpga:0302001

Note: Type of Document - PDF; prepared on Linux PC; to print on PostScript; pages: 30
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Web page: http://129.3.20.41

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Related research
Keywords: matching supermodular games tarski's fixed-point theorem

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Find related papers by JEL classification:
C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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References listed on IDEAS
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. 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)
  2. 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)
  3. 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)
  4. Sotomayor, Marilda, 1999. "Three remarks on the many-to-many stable matching problem," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 55-70, July. [Downloadable!] (restricted)
  5. 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)
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. 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. [Downloadable!] (restricted)
    Other versions:
  2. Paul Milgrom, 2003. "Matching with Contracts," Working Papers 03003, Stanford University, Department of Economics. [Downloadable!]
    Other versions:
  3. Federico Echenique & Jorge Oviedo, 2003. "A Theory of Stability in Many-to-many Matching Markets," Levine's Working Paper Archive 666156000000000374, UCLA Department of Economics. [Downloadable!]
    Other versions:
  4. David Cantala & Francisco Sánchez, 2008. "Welfare and stability in senior matching markets," International Journal of Game Theory, Springer, vol. 36(3), pages 369-392, March. [Downloadable!] (restricted)
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