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Core Many-To-One Matchings by Fixed-Point Methods

  • Echenique, Federico
  • Oviedo, Jorge

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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Paper provided by California Institute of Technology, Division of the Humanities and Social Sciences in its series Working Papers with number 1140.

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Date of creation: Sep 2002
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Publication status: Published: Published in Journal of Economic Theory, 115 (2004) 358-376.
Handle: RePEc:clt:sswopa:1140
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Order Information: Postal: Working Paper Assistant, Division of the Humanities and Social Sciences, 228-77, Caltech, Pasadena CA 91125
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  1. Sotomayor, Marilda, 1999. "Three remarks on the many-to-many stable matching problem," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 55-70, July.
  2. 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.
  3. 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.
  4. Ahmet Alkan, 2002. "A class of multipartner matching markets with a strong lattice structure," Economic Theory, Springer, vol. 19(4), pages 737-746.
  5. 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.
  6. Adachi, Hiroyuki, 2000. "On a characterization of stable matchings," Economics Letters, Elsevier, vol. 68(1), pages 43-49, July.
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