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An algorithm to compute the full set of many-to-many stable matchings

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  • Martinez, Ruth
  • Masso, Jordi
  • Neme, Alejandro
  • Oviedo, Jorge

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  • 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.
    • Handle: RePEc:eee:matsoc:v:47:y:2004:i:2:p:187-210
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    References listed on IDEAS

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    1. Ahmet Alkan, 2001. "original papers : On preferences over subsets and the lattice structure of stable matchings," Review of Economic Design, Springer;Society for Economic Design, vol. 6(1), pages 99-111.
    2. Charles Blair, 1988. "The Lattice Structure of the Set of Stable Matchings with Multiple Partners," Mathematics of Operations Research, INFORMS, vol. 13(4), pages 619-628, November.
    3. Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, vol. 52(1), pages 47-57, January.
    4. Marilda Sotomayor, 1999. "The lattice structure of the set of stable outcomes of the multiple partners assignment game," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(4), pages 567-583.
    5. Sotomayor, Marilda, 1999. "Three remarks on the many-to-many stable matching problem," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 55-70, July.
    6. 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.
    7. Alvin E. Roth, 1985. "Conflict and Coincidence of Interest in Job Matching: Some New Results and Open Questions," Mathematics of Operations Research, INFORMS, vol. 10(3), pages 379-389, August.
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    Citations

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    Cited by:

    1. Bonifacio, Agustín G. & Juarez, Noelia & Neme, Pablo & Oviedo, Jorge, 2022. "Cycles to compute the full set of many-to-many stable matchings," Mathematical Social Sciences, Elsevier, vol. 117(C), pages 20-29.
    2. Paula Jaramillo & Çaǧatay Kayı & Flip Klijn, 2014. "On the exhaustiveness of truncation and dropping strategies in many-to-many matching markets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(4), pages 793-811, April.
    3. Alvin Roth, 2008. "Deferred acceptance algorithms: history, theory, practice, and open questions," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 537-569, March.
    4. 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.
    5. Chen, Ning & Li, Mengling, 2013. "Ties matter: improving efficiency in course allocation by introducing ties," MPRA Paper 47031, University Library of Munich, Germany.
    6. Eliana Pepa Risma, 2022. "Matching with contracts: calculation of the complete set of stable allocations," Theory and Decision, Springer, vol. 93(3), pages 449-461, October.
    7. Klijn, Flip & Yazıcı, Ayşe, 2014. "A many-to-many ‘rural hospital theorem’," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 63-73.
    8. Kominers, Scott Duke, 2010. "Matching with preferences over colleagues solves classical matching," Games and Economic Behavior, Elsevier, vol. 68(2), pages 773-780, March.
    9. Ayşe Yazıcı, 2017. "Probabilistic stable rules and Nash equilibrium in two-sided matching problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(1), pages 103-124, March.
    10. Juárez, Noelia & Neme, Pablo & Oviedo, Jorge, 2022. "Lattice structure of the random stable set in many-to-many matching markets," Games and Economic Behavior, Elsevier, vol. 132(C), pages 255-273.
    11. Agustin G. Bonifacio & Nadia Guiñazú & Noelia Juarez & Pablo Neme & Jorge Oviedo, 2024. "The lattice of envy-free many-to-many matchings with contracts," Theory and Decision, Springer, vol. 96(1), pages 113-134, February.
    12. Bettina Klaus & David F. Manlove & Francesca Rossi, 2014. "Matching under Preferences," Cahiers de Recherches Economiques du Département d'économie 14.07, Université de Lausanne, Faculté des HEC, Département d’économie.
    13. Mandal, Pinaki & Roy, Souvik, 2021. "Matchings under Stability, Minimum Regret, and Forced and Forbidden Pairs in Marriage Problem," MPRA Paper 107213, University Library of Munich, Germany.
    14. Gregory Gutin & Philip R. Neary & Anders Yeo, 2022. "Finding all stable matchings with assignment constraints," Papers 2204.03989, arXiv.org, revised Jun 2024.
    15. Jiao, Zhenhua & Tian, Guoqiang, 2017. "The Blocking Lemma and strategy-proofness in many-to-many matchings," Games and Economic Behavior, Elsevier, vol. 102(C), pages 44-55.
    16. Pavlos Eirinakis & Dimitrios Magos & Ioannis Mourtos & Panayiotis Miliotis, 2012. "Finding All Stable Pairs and Solutions to the Many-to-Many Stable Matching Problem," INFORMS Journal on Computing, INFORMS, vol. 24(2), pages 245-259, May.
    17. Papai, Szilvia, 2004. "Unique stability in simple coalition formation games," Games and Economic Behavior, Elsevier, vol. 48(2), pages 337-354, August.

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