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The Core Matchings of Markets with Transfers

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  • Christopher P. Chambers
  • Federico Echenique

Abstract

We characterize the structure of the set of core matchings of an assignment game (a two-sided market with transfers). Such a set satisfies a property we call consistency. Consistency of a set of matchings states that, for any matching v, if, for each agent i there exists a matching ? in the set for which ?(i) = v(i), then v is in the set. A set of matchings satisfies consistency if and only if there is an assignment game for which all elements of the set maximize the surplus. (JEL C78)

Suggested Citation

  • Christopher P. Chambers & Federico Echenique, 2015. "The Core Matchings of Markets with Transfers," American Economic Journal: Microeconomics, American Economic Association, vol. 7(1), pages 144-164, February.
    • Handle: RePEc:aea:aejmic:v:7:y:2015:i:1:p:144-64
    Note: DOI: 10.1257/mic.20130089
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    References listed on IDEAS

    as
    1. Eugene Choo & Aloysius Siow, 2006. "Who Marries Whom and Why," Journal of Political Economy, University of Chicago Press, vol. 114(1), pages 175-201, February.
    2. Becker, Gary S, 1973. "A Theory of Marriage: Part I," Journal of Political Economy, University of Chicago Press, vol. 81(4), pages 813-846, July-Aug..
    3. Jun Wako, 2006. "Another proof that assignment games have singleton cores only if multiple optimal matchings exist," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(1), pages 213-217, September.
    4. Federico Echenique & Sangmok Lee & Matthew Shum & M. Bumin Yenmez, 2013. "The Revealed Preference Theory of Stable and Extremal Stable Matchings," Econometrica, Econometric Society, vol. 81(1), pages 153-171, January.
    5. Federico Echenique, 2008. "What Matchings Can Be Stable? The Testable Implications of Matching Theory," Mathematics of Operations Research, INFORMS, vol. 33(3), pages 757-768, August.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Vijay V. Vazirani, 2023. "LP-Duality Theory and the Cores of Games," Papers 2302.07627, arXiv.org, revised Mar 2023.
    2. Federico Echenique & SangMok Lee & Matthew Shum & M. Bumin Yenmez, 2021. "Stability and Median Rationalizability for Aggregate Matchings," Games, MDPI, vol. 12(2), pages 1-15, April.
    3. Vijay V. Vazirani, 2022. "New Characterizations of Core Imputations of Matching and $b$-Matching Games," Papers 2202.00619, arXiv.org, revised Dec 2022.
    4. Delacrétaz, David & Loertscher, Simon & Marx, Leslie M. & Wilkening, Tom, 2019. "Two-sided allocation problems, decomposability, and the impossibility of efficient trade," Journal of Economic Theory, Elsevier, vol. 179(C), pages 416-454.
    5. Agatsuma, Yasushi, 2016. "Testable implications of the core in TU market games," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 23-29.
    6. R. Branzei & E. Gutiérrez & N. Llorca & J. Sánchez-Soriano, 2021. "Does it make sense to analyse a two-sided market as a multi-choice game?," Annals of Operations Research, Springer, vol. 301(1), pages 17-40, June.

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    More about this item

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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