IDEAS home Printed from https://ideas.repec.org/p/inn/wpaper/2018-02.html
   My bibliography  Save this paper

Pairwise stable matching in large economies

Author

Listed:
  • Michael Greinecker
  • Christopher Kah

Abstract

We formulate a general model and stability notion for two-sided pairwise matching problems with individually insignificant agents. Matchings are formulated as joint distributions over the characteristics of the populations to be matched. These characteristics can be high-dimensional and need not be included in compact spaces. Stable matchings exist with and without transfers and stable matchings correspond exactly to limits of stable matchings for finite agent models. We can embed existing continuum matching models and stability notions with transferable utility as special cases of our model and stability notion. In contrast to finite agent matching models, stable matchings exist under a general class of externalities. This might pave the way for integrating matching problems in other economic models.

Suggested Citation

  • Michael Greinecker & Christopher Kah, 2018. "Pairwise stable matching in large economies," Working Papers 2018-02, Faculty of Economics and Statistics, Universität Innsbruck.
    • Handle: RePEc:inn:wpaper:2018-02
    as

    Download full text from publisher

    File URL: https://www2.uibk.ac.at/downloads/c4041030/wpaper/2018-02.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Cole, Harold L. & Mailath, George J. & Postlewaite, Andrew, 2001. "Efficient Non-Contractible Investments in Large Economies," Journal of Economic Theory, Elsevier, vol. 101(2), pages 333-373, December.
    2. Pierre-André Chiappori & Robert McCann & Lars Nesheim, 2010. "Hedonic price equilibria, stable matching, and optimal transport: equivalence, topology, and uniqueness," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(2), pages 317-354, February.
    3. Bryan Ellickson & Birgit Grodal & Suzanne Scotchmer & William R. Zame, 1999. "Clubs and the Market," Econometrica, Econometric Society, vol. 67(5), pages 1185-1218, 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. Chiappori, Pierre-André & Reny, Philip J., 2016. "Matching to share risk," Theoretical Economics, Econometric Society, vol. 11(1), January.
    6. Cole, Harold L. & Prescott, Edward C., 1997. "Valuation Equilibrium with Clubs," Journal of Economic Theory, Elsevier, vol. 74(1), pages 19-39, May.
    7. Itai Ashlagi & Yash Kanoria & Jacob D. Leshno, 2017. "Unbalanced Random Matching Markets: The Stark Effect of Competition," Journal of Political Economy, University of Chicago Press, vol. 125(1), pages 69-98.
    8. Pierre-André Chiappori & Bernard Salanié, 2016. "The Econometrics of Matching Models," Journal of Economic Literature, American Economic Association, vol. 54(3), pages 832-861, September.
    9. Chiappori, Pierre-André & Gugl, Elisabeth, 2020. "Transferable utility and demand functions," Theoretical Economics, Econometric Society, vol. 15(4), November.
    10. Eduardo M. Azevedo & Jacob D. Leshno, 2016. "A Supply and Demand Framework for Two-Sided Matching Markets," Journal of Political Economy, University of Chicago Press, vol. 124(5), pages 1235-1268.
    11. Mourad Baïou & Michel Balinski, 2002. "The Stable Allocation (or Ordinal Transportation) Problem," Mathematics of Operations Research, INFORMS, vol. 27(3), pages 485-503, August.
    12. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, October.
    13. Mourad Baïou & Michel Balinski, 2002. "Erratum: The Stable Allocation (or Ordinal Transportation) Problem," Mathematics of Operations Research, INFORMS, vol. 27(4), pages 662-680, November.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Michael Greinecker & Christopher Kah, 2018. "Pairwise stable matching in large economies," Graz Economics Papers 2018-01, University of Graz, Department of Economics.
    2. Michael Greinecker & Christopher Kah, 2021. "Pairwise Stable Matching in Large Economies," Econometrica, Econometric Society, vol. 89(6), pages 2929-2974, November.
    3. Manjunath, Vikram, 2016. "Fractional matching markets," Games and Economic Behavior, Elsevier, vol. 100(C), pages 321-336.
    4. Laurens Cherchye & Thomas Demuynck & Bram De Rock & Frederic Vermeulen, 2017. "Household Consumption When the Marriage Is Stable," American Economic Review, American Economic Association, vol. 107(6), pages 1507-1534, June.
    5. Guillaume Haeringer & Vincent Iehlé, 2019. "Two-Sided Matching with (Almost) One-Sided Preferences," American Economic Journal: Microeconomics, American Economic Association, vol. 11(3), pages 155-190, August.
    6. Scotchmer, Suzanne & Shannon, Chris, 2019. "Verifiability and group formation in markets," Journal of Economic Theory, Elsevier, vol. 183(C), pages 417-477.
    7. Aue, Robert & Bach, Maximilian & Heigle, Julia & Klein, Thilo & Pfeiffer, Friedhelm & Zapp, Kristina, 2020. "The implication of school admission rules for segregation and educational inequality: Research report," ZEW Expertises, ZEW - Leibniz Centre for European Economic Research, number 223254, June.
    8. Alfred Galichon & Simon Weber, 2024. "Matching under Imperfectly Transferable Utility," Papers 2403.05222, arXiv.org, revised Oct 2024.
    9. Hector Chade & Jan Eeckhout & Lones Smith, 2017. "Sorting through Search and Matching Models in Economics," Journal of Economic Literature, American Economic Association, vol. 55(2), pages 493-544, June.
    10. Pierre-André Chiappori & Bernard Salanié, 2016. "The Econometrics of Matching Models," Journal of Economic Literature, American Economic Association, vol. 54(3), pages 832-861, September.
    11. Nir Dagan & Oscar Volij, 2000. "Formation of Nations in a Welfare‐State Minded World," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 2(2), pages 157-181, April.
    12. Atı̇la Abdulkadı̇roğlu & Joshua D. Angrist & Yusuke Narita & Parag Pathak, 2022. "Breaking Ties: Regression Discontinuity Design Meets Market Design," Econometrica, Econometric Society, vol. 90(1), pages 117-151, January.
    13. Baiyu Dong & Yu-Wei Hsieh & Xing Zhang, 2022. "Implementing Maximum Likelihood Estimation of Empirical Matching Models," Computational Economics, Springer;Society for Computational Economics, vol. 59(1), pages 1-32, January.
    14. Pierre-André Chiappori & Monica Costa Dias & Costas Meghir, 2018. "The Marriage Market, Labor Supply, and Education Choice," Journal of Political Economy, University of Chicago Press, vol. 126(S1), pages 26-72.
    15. Ellickson, Bryan & Grodal, Birgit & Scotchmer, Suzanne & Zame, William R., 2001. "Clubs and the Market: Large Finite Economies," Journal of Economic Theory, Elsevier, vol. 101(1), pages 40-77, November.
    16. Philippe Jehiel & Laurent Lamy, 2018. "A Mechanism Design Approach to the Tiebout Hypothesis," Journal of Political Economy, University of Chicago Press, vol. 126(2), pages 735-760.
    17. John P. Conley & Myrna Holtz Wooders, 1998. "The Tiebout Hypothesis: On the Existence of Pareto Efficient Competitive Equilibrium," Working Papers mwooders-98-06, University of Toronto, Department of Economics.
    18. Michel Balinski, 2007. "Equitable representation and recruitment," Annals of Operations Research, Springer, vol. 149(1), pages 27-36, February.
    19. Alexander V. Kolesnikov & Fedor Sandomirskiy & Aleh Tsyvinski & Alexander P. Zimin, 2022. "Beckmann's approach to multi-item multi-bidder auctions," Papers 2203.06837, arXiv.org, revised Sep 2022.
    20. Pierre-André Chiappori & Alfred Galichon & Bernard Salanié, 2019. "On Human Capital and Team Stability," Journal of Human Capital, University of Chicago Press, vol. 13(2), pages 236-259.

    More about this item

    Keywords

    Stable matching; economies in distributional form; large markets;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inn:wpaper:2018-02. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Janette Walde (email available below). General contact details of provider: https://edirc.repec.org/data/fuibkat.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.