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Reallocation with Priorities

Author

Listed:
  • Julien Combe

    (CREST, Ecole Polytechnique, France)

  • Jan Christoph Schlegel

    (City, University of London, United Kingdom)

Abstract
We consider a reallocation problem with priorities where each agent is initially endowed with a house and is willing to exchange it but each house has a priority ordering over the agents of the market. In this setting, it is well known that there is no individually rational and stable mechanism. As a result, the literature has introduced a modified stability notion called µ0-stability. In contrast to college admission problems, in which priorities are present but there is no initial endowment, we show that the modified Deferred Acceptance mechanism identified in the literature is not the only individually rational, strategy-proof and µ0-stable mechanism. By introducing a new axiom called the independence of irrelevant agents and using the standard axiom of unanimity, we show that the modified Deferred Acceptance mechanism is the unique mechanism that is individually rational, strategy-proof, µ0-stable, unanimous and independent of irrelevant agents.

Suggested Citation

  • Julien Combe & Jan Christoph Schlegel, 2021. "Reallocation with Priorities," Working Papers 2021-09, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2021-09
    as

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    File URL: http://crest.science/RePEc/wpstorage/2021-09.pdf
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    References listed on IDEAS

    as
    1. Ehlers, Lars & Klaus, Bettina, 2016. "Object allocation via deferred-acceptance: Strategy-proofness and comparative statics," Games and Economic Behavior, Elsevier, vol. 97(C), pages 128-146.
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    4. Pablo Guillen & Onur Kesten, 2012. "Matching Markets With Mixed Ownership: The Case For A Real‐Life Assignment Mechanism," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 53(3), pages 1027-1046, August.
    5. Haluk I. Ergin, 2002. "Efficient Resource Allocation on the Basis of Priorities," Econometrica, Econometric Society, vol. 70(6), pages 2489-2497, November.
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    7. Onur Kesten, 2010. "School Choice with Consent," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 125(3), pages 1297-1348.
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    Cited by:

    1. Afacan, Mustafa Oǧuz, 2024. "Non-vetoed matching with status quo," Journal of Mathematical Economics, Elsevier, vol. 111(C).

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    More about this item

    Keywords

    Matching; Housing Market; Reallocation; Stability; Priorities.;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design

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