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Reallocation with Priorities and Minimal Envy Mechanisms

Author

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  • Julien Combe

    (FAIRPLAY - IA coopérative : équité, vie privée, incitations - CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - CNRS - Centre National de la Recherche Scientifique - Inria Saclay - Ile de France - Inria - Institut National de Recherche en Informatique et en Automatique - IP Paris - Institut Polytechnique de Paris - Criteo AI Lab - Criteo [Paris], IP Paris - Institut Polytechnique de Paris, CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - CNRS - Centre National de la Recherche Scientifique, X - École polytechnique - IP Paris - Institut Polytechnique de Paris)

Abstract
We investigate the problem of reallocation with priorities where one has to assign objects or positions to individuals. Agents can have an initial ownership over an object. Each object has a priority ordering over the agents. In this framework, there is no mechanism that is both individually rational (IR) and stable, i.e. has no blocking pairs. Given this impossibility, an alternative approach is to compare mechanisms based on the blocking pairs they generate. A mechanism has minimal envy within a set of mechanisms if there is no other mechanism in the set that always leads to a set of blocking pairs included in the one of the former mechanism. Our main result shows that the modified Deferred Acceptance mechanism (Guillen and Kesten in Int Econ Rev 53(3):1027–1046, 2012), is a minimal envy mechanism in the set of IR and strategy-proof mechanisms. We also show that an extension of the Top Trading Cycle (Karakaya et al. in J Econ Theory 184:104948, 2019) mechanism is a minimal envy mechanism in the set of IR, strategy-proof and Pareto-efficient mechanisms. These two results extend the existing ones in school choice.

Suggested Citation

  • Julien Combe, 2022. "Reallocation with Priorities and Minimal Envy Mechanisms," Post-Print hal-03951678, HAL.
    • Handle: RePEc:hal:journl:hal-03951678
    DOI: 10.1007/s00199-022-01465-x
    Note: View the original document on HAL open archive server: https://inria.hal.science/hal-03951678
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    References listed on IDEAS

    as
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    2. Atila Abdulkadiroğlu & Yeon-Koo Che & Parag A. Pathak & Alvin E. Roth & Olivier Tercieux, 2020. "Efficiency, Justified Envy, and Incentives in Priority-Based Matching," American Economic Review: Insights, American Economic Association, vol. 2(4), pages 425-442, December.
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    Cited by:

    1. Battal Doğan & M. Bumin Yenmez, 2023. "When does an additional stage improve welfare in centralized assignment?," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(4), pages 1145-1173, November.
    2. Tayfun Sönmez & M. Utku Ünver, 2024. "Matching under Non-transferable Utility: Applications," Boston College Working Papers in Economics 1069, Boston College Department of Economics.
    3. Peter Doe, 2024. "Matching With Pre-Existing Binding Agreements: The Agreeable Core," Papers 2406.08700, arXiv.org, revised Oct 2024.
    4. Doudou Gong & Bas Dietzenbacher & Hans Peters, 2024. "Mechanisms and axiomatics for division problems with single-dipped preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 78(3), pages 789-813, November.
    5. Morrill, Thayer & Roth, Alvin E., 2024. "Top trading cycles," Journal of Mathematical Economics, Elsevier, vol. 112(C).

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    More about this item

    Keywords

    Matching; Reallocation with priorities; Minimal envy mechanisms;
    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
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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