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Impossibility of weakly stable and strategy-proof mechanism

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  • Cho, Sung-Ho
  • Koshimura, Miyuki
  • Mandal, Pinaki
  • Yahiro, Kentaro
  • Yokoo, Makoto

Abstract

Many real matching markets are subject to distributional constraints. When the set of feasible matchings is restricted by some distributional constraints, a stable matching may not exist. In contrast, a weakly stable matching is guaranteed to exist under a very general class of constraints that satisfies a condition called heredity. However, it has been an open question whether a weakly stable matching can be obtained by a strategy-proof mechanism. We negatively answer this open question; no weakly stable and strategy-proof mechanism exists under any heredity feasibility constraint in general.

Suggested Citation

  • Cho, Sung-Ho & Koshimura, Miyuki & Mandal, Pinaki & Yahiro, Kentaro & Yokoo, Makoto, 2022. "Impossibility of weakly stable and strategy-proof mechanism," Economics Letters, Elsevier, vol. 217(C).
    • Handle: RePEc:eee:ecolet:v:217:y:2022:i:c:s0165176522002269
    DOI: 10.1016/j.econlet.2022.110675
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    References listed on IDEAS

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    1. Ehlers, Lars & Hafalir, Isa E. & Yenmez, M. Bumin & Yildirim, Muhammed A., 2014. "School choice with controlled choice constraints: Hard bounds versus soft bounds," Journal of Economic Theory, Elsevier, vol. 153(C), pages 648-683.
    2. Yuichiro Kamada & Fuhito Kojima, 2015. "Efficient Matching under Distributional Constraints: Theory and Applications," American Economic Review, American Economic Association, vol. 105(1), pages 67-99, January.
    3. Haris Aziz & Anton Baychkov & Peter Biro, 2021. "Cutoff stability under distributional constraints with an application to summer internship matching," Papers 2102.02931, arXiv.org, revised Oct 2023.
    4. Kojima, Fuhito & Tamura, Akihisa & Yokoo, Makoto, 2018. "Designing matching mechanisms under constraints: An approach from discrete convex analysis," Journal of Economic Theory, Elsevier, vol. 176(C), pages 803-833.
    5. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
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    More about this item

    Keywords

    Two-sided matching; Weak stability; Strategy-proofness;
    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
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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