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Stability and strategy-proofness for matching with interval constraints

Author

Listed:
  • Tsuyoshi Adachi

    (Faculty of Political Science and Economics, Waseda University)

  • Yuki Ishibashi

    (Graduate School of Economics, Waseda University)

Abstract

We consider a matching problem with interval constraints under the hierarchical region structure. We proposes new stability, interval respecting stability, for matching problems with interval constraints, which defines ceiling respecting stability (Kamada and Kojima, 2018) using a blocking coalition instead of a pair, following floor respecting stability (Akin, 2021). Interval respecting stability coincides with floor respecting stability in problems with floor constraints and implies ceiling respecting stability in problems with ceiling constraints. In addition, interval respecting stability generally implies Pareto efficiency, unlike ceiling respecting stability. We also propose a generalized flexible deferred acceptance algorithm for a problem with interval constraints, which is a flexible deferred acceptance algorithm (i.e., cumulative offer process) that allocates quotas between regions, reserving additional numbers for doctors’ future offers needed to fill the floor constraints even if there are no offers now. Under acceptability, we show that further combining the above algorithm with the serial dictatorship yields an algorithm that satisfies interval respecting stability. We also show that the combinded algorithm is strategy-proof for doctors.

Suggested Citation

  • Tsuyoshi Adachi & Yuki Ishibashi, 2022. "Stability and strategy-proofness for matching with interval constraints," Working Papers 2124, Waseda University, Faculty of Political Science and Economics.
    • Handle: RePEc:wap:wpaper:2124
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    References listed on IDEAS

    as
    1. Fuhito Kojima & Mihai Manea, 2010. "Axioms for Deferred Acceptance," Econometrica, Econometric Society, vol. 78(2), pages 633-653, March.
    2. 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.
    3. EHLERS, Lars, 2010. "School Choice with Control," Cahiers de recherche 2010-05, Universite de Montreal, Departement de sciences economiques.
    4. Aygün, Orhan & Turhan, Bertan, 2020. "Dynamic reserves in matching markets," Journal of Economic Theory, Elsevier, vol. 188(C).
    5. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
    6. Ahmet Alkan, 2001. "original papers : On preferences over subsets and the lattice structure of stable matchings," Review of Economic Design, Springer;Society for Economic Design, vol. 6(1), pages 99-111.
    7. Akin, Sumeyra, 2021. "Matching with floor constraints," Theoretical Economics, Econometric Society, vol. 16(3), July.
    8. 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.
    9. John William Hatfield & Scott Duke Kominers & Alexander Westkamp, 2021. "Stability, Strategy-Proofness, and Cumulative Offer Mechanisms [Stability and Incentives for College Admissions with Budget Constraints]," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 88(3), pages 1457-1502.
    10. Hirata, Daisuke & Kasuya, Yusuke, 2014. "Cumulative offer process is order-independent," Economics Letters, Elsevier, vol. 124(1), pages 37-40.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Matching; Interval constraints; Stability; Strategy-proofness; Cumulative offer process;
    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
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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