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Stability concepts in matching under distributional constraints

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  • Kamada, Yuichiro
  • Kojima, Fuhito

Abstract

Many real matching markets are subject to distributional constraints. To guide market designers faced with constraints, we propose new stability concepts. A matching is strongly stable if satisfying blocking pairs inevitably violates a constraint. We show that a strongly stable matching may not exist, and that existence is guaranteed if and only if all distributional constraints are trivial. To overcome this difficulty, we propose a more permissive concept, weak stability. We demonstrate a weakly stable matching always exists, implies efficiency, and is characterized by standard normative axioms. These results are obtained in a more general environment than those in existing studies, accommodating a wide variety of applications.

Suggested Citation

  • Kamada, Yuichiro & Kojima, Fuhito, 2017. "Stability concepts in matching under distributional constraints," Journal of Economic Theory, Elsevier, vol. 168(C), pages 107-142.
    • Handle: RePEc:eee:jetheo:v:168:y:2017:i:c:p:107-142
    DOI: 10.1016/j.jet.2016.12.006
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    References listed on IDEAS

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    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • 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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