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The properness of weak stability notions

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  • Zhang, Luosai

Abstract

Multiple weak stability notions have been proposed for two-sided matching problems, each based on a different perspective to justify the existence of certain blocking pairs. We introduce a criterion, called properness, to evaluate these weak stability notions. We say a notion of weak stability is proper if, whenever a matching is weakly stable, every matching that is more stable than it (admitting a subset of blocking pairs) is also weakly stable. We show that among existing notions of weak stability: the von Neumann and Morgenstern stable set, reasonable stability, α-equitability, partial stability, and the Tang-Zhang weak stability are proper, whereas the Klijn-Massó weak stability, essential stability, and priority-neutrality are not proper.

Suggested Citation

  • Zhang, Luosai, 2025. "The properness of weak stability notions," Economics Letters, Elsevier, vol. 247(C).
    • Handle: RePEc:eee:ecolet:v:247:y:2025:i:c:s0165176524006475
    DOI: 10.1016/j.econlet.2024.112163
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    References listed on IDEAS

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