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Unique stable matchings

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  • Gutin, Gregory Z.
  • Neary, Philip R.
  • Yeo, Anders

Abstract

In this paper we consider the issue of a unique prediction in one-to-one two-sided matching markets, as defined by Gale and Shapley (1962), and we prove the following: TheoremLet P be a one-to-one two-sided matching market and letP⁎be its associated normal form, a (weakly) smaller matching market with the same set of stable matchings that can be obtained using procedures introduced inIrving and Leather (1986)andBalinski and Ratier (1997). The following three statements are equivalent:(a)P has a unique stable matching.(b)Preferences onP⁎are acyclic, as defined byChung (2000).(c)InP⁎every market participant's preference list is a singleton.

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  • Gutin, Gregory Z. & Neary, Philip R. & Yeo, Anders, 2023. "Unique stable matchings," Games and Economic Behavior, Elsevier, vol. 141(C), pages 529-547.
    • Handle: RePEc:eee:gamebe:v:141:y:2023:i:c:p:529-547
    DOI: 10.1016/j.geb.2023.07.010
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