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A direct proof of the short-side advantage in random matching markets

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  • Mauras, Simon
  • Prałat, Paweł
  • Vetta, Adrian

Abstract

We study the stable matching problem under the random matching model where the preferences of the doctors and hospitals are sampled uniformly and independently at random. In a balanced market with n doctors and n hospitals, the doctor-proposing deferred-acceptance algorithm gives doctors an expected rank of order log⁡n for their partners and hospitals an expected rank of order nlog⁡n for their partners (Pittel, 1989; Wilson, 1972). This situation is reversed in an unbalanced market with n+1 doctors and n hospitals (Ashlagi et al., 2017), a phenomenon known as the short-side advantage. The current proofs (Ashlagi et al., 2017; Cai and Thomas, 2022) of this fact are indirect, counter-intuitively being based upon analyzing the hospital-proposing deferred-acceptance algorithm. In this paper we provide a direct proof of the short-side advantage, explicitly analyzing the doctor-proposing deferred-acceptance algorithm. Our proof sheds light on how and why the phenomenon arises.

Suggested Citation

  • Mauras, Simon & Prałat, Paweł & Vetta, Adrian, 2025. "A direct proof of the short-side advantage in random matching markets," Games and Economic Behavior, Elsevier, vol. 154(C), pages 53-61.
    • Handle: RePEc:eee:gamebe:v:154:y:2025:i:c:p:53-61
    DOI: 10.1016/j.geb.2025.08.013
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