Stable Marriage: Loyalty vs. Competition
Amit Ronen, Jonah Evan Hess, Yael Belfer, Simon Mauras, Alon Eden

TL;DR
This paper investigates how loyalty in hospitals affects the stable matching problem, revealing that even high loyalty cannot prevent the detrimental impact of competition on doctors' match quality in unbalanced markets.
Contribution
It introduces a model of hospital loyalty in stable matching, showing that high loyalty does not significantly mitigate the adverse effects of competition.
Findings
Loyalty parameter $k$ influences stability but does not eliminate competition effects.
In unbalanced markets, doctors' expected rank remains high despite high hospital loyalty.
Competition's impact on match quality is more severe than the proposing side advantage.
Abstract
We consider the stable matching problem (e.g. between doctors and hospitals) in a one-to-one matching setting, where preferences are drawn uniformly at random. It is known that when doctors propose and the number of doctors equals the number of hospitals, then the expected rank of doctors for their match is , while the expected rank of the hospitals for their match is , where is the size of each side of the market. However, when adding even a single doctor, [Ashlagi, Kanoria and Leshno, 2017] show that the tables have turned: doctors have expected rank of while hospitals have expected rank of . That is, (slight) competition has a much more dramatically harmful effect than the benefit of being on the proposing side. Motivated by settings where agents inflate their value for an item if it is already allocated to them…
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Taxonomy
TopicsGender, Labor, and Family Dynamics
