On likely solutions of the stable matching problem with unequal numbers of men and women

TL;DR

This paper analyzes the stable matching problem with unequal numbers of men and women, deriving asymptotic formulas for the expected number of stable matchings and probability distributions of total ranks.

Contribution

It provides new asymptotic formulas for the expected number of stable matchings and the probability distributions of total ranks in the unequal case.

Findings

Asymptotic formulas for expected stable matchings

Probability of concentration for total ranks

Extension of prior work to unequal numbers

Abstract

Following up a recent work by Ashlagi, Kanoria and Leshno, we study a stable matching problem with unequal numbers of men and women, and independent uniform preferences. The asymptotic formulas for the expected number of stable matchings, and for the probabilities of one point--concentration for the range of husbands' total ranks and for the range of wives' total ranks are obtained.