Which side chooses in large random matching markets?


March 14, 2013


Yashodhan Kanoria




We analyze large random two-sided matching markets with different numbers of men and women. We show that being on the short side of the market confers a large advantage, in a sense that the short side roughly chooses the matching while the long side roughly gets chosen. In addition, the matching is roughly the same under all stable matchings. Consider a market with n men and n+k women, for arbitrary 1 = k = n/2. We show that, with high probability, the men’s average rank of wives is less than 5log(n/k) in any stable match. Further, men’s average rank of wives in the women-optimal stable match (WOSM) is within a factor 1+ε of that in the men-optimal stable match (MOSM). On the other hand, the women’s average rank of husbands is at least n/(5 log(n/k)) in all stable matches, and is again very nearly the same in the WOSM and MOSM. Thus, our results imply that the core is likely to be “small”. Simulations show that the same features arise even in small markets.

(Joint work with Itai Ashlagi and Jacob D. Leshno)


Yashodhan Kanoria

Yash Kanoria is a postdoctoral fellow at Microsoft Research New England. His current research interests include matching markets, graphical models and probability. In Fall 2013, he will join the Decision, Risk and Operations faculty at Columbia Business School.