We analyze large random matching markets with unequal numbers of men and women. We find that being on the short side of the market confers a large advantage. For each agent, assign a rank of 1 to the agent's most preferred partner, a rank of 2 to the next most preferred partner and so forth. If there are n men and n + 1 women then, we show that with high probability, in any stable matching, the men's average rank of their wives is no more than 3 log n, whereas the women's average rank of their husbands is at least n/(3 log n). Furthermore, with high probability, the fraction of agents with multiple stable partners is vanishing as the market grows large, i.e., such unbalanced random matching markets have a ‘small core’. Our results suggest that a ‘small core’ may be generic in matching markets, contrary to prior beliefs. (Based on joint work with Itai Ashlagi and Jacob Leshno)
Yashodhan Kanoria is an Assistant Professor in the Decision, Risk and Operations Division at the Columbia Business School. He obtained a B.Tech. from IIT Bombay and a Ph.D. from Stanford University, both in Electrical Engineering. His current research interests include matching markets, graphical models, and probability.