Bray Theory Workshop

We study competition in matching markets with random heterogeneous preferences by considering markets with an unequal number of agents on either side. First, we give a tight description of stable outcomes, showing that matching markets are extremely competitive. Each agent on the short side of the market is matched to one of his top preferences and each agent on the long side does almost no better than being matched to a random partner. Second, we show that even the slightest imbalance leads to competition that yields an essentially unique stable matching. Our results suggest that any matching market is likely to have a small core, explaining why empirically small cores are ubiquitous. Paper can be found at: http://www.columbia.edu/~jl4130/AKL-Unbalanced%20Matching.pdf