Unbalanced Random Matching Markets: The Stark Effect of Competition
研究了双方人数不等的随机偏好匹配市场中的竞争，发现轻微不平衡就会导致唯一稳定匹配，短边方获得高匹配质量，长边方几乎只能随机配对。
We study competition in matching markets with random heterogeneous preferences and an unequal number of agents on either side. First, we show that even the slightest imbalance yields an essentially unique stable matching. Second, 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 with one of his top choices, and each agent on the long side either is unmatched or does almost no better than being matched with a random partner. Our results suggest that any matching market is likely to have a small core, explaining why small cores are empirically ubiquitous.