Chaos and Unraveling in Matching Markets

We study how information perturbations can destabilize two-sided matching markets. In our model, agents arrive on the market over two periods, while agents in the first period do not know the types of those arriving later. Agents already present in the market may match early or wait for the small group of new entrants. Despite the lack of discounting or risk aversion, this perturbation creates incentives to match early and leave the market before the new agents arrive. These incentives do not disappear as the market gets large. Moreover, we identify a new adverse phenomenon in this setting: as markets get large the probability of \emph{chaos} -- where no early matching scheme for existing agents is robust to pairwise deviations -- approaches 1. These results are independent of the distribution of agents' types and robust to asymmetries between the two sides of the market. Our findings thus suggest that matching markets are extremely sensitive to institutional details and uncertainty.