Rigidity of Transfers and Unraveling in Matching Markets

We study the role of transfers in the timing of matching. In our model, some agents have the option of matching early and exiting in period 1, before others arrive in period 2; in period 2 there is a centralized institution that implements a stable matching after all agents arrive. We prove that without flexible transfers, as the market gets large, on average at least one quarter of all agents in period 1 have strict incentives to match early and skip the centralized matching, if they anticipate others are participating in the centralized matching of period 2. We define a minimal notion of sequential stability and prove that without flexible transfers the probability of sequential stability tends to 0 as the market gets large. We show that flexible transfers eliminate these timing problems