This paper examines college application behavior in a centralized matching mar- ket where students face demand uncertainty. Using a large field dataset from Chinese college admissions, we provide evidence of demand uncertainty by exploiting varia- tion in assignment mechanisms and other institutional features. We estimate a model of student decision-making with heterogeneous strategies and find that, relative to the benchmark with correct common priors, about 15% of students applied more pes- simistically and 24% more optimistically. The welfare effects of assignment mechanisms are also heterogeneous: optimistic and pessimistic students with high priority benefited from the transition from the Immediate Acceptance mechanism to the Chinese Parallel mechanism.