Sorting and matching under rank uncertainty

This paper analyzes a decentralized matching environment in which agents privately observe their ability but must choose between two mutually exclusive sectors before learning their relative rank. The sectors differ in their payoff distributions, and positions within each are assigned via positive assortative matching. Thus, outcomes depend both on ability and on the endogenous congestion created by agents’ sectoral choices. I characterize the unique symmetric Bayesian Nash equilibrium, which exhibits a cutoff structure: high-ability agents select the high-payoff sector with certainty, while low-ability agents mix to trade off match quality against the risk of being crowded out. The equilibrium choice probability is continuous within groups but displays a discontinuous jump at the sorting threshold. A key welfare finding is that rank uncertainty can raise the expected utility of some low-ability agents relative to a complete information benchmark. The analysis shows how private information induces endogenous discontinuities in strategies and heterogeneous welfare effects across types.