In a seminal paper, Rothschild and Stiglitz (1976) show that competitive markets with incomplete information in which firms offer contracts to screen privately informed agents may have no equilibrium. In this paper, we argue that frictions in the form of delay or congestion provide a natural solution to the nonexistence problem. To show this, we extend the concept of competitive search equilibrium by Moen (1997) to markets with incomplete information. Our main result is that a separating equilibrium always exists. In particular, the separating equilibrium cannot be broken by a profitable pooling offer as the latter attracts only the lowest types in the population due to the ensuing congestion.
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