Abstract
We consider a market with two sellers, each having one unit of identical product, who compete for potential buyers with one-unit demand and a private valuation of this product. First, firms simultaneously post their prices. Then buyers observe these prices and choose a seller to submit a request for purchase depending on their private valuation of the product. This framework is between the directed search theory and the theory of competing mechanisms. We prove that the private information about the consumer's willingness to pay produces an equilibrium price dispersion and endogenous consumer separation.
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