Competitive price discrimination, imperfect information, and consumer search

I study a homogeneous goods' model in which a consumer attains consumption opportunities via sequential search. Whenever a firm is visited by the consumer, the firm observes a private signal about the consumer's valuation and price discriminates based on this information. If the signal is sufficiently precise and search costs are at intermediate levels, an equilibrium in which the consumer visits multiple firms with positive probability emerges. At low search costs, firms offer low prices to deter search, and the consumer does not visit multiple firms. The equilibrium prices are minimal if search costs are negligible and, if the signal is sufficiently precise, the equilibrium prices are maximal at intermediate levels of search costs.