Price Experimentation with Strategic Buyers

A two-period model in which a monopolist endeavors to learn about the permanent demand parameter of a specific repeat buyer is presented. The buyer may strategically reject the seller's first-period offer for one of two reasons. First, in order to conceal information (i.e., to pool), a high-valuation buyer may reject high prices that would never be accepted by a low-valuation buyer. Second, in order to reveal information (i.e., to signal), a low-valuation buyer may reject low prices that would always be accepted by a high-valuation buyer. Given this, the seller often finds it optimal to post prices that reveal no useful information. Indeed, in the equilibrium where there is no signaling, the seller never charges an informative first-period price. Learning may occur in the equilibrium where there is maximal signaling, but the scope for learning appears to be quite limited even in this case. Indeed, in order to preempt information transmission through signaling, the seller may set a first-period price strictly below the buyer's lowest possible valuation.