Price discrimination through communication

We study a seller's optimal mechanism for maximizing revenue when the buyer may present evidence relevant to the buyer's value, or when different types of buyer have a differential ability to communicate. We introduce a dynamic bargaining protocol in which the buyer first makes a sequence of concessions in a cheap talk phase, and then at a time determined by the seller, the buyer presents evidence to support his previous assertions, and then the seller makes a take-it-or-leave-it offer. Our main result is that the optimal mechanism can be implemented as a sequential equilibrium of our dynamic bargaining protocol. Unlike the optimal mechanism to which the seller can commit, the equilibrium of the bargaining protocol also provides incentives for the seller to behave as required. We thereby provide a natural procedure whereby the seller can optimally price discriminate on the basis of the buyer's evidence.