Optimal Sales Mechanism with Outside Options

This paper studies the optimal design of sales mechanisms when a buyer can quit the negotiation for an outside option at any time. The main results show that the profit-maximizing mechanism reduces price over time, and thus a set of buyer types delay purchasing the good. Moreover, to prevent the buyer from quitting the negotiation, the profit- maximizing mechanism also features an upfront payment, which is compensated later by an additional price discount. The seller can implement the profit-maximizing mechanism by offering a menu of European options.