The Value of Observability in Dynamic Pricing

Abstract

Research on dynamic pricing has been growing during the last four decades due to its use in practice by a variety of companies as well as the several model variants that can be considered. In this work, we consider the particular pricing problem where a firm wants to sell one item to a single buyer in order to maximize expected revenues. The firm commits to a price function over an infinite horizon. The buyer has a private value for the item and purchases at the time when his utility is maximized. In our model, the buyer is more impatient than the seller and we study how important is to observe the buyer time arrival in terms of the seller's expected revenue. When the seller can observe the arrival of the buyer, she can make the price function contingent on the buyer's arrival time. On the contrary, when the seller cannot observe the arrival, her price function is fixed at time zero for the whole horizon. The value of observabilityis defined as the worst case ratio between the expected revenue of the seller when she observes the buyer's arrival and that when she does not. Our main result is to prove that in a very general setting, the value of observability is at most~4.911. To obtain this result we fully characterize the observable setting and use this solution to construct a random and periodic price function for the unobservable case.