Selling with Binding Reservations in the Presence of Strategic Consumers

Abstract

We analyze a revenue management problem in which a seller endowed with an initial inventory operates a selling with binding reservations scheme. Upon arrival, each consumer, trying to maximize his own utility, must decide either to buy at the full price and get the item immediately or to place a nonwithdrawable reservation at a discount price and wait until the end of the sales season where the leftover units are allocated according to first-come-first-serve priority. We prove the existence of an equilibrium consumer's strategy in this game and develop a simple and accurate asymptotic approximation for it. Through an extensive numerical study, we find that our proposed mechanism delivers higher revenues than the markdown practice with a preannounced fixed discount. The benefit is more emphasized when the seller is more patient than the consumers and (1) the ratio between the number of units put up for sale and the expected demand is moderate and/or (2) the heterogeneity of the consumers' valuations is moderate to high. In our numerical experiments, the revenue gap can reach more than 12%, which is quite significant for retail businesses that typically operate with narrow margins.