Using Contingent Markdown with Reservation to Profit from Strategic Consumer Behavior

Abstract

We examine a contingent price markdown (CM) mechanism with guaranteed reservation under which a retailer sells multiple units to forward‐looking consumers who arrive over time according to a Poisson process. During the early part of the selling season, each arriving consumer can either purchase a unit by paying the regular price or reserve a unit at the discount price. Reserved units can only be claimed later when the number of guaranteed reservations meets a pre‐specified threshold, or at the end of the selling season, whichever comes first. Immediately after the number of guaranteed reservations meets the pre‐specified threshold, the retailer will reduce its selling price to the discount price so that all subsequent arriving consumers can take immediate possession by paying the low price. We study the consumer purchasing behavior in equilibrium when the retailer adopts such a selling mechanism, and compare the performance of our mechanism against two benchmarks: fixed price (FP) and pre‐announced discount (PD). Through an extensive numerical analysis, we identify market conditions under which CM dominates both FP and PD in terms of the retailer's revenue and consumer's surplus. Finally, through a fluid approximation to the stochastic model, we simplify the computation of the equilibrium strategy and the optimal revenues, and verify that the key insights obtained from the stochastic model still hold.