Revenue Management with Strategic Customers: Last-Minute Selling and Opaque Selling

Companies in a variety of industries (e.g., airlines, hotels, theaters) often use last-minute sales to dispose of unsold capacity. Although this may generate incremental revenues in a short term, the long-term consequences of such a strategy are not immediately obvious: more discounted last-minute tickets may lead to more consumers anticipating the discount and delaying the purchase rather than buying at the regular (higher) prices, and hence potentially reducing revenues for the company. To mitigate such behavior, many service providers have turned to opaque intermediaries such as hotwire.com that hide many descriptive attributes of the service (e.g., departure times for airline tickets) so that the buyer cannot fully predict the ultimate service provider. Using a stylized economic model, this paper attempts to explain and compare the benefits of last-minute sales directly to consumers vs. through an opaque intermediary. We utilize the notion of rational expectations to model consumer purchasing decisions: consumers make early purchase decisions based on expectations regarding future availability, and these expectations are correct in equilibrium. We show that direct last-minute sales are preferred over selling through an opaque intermediary when consumer valuations for travel are high and/or there is little service differentiation between competing service providers; otherwise, opaque selling dominates. Moreover, contrary to the usual belief that such sales are purely mechanisms for disposal of unused capacity, we show that opaque selling becomes more and more preferred over direct last-minute selling as the probability of having high demand increases. When firms randomize between opaque selling and last-minute selling strategies, they are increasingly likely to choose opaque selling strategy as the probability of high demand increases. When firms with unequal capacities use opaque selling strategy, consumers know more clearly where the opaque ticket is from and the efficacy of opaque selling decreases.