The Economics of Buyer Uncertainty: Advance Selling vs. Probabilistic Selling

Although advance selling and probabilistic selling differ in both motivation and implementation, we argue that they share a common characteristic—both offer consumers a choice involving buyer uncertainty. We develop a formal model to examine the general economics of purchase options that involve buyer uncertainty, explore the differences in buyer uncertainty created via these two strategies, and derive conditions under which one dominates the other. We show that the seller can address unobservable buyer heterogeneity by inducing sales involving buyer uncertainty via two different mechanisms: (1) homogenizing heterogeneous consumers and (2) separating heterogeneous consumers. Offering advance sales encourages customers to purchase while they are uncertain about their consumption states (more homogeneous), but offering probabilistic goods encourages customers to reveal their heterogeneity via self-selecting whether or not to purchase the uncertain product. The relative attractiveness of these two selling strategies depends on the degree of two types of buyer heterogeneity: (1) MaxValue-Heterogeneity, which is the variation in consumers' valuations for their preferred good, and (2) Strength-Heterogeneity, which is the variation in the strength of consumers' preferences. Neither strategy is advantageous unless the market exhibits sufficient MaxValue-Heterogeneity. However, whereas Strength-Heterogeneity can destroy the profit advantage of advance selling, a mid-range of Strength-Heterogeneity is necessary for probabilistic selling to be advantageous.