The Market for Surprises: Selling Substitute Goods through Lotteries

Abstract

In this paper, we solve the revenue maximization problem of a multi-product monopolist when the products are substitutes. We consider a Hotelling model with two horizontally differentiated goods located at the endpoints of the segment. Consumers are located uniformly on the segment; their valuations for each good are equal to the base consumption value minus distance costs. When the base consumption value is high, the seller maximizes her expected profit by offering a menu of base and opaque goods. In particular, a single half-half lottery over base goods is optimal under concave and linear costs. When base consumption value is low, only base goods are sold. Finally, when base consumption value is intermediate, the optimal mechanism may entail the offering of lotteries with the positive probability of no delivery. Our findings can explain the emergence of opaque goods sales (e.g., hotel bookings without a complete description of the hotel through hotwire.com or priceline.com) as the outcome of the industry's search for the optimal selling scheme.