Probabilistic Selling in Vertically Differentiated Markets
Xerox Chair of Computer and Information Systems
Simon Business School
University of Rochester
Friday, Sep 3
9 – 10 am | Zoom
This paper studies two fundamental questions regarding probabilistic selling in a vertical market: when is probabilistic selling profitable and how to design it optimally? For the first question, we identify an important but overlooked economic mechanism driving probabilistic selling in vertical markets: convexity of consumer preferences. In stark contrast with the literature finding that probabilistic selling is never profitable unless there is excess capacity or bounded rationality, we find that with an alternative utility function capable of representing convex preference, probabilistic selling is always profitable without excess capacity and with rational consumers. For the second question, we study the optimal design of probabilistic goods where the two component goods are of different qualities and their prices are endogenous. We develop an efficient algorithm to compute the optimal design when consumers have Cobb-Douglas utility functions and obtain an important structural property of the optimal prices of the two component goods: the optimal price of the high-quality good increases while the optimal price of the low-quality good decreases upon the introduction of probabilistic selling, thereby increasing the market coverage of the goods without launching an actual new product line. We also obtain closed-form solutions for a special case of Cobb-Douglas utility function that is widely used in the economics literature on vertical product differentiation.