Probabilistic Selling in Vertically Differentiated Markets

  • He, Y. (Guest lecturer)
  • Huaxia Rui (Co-author)

Activity: Talks and presentationsConference presentations


This paper studies two fundamental questions regarding probabilistic selling in vertically differentiated markets: when is it profitable and how to design it optimally? For the first question, we identify an important but overlooked economic mechanism driving probabilistic selling in vertically differentiated 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 many alternative utility functions 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 selling where prices of the two quality-differentiated component goods are endogenous. We first obtain a general characterization of an important structural property regarding the optimal prices of component goods, before focusing on the Cobb-Douglas utility functions for which we develop an efficient algorithm to compute the optimal design of the probabilistic good and the optimal component goods prices. We show that 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. Such an analytical tractability further allows us to explore the optimal selling of multiple probabilistic goods.
Period15. Dec 202117. Dec 2021
Event titleThe 32nd Workshop on Information Systems Economics
Event typeWorkshop
LocationTexas, United States