Vertically probabilistic selling mechanism under asymmetric quality-tier competition: An analytical exploration

Compared with the existing literature that focuses on horizontal features of probabilistic selling (PS), PS in vertical quality markets is receiving significant attention in the travel and marketing industries, both in the United States and China. Focusing on a general framework for a vertically PS mechanism that involves firm asymmetric quality-tier competition and the active role of an intermediary retailer, we consider a duopoly, where the leader firm can endogenously generate differentiated quality PS products via either the direct channel or the indirect channel through an intermediary retailer, while the follower firm sells transparent products by providing exogenously differentiated quality levels. Utilizing Stackelberg game theory, we construct an economic model involving PS under asymmetric competition by quantifying probabilistic products in terms of expected quality and provide firms with profit-maximizing strategies under three scenarios. Second, we theoretically analyze three strategies to identify the advantages of PS, and further conduct a comparison of PS and traditional selling (TS) in terms of revenue pricing, social welfare and consumer surplus. Our results suggest that (i.) PS is not always profitable; only if the expected quality level is low could PS be effective; (ii.) PS could weaken asymmetric quality-tier competition and further mitigate cannibalization effect. In our duopoly model, if there were no probabilistic sales, the equilibrium would eventually converge to a situation where one Firm produces a high-quality product and the other produces a relatively low-quality product. Finally, we extend our model by incorporating attitude to risk and word-of-mouth persuasion. These additions enhance the applicability of our conclusions.