Probabilistic selling in quality-differentiated markets

Abstract

Probabilistic selling-the sale of synthetic products consisting of a lottery between two distinct goods-has been extensively analyzed in horizontal markets. In this research, we investigate probabilistic selling in quality-differentiated markets. This is an important new dimension of inquiry because of the widespread prevalence of quality-differentiated markets as well as significant differences in the preference structure across these markets. In fact, this latter consideration casts doubt as to whether probabilistic selling will even emerge in quality-differentiated markets. We find that probabilistic selling emerges in quality-differentiated markets as a way to profitably dispose excess capacity; moreover, probabilistic selling remains viable even under endogenous quality choice. In addition, in markets where sellers employ "strong" quality differentiation, the introduction of an intermediate probabilistic good actually causes closer quality levels in a product line and enhances consumer welfare. In contrast, in markets where sellers employ "weak" quality differentiation, the introduction of an intermediate probabilistic good increases quality separation and degrades consumer welfare. Overall, we view our contribution as one of characterizing the optimality, implementation, and policy implications of probabilistic selling in quality-differentiated markets.