Robust product design and pricing

We study design and pricing by a monopolist who has no information about the distribution of consumers’ tastes and maximizes her profit under the worst-case scenario. We show that her optimal strategy takes a simple form of dividing the taste space into a finite number of equal-length intervals and serving consumers on a randomly chosen interval. We obtain this result by studying the dual problem of finding a distribution of consumers’ tastes that minimizes the seller’s profit and establishing strong duality. The profit-minimizing distributions exhibit a uniformity property, assigning equal probability mass to a finite number of partition cells of equal width. Through the dual, we also determine the seller’s lowest profit in the Bayesian setting, establish that it is strictly positive, and derive the set of achievable profits.