Continuous learning dynamics in two-buyer pricing problem

This paper studies a monopoly pricing problem in a situation where the firm has uncertainty about the buyers’ preferences. We examine continuous learning dynamics, where the firm sells some quality-price bundles and adjusts them using only local information about the buyers’ preferences. The learning dynamics define different learning paths, and we compute how much profit the paths make, how long it takes to learn the optimal tariff, and how the buyers’ utilities change during the learning period. We also compute the optimal learning path in terms of discounted profit with dynamic programming and complete information. We examine how close the optimal path is to the learning dynamics that use only limited information. Numerical examples show that the optimal path may involve jumps, where the buyer types switch from one bundle to another, and these are something the learning dynamics cannot discover. The learning dynamics have, however, the benefit that they can be generalized to pricing problems with many buyer types and qualities.