Title: Continuous learning methods in two-buyer pricing problem
Authors: Kimmo Berg and Harri Ehtamo
Systems Analysis Laboratory
Aalto University School of Science and Technology
P.O. Box 11100, 00076 Aalto, FINLAND
Date: November, 2010
Status: Systems Analysis Laboratory Research Reports E24 November 2010
Abstract: This paper presents continuous learning methods in a monopoly pricing problem where the firm has uncertainty about the buyers' preferences. The firm designs a menu of quality-price bundles and adjusts them using only local information about the buyers' preferences. The learning methods define different paths, and we compare how much profit the firm makes on these paths, how long it takes to learn the optimal tariff, and how the buyers' utilities change during the learning period. We also present a way to compute the optimal path in terms of discounted profit with dynamic programming and complete information. Numerical examples show that the optimal path may involve jumps where the buyer types switch from one bundle to another, and this is a property which is difficult to include in the learning methods. The learning methods have, however, the benefit that they can be generalized to pricing problems with many buyers types and qualities.
Keywords: pricing, learning, limited information, buyer-seller game, mechanism design