A learning approach for nonlinear pricing problem

Abstract

Quantity discounts are frequent both in everyday life and in business. Take, for example, product pricing, gas and electricity pricing, transportation and postage pricing, telecommunications, cable TV and Internet access pricing. These are all examples of nonlinear pricing, where the selling firm designs differentiated products and prices them according to the firm's marketing strategy. Nonlinear pricing is also a general model of incomplete information and it has a plenty of applications, such as regulation, taxation and designing labor contracts. This Dissertation develops a new learning approach for the nonlinear pricing problem, where the selling firm has limited information about the buyers' preferences. The main contributions are i) to show how the firm can learn what kind of products should be put up for sale, and what information the firm needs to do this, ii) to introduce a new approach in modeling incomplete information using optimality conditions, iii) to analyze mathematically the general pricing problem with many buyer types and multiple quality dimensions, and iv) to examine the computational issues of solving the pricing problem. The learning method is based on selling the product repeatedly. The firm sets linear tariffs, from which the buyers select the product they wish to consume. This reveals the buyers' marginal valuations, which is exactly the information that is needed to evaluate the optimality conditions. By evaluating the different optimality conditions, the firm learns the buyers who get the same product at the optimum and the buyers who are excluded. Different learning paths are examined in terms of profit, learning time and the buyers' preferences.