The doctoral dissertations of the former Helsinki University of Technology (TKK) and Aalto University Schools of Technology (CHEM, ELEC, ENG, SCI) published in electronic format are available in the electronic publications archive of Aalto University - Aaltodoc.

A Learning Approach for Nonlinear Pricing Problem

Kimmo Berg

Doctoral dissertation for the degree of Doctor of Science in Technology to be presented with due permission of the Faculty of Information and Natural Sciences for public examination and debate in Auditorium E at the Aalto University School of Science and Technology (Espoo, Finland) on the 14th of January 2011 at 12 noon.

Overview in PDF format (ISBN 978-952-60-3544-4)   [201 KB]
Dissertation is also available in print (ISBN 978-952-60-3538-3)


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.

This thesis consists of an overview and of the following 5 publications:

  1. Harri Ehtamo, Kimmo Berg, and Mitri Kitti. 2010. An adjustment scheme for nonlinear pricing problem with two buyers. European Journal of Operational Research, volume 201, number 1, pages 259-266. © 2009 Elsevier Science. By permission.
  2. Kimmo Berg and Harri Ehtamo. 2009. Learning in nonlinear pricing with unknown utility functions. Annals of Operations Research, volume 172, number 1, pages 375-392.
  3. Kimmo Berg and Harri Ehtamo. 2008. Multidimensional screening: Online computation and limited information. In: Dieter Fensel and Hannes Werthner (editors). Proceedings of the 10th International Conference on Electronic Commerce (ICEC 2008). Innsbruck, Austria. 19-22 August 2008. New York, NY, USA. ACM. ACM International Conference Proceedings Series, volume 342, article 41, 10 pages. ISBN 978-1-60558-075-3.
  4. Kimmo Berg and Harri Ehtamo. 2010. Interpretation of Lagrange multipliers in nonlinear pricing problem. Optimization Letters, volume 4, number 2, pages 275-285.
  5. Kimmo Berg and Harri Ehtamo. 2010. Continuous learning methods in two-buyer pricing problem. Espoo, Finland: Aalto University School of Science and Technology. 25 pages. Aalto University School of Science and Technology, Systems Analysis Laboratory Research Reports, Series E, Report E24. ISBN 978-952-60-3476-8. ISSN 1456-5218. © 2010 by authors.

Keywords: nonlinear pricing, incomplete information, learning, adjustment, mechanism design, computation

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Last update 2011-07-22