An adjustment scheme for nonlinear pricing problem with two buyers

0377-2217/$ see front matter 2009 Elsevier B.V. A doi:10.1016/j.ejor.2009.01.037 * Corresponding author. Tel.: +358 9 4515881; fax: E-mail addresses: [email protected] (H. Ehtamo), k [email protected] (M. Kitti). 1 Using an offline algorithm to solve a problem at problem data is available from the beginning. In cont process its data incrementally, without having the entir We examine a contracting problem with asymmetric information in a monopoly pricing setting. Traditionally, the problem is modeled as a one-period Bayesian game, where the incomplete information about the buyers’ preferences is handled with some subjective probability distribution. Here we suggest an iterative online method to solve the problem. We show that, when the buyers behave myopically, the seller can learn the optimal tariff by selling the product repeatedly. In a practical modification of the method, the seller offers linear tariffs and adjusts them until optimality is reached. The adjustment can be seen as gradient adjustment, and it can be done with limited information and so that it benefits both the seller and the buyers. Our method uses special features of the problem and it is easily implementable. 2009 Elsevier B.V. All rights reserved.