Learning Demand Curves in B2B Pricing

Huashuai Qu, Ilya O. Ryzhov, Michael C. Fu, Eric Bergerson Megan, and Kurka Ludek Kopacek, Learning Demand Curves in B2B Pricing: A New Framework and Case Study, Production and Operations Management, Volume 29, Issue 5, May 2020, Pages: 1287-1306.

In business-to-business (B2B) pricing, a seller seeks to maximize revenue obtained from high-volume transactions involving a wide variety of buyers, products, and other characteristics. Buyer response is highly uncertain, and the seller only observes whether buyers accept or reject the offered prices. These deals are also subject to high opportunity cost, since revenue is zero if the price is rejected. The seller must adapt to this uncertain environment and learn quickly from new deals as they take place. We propose a new framework for statistical and optimal learning in this problem, based on approximate Bayesian inference, which has the ability to measure and update the seller’s uncertainty about the demand curve based on new deals. In a case study, based on historical data, we show that our approach offers significant practical benefits.

 Learning demand curves:

We would like to retain the multivariate normal distribution in order to use the power of correlated beliefs. Since this is not possible using standard Bayesian updating, we use the methods of approximate Bayesian inference (Ryzhov 2015). Essentially, if the posterior distribution is not conjugate with the prior, we replace it by a simpler distribution that does belong to our chosen family (multivariate normal), and optimally approximates the true, non-normal posterior.

Case study:

Historical transaction data were provided by Vendavo in anonymized form. The part of the data used to train the model consisted of 50,000 individual observations (both historical wins and historical losses were recorded). The available information included categorical features for product and customer types; at the most detailed level, there were 1881 different products and 2051 different customers.

Cumulative Revenues for 100 Deals (Averaged over 1000 Macroreplications)