A Representative Consumer Model in Data-Driven Multiproduct Pricing Optimization

We develop a data-driven approach for the multiproduct pricing problem, using the theory of a representative consumer in discrete choice. We establish a set of mathematical relationships between product prices and demand for each product in the system, including that of the outside option. We provide identification conditions to recover the underlying representative consumer model and show that, with sufficient pricing experiments, the approach can identify the underlying demand model (more precisely, the associated perturbation function in the representative consumer model) accurately up to a constant shift and a given tolerance level. This holds even when the demand data obtained are a noisy realization of the theoretical demand. We use this approach to solve the multiproduct pricing problem using a (mixed integer) linear optimization method. Extensive tests using both synthetic and industry data clearly demonstrate the benefits of this approach, which addresses the issue of model misspecification in traditional pricing methods using discrete choice models and circumvents the computational issues associated with pricing methods that assume a known consumer valuation of each product.