We develop a data-driven approach for the multi-product pricing problem, using the theory of a represen- tative 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 pertu- bation 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 noisy realization of the theoretical demand. We use this approach to solve the multi-product pricing problem using a (mixed integer) linear optimization method. Extensive tests using both synthetic and industry data clearly demonstrates 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.
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