Constrained Bayesian Neural Network utility in the design of price promotions

This paper introduces a discrete choice model with a flexible utility function in the form of a Bayesian Neural Network with consumer preference heterogeneity. Adapting Hamiltonian Monte Carlo to the model structure allows us to enforce a qualitative prior constraint on the shape of the utility function stipulating that it be decreasing in price. We further account for model uncertainty with Bayesian Model Averaging. The predictive distribution of our model is thus obtained as a weighted average of predictive distributions of admissible neural network structures weighted by the posterior probability of each model. We apply our approach to a panel of IRI coffee purchase data that combines consumer and store-level marketing information. We obtain model-averaged predictive densities for own and cross price elasticity and corresponding revenue change predictions in a counterfactual experiment, simulating several levels of price promotion. Our framework allows managers to utilize a flexible data-driven method for analyzing both the form of consumer utility and individual preference variations, as a valuable tool for making strategic pricing decisions.