The Blessing of Strategic Customers in Personalized Pricing

We consider a feature-based personalized pricing problem in which the buyer is strategic: given the seller's pricing policy, the buyer can augment the features that they reveal to the seller to obtain a low price for the product. We model the seller's pricing problem as a stochastic program over an infinite-dimensional space of pricing policies where the radii by which the buyer can perturb the features are strictly positive. We establish that the sample average approximation of this problem is asymptotically consistent; that is, we prove that the objective value of the sample average approximation converges almost surely to the objective value of the stochastic problem as the number of samples tends to infinity under mild technical assumptions. This consistency guarantee thus shows that incorporating strategic consumer behavior into a data-driven pricing problem can, in addition to making the pricing problem more realistic, also help prevent overfitting.