Orateur
Description
We consider a 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 in order 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 in which the radii by which the buyer can strategically perturb their features is a strictly positive random variable. We establish for this problem that the objective value of the sample average approximation converges almost surely to the objective value of the infinite-dimensional stochastic problem as the number of samples tends to infinity. This asymptotic consistency result shows that incorporating strategic behavior into an infinite-dimensional stochastic programming problem can, in addition to making the problem more realistic, help prevent the sample average approximation from overfitting.
