Bounded Experimentation in a Calibrated Model of Advertising

A seller sets up an advertising policy so as to maximize a flow of discounted utility over time in a scenario characterized by two essential issues. First, the seller is ignorant from the outset of the prospective customers' willingness to buy and runs a Bayesian learning process in parallel to the advertising policy. Second, the room for the seller to learn is limited by the fact that the number of prospects is bounded and, moreover, each prospect exhibits some degree of satiation with respect to advertising, which prevents the seller from addressing advertisements repeatedly to a given prospect. This idea of satiation is justified by the data used and some recent studies in psychology. We calibrate some parameters of the model using real data from banking and solve it numerically using dynamic programming. We compute the optimal policy, perform some sensitivity analyses with regard to parameters and initial beliefs, and make comparisons with a suboptimal policy in which future (but not past) learning is ignored in every period