Optimal dynamic advertising policies and equilibria

The objective of this paper is to present a special application field of optimal control and differential game theories which is of interest to management scientists. After introducing the Vidale-Wolfe’s and Nerlove- Arrow’s dynamic models for advertising processes, I will focus on a few exemplary problems. At a first investigation level, we find some optimal control problems, then the more interesting and challenging problems in the framework of game theory. The view of all problems is unified by the common reference to the same two basic dynamic models.