Equivalence between sethi advertising model and a scalar LQ differential game

It is proven in this paper that, under certain conditions, the closed-loop Nash equilibrium of the Sethi advertising model is equivalent to that of a standard scalar LQ differential game. By this way, some properties of the advertising duopoly model, such as the existence and uniqueness of the closed-loop Nash equilibrium, can be analyzed more deeply based on the existing result of an LQ differential game.