Feedback competitive advertising strategies with a general objective function

We introduce a general objective function, which incorporates competitive s ituations, such as conservative, punitive, and predatory advertising. Linki ng together the particular situations into a two-parameter family of max-mi n problems, and using the Lanchester model to describe the dynamics of the market, a bilinear-quadratic differential game is obtained. For this game, we find saddle-point feedback time-invariant advertising strategies and sho w when these strategies are Nash equilibrium strategies. In an empirical ap plication involving duopolistic competition in the cola market, we find evi dence of a punitive motivation for the advertising strategies.