OLIGOPOLY MODELS FOR OPTIMAL ADVERTISING WHEN PRODUCTION COSTS OBEY A LEARNING-CURVE

A study was made of the problem of characterizing an optimal advertising policy over time is an important question in the field of marketing. It is especially important during the period of the introduction of a new product; and it also during this time that the production learning curve phenomenon is pronounced. Oligopoly models which combine elements of F. M. Bass's demand growth models, the M. L. Vidale-H. B. Wolfe and S. Ozga advertising models with linear or quadratic costs, and the production learning curve. In the monopoly case (n equals 1), the optimal advertising function is derived by applying Green's theorem. In the duopoly (n equals 2) and triopoly ( equals 3) cases the authors use discrete differential game models, and find Nash equilibrium solutions. In each of these models the form of the optimal policy is easy to find, but because of the complicated nature of the resulting differential equations, closed form solutions for the optimal state and control trajectories are impossible to fine. A computer was used to compute these optimal trajectories and plot them for various parameter settings.