We examine an oligopoly model of advertising competition where each firm's market share depends on its own and its competitors' advertising decisions. A differential game model is developed and used to derive the closed-loop Nash equilibrium under symmetric as well as asymmetric competition. We...

This paper presents a review of recent developments that have taken place in the area of dynamic optimal control models in advertising subsequent to the comprehensive survey of the literature by Sethi in 1977. The basic problem underlying these models is that of determining optimal advertising...

This paper considers an optimal-control problem for the dynamics of the Vidale-Wolfe advertising model, the optimal control being the rate of advertising expenditure to achieve a terminal market share within specified limits in a way that maximizes the present value of net profit streams over a...

This paper examines the feasibility of implementing Linear Quadratic Gaussian (LQG) Control in structural cointegrated VAR models and sheds some light on the two major problems generated by such implementation. The first aspect to be taken into account is the effect of the presence of unit roots...

This paper specifies and interprets those direct relations which exist between the dual concepts of complete controllabil-ity/observability (Kalman, 1960), on the one hand, and the con-cept of the regular technique of production (Schefold, 1971), on the other. Specifically, it shows, first, that...

Nous présentons un exemple archétypal de jeu à champ moyen. Cet exemple est important à deux égards. Tout d'abord, il est suffisamment simple pour permettre l'obtention de solutions explicites : les fonctions de Bellman sont quadratiques, les mesures stationnaires gaussiennes et l'étude de...

In this article, we present a reference case of mean field games. This case can be seen as a reference for two main reasons. First, the case is simple enough to allow for explicit resolution: Bellman functions are quadratic, stationary measures are normal and stability can be dealt with...

What is an optimal or a sustainable external debt - for a country, region or sector? How should one monitor and evaluate debt to preclude a crisis? We use stochastic optimal control/dynamic programming to derive an optimal debt. The deviation of the actual from the optimal will serve as a...

In this paper I study the optimal control path for a (capital or pollution) stock which accumulates time with a lag to its control. It is shown that the optimal control path is non-monotonic and cyclical in general, but it is monotonic if the objective function is additively separable in the...