This paper analyzes dynamic advertising and pricing policies in a durable-good duopoly. The proposed infinite-horizon model, while general enough to capture dynamic price and advertising interactions in a competitive setting, also permits closed-form solutions. We use differential game theory to...

To increase the sales of their products through advertising, firms must integrate their brand-advertising strategy for capturing market share from competitors and their generic-advertising strategy for increasing primary demand for the category. This paper examines whether, when, and how much...

Cooperative (co-op) advertising is an important instrument for aligning manufacturer and retailer decisions in supply chains. In this, the manufacturer announces a co-op advertising policy, i.e., a participation rate that specifies the percentage of the retailer's advertising expenditure that it...

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 a variation of the Vidale-Wolfe advertising model for which the maximum value of the objective function and the form of the optimal feedback advertising control are identical in both a deterministic and a stochastic environment. The stochastic environment is due to a white...

A nearly explicit feedback Stackelberg-Nash equilibrium is obtained in a dynamic distribution channel consisting of a manufacturer and two competing asymmetric retailers engaged in promoting the manufacturer's product to be sold through the retailers. The manufacturer decides on its support for...

In this paper we characterize the feedback equilibrium of a general infinite-horizon Stackelberg-Nash differential game where the roles of the players are mixed. By mixed we mean that one player is a leader on some decisions and a follower on other decisions. We prove a verification theorem that...

My assignment for this lecture is to discuss applications of optimal control theory to Management Science problems. Since the field of Management Science encompasses production, finance, and marketing as its main functional areas which themselves are rather vast, it will not be possible to...

This paper considers an optimal control problem for the dynamics of the Nerlove-­Arrow advertising model, the optimal control being the rate of advertising expenditure required to maximize the present value of net profit streams (or, sales) over a finite horizon subject to a budget constraint....

Several nonlinear stochastic models are developed for a dynamic profit-maximizing firm with respect to its price and (possibly) advertising decisions under threat of entry. The optimal price ­advertising policies for these models are characterized by the use of the Maximum Principle. While the...