Wayne L. Winston

A birth–death model of advertising and pricing

This paper employs the methods currently used to solve many queuing control models in order to investigate the behavior of a firms optimal advertising and pricing strategies over time. Given that a firms market position expands or deteriorates in a probabilistic way which depends upon the current position, the rate of advertising, and the price the firm charges, we present conditions which ensure that the optimal level of advertising is a monotonic function of the firms market position, and we discuss the economic meaning of these conditions. Furthermore, although the primary focus is upon a non-competitive environment, we develop the above model as a non-zero sum, two-person stochastic game and show that an equilibrium strategy exists which is simple to compute.

Markov Models of Advertising and Pricing Decisions

This paper uses Markov decision analysis to study the properties of optimal advertising and pricing decisions in a dynamic, stochastic environment. We are primarily concerned with exhibiting and interpreting properties of the Markovian transition probabilities and one-period reward functions that imply that the optimal advertising levels and optimal prices always increase or always decrease as a function of the firms market position. This is done in both non-competitive and competitive situations. In the former, total discounted reward for a single firm is the objective, whereas in the latter we use the concept of stochastic games to construct what is known as a discounted equilibrium point for two competing firms.