Stochastic Dynamic Pricing and Advertising in Isoelastic Oligopoly Models

In this paper we analyze stochastic dynamic pricing and advertising differential games in special oligopoly markets with constant price and advertising elasticities. We consider the sale of perishable as well as durable goods and include adoption effects in the demand. For the individual firms we derive solution formulas of the value function and of the optimal feedback policies. Furthermore, efficient simulation techniques are used to evaluate optimally controlled sales processes over time. This way the evolution of optimal controls as well as the firm's profit distributions are analyzed. Moreover, we show that the market power of the competing firms is exactly the same as in the deterministic version of the model. We also find that as soon as saturation effects in the demand are involved, the optimal profits of the deterministic model can be dominated by the optimal expected profits of the stochastic model