Stochastic Control of Competition Through Prices

We assume that the price of a product set by a firm affects its immediate profit rate as well as the probabilistic rate of arrival of new firms into the industry. Therefore, the firm's optimal dynamic pricing strategy must balance the increased current profits from setting a high price against the expected dilution of future profits due to additional competition. We provide a continuous-time Markov decision model and characterize the structure of the optimal control strategy and its sensitivity to the problem parameters. We also indicate the relationship of our problem to the queue control literature.