A Dynamic Cournot Model with Brownian Motion

Abstract

In this paper we develop a stochastic version of a dynamic Cournot model. The model is dynamic because firms are slow to adjust output in response to changes in their economic environment. The model is stochastic because management may make errors in identifying the best course of action in a dynamic setting. We capture these behavioral errors with Brownian motion. The model demonstrates that the limiting output level of the game is a random variable, rather than a constant that is found in the non-stochastic case. In addition, the limiting variance in firm output is smaller with more firms. Finally, the model predicts that firm failure is more likely in smaller markets and for firms that are smaller and less efficient at managing errors.