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.
Highlights
The starting point of oligopoly theory is the static Cournot model
Tremblay cause firms are slow to change their strategic variables, causing it to take time for firms to reach equilibrium. This can occur when change is costly, which forces firms into a differential oligopoly game. In cases such as these, the strategic variable evolves to a limiting outcome that differs from the static Nash equilibrium that would occur if the change was instantaneous
We have extended the dynamic Cournot model to include behavioral errors on the part of management
Summary
The starting point of oligopoly theory is the static Cournot model. It provides an example of Nash equilibrium and embeds a variety of possible market outcomes. Tremblay cause firms are slow to change their strategic variables, causing it to take time for firms to reach equilibrium This can occur when change is costly, which forces firms into a differential oligopoly game. In cases such as these, the strategic variable (output or price) evolves to a limiting outcome that differs from the static Nash equilibrium that would occur if the change was instantaneous (i.e., the cost of change is zero). We are the first to incorporate Brownian motion into an oligopoly model By adding this stochastic component, we are able to show that output converges to a random variable rather than a constant, as in the deterministic dynamic Cournot model.
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