This paper examines the strategic interaction between two firms competing using advertising.  The simulation is based on the Cournot analytical duopoly model.  The paper discusses the analytical model and then discusses the simulation model.  The paper discusses the ways in which the simulation model is different, usually for pragmatic reasons, to the analytical model.  The paper shows results of the model for a number of competitive scenarios.  These scenarios demonstrate that small changes in model parameters lead to large differences in firm and industry behavior.  The paper demonstrates that positive spillover (cooperation) reduces the impact of advertising and negative spillover (predation) increases the impact of advertising.