Continuous-time dynamic games for the Cournot adjustment process for competing oligopolists

Under the assumption of an iso-elastic demand function, we consider a continuous-time dynamic Cournot adjustment game for n oligopolists. We first show the existence and uniqueness of a positive Cournot equilibrium and, for any n, we show that positive response functions are bounded in time. For the n = 3 case, we analytically show that the positive equilibrium is locally asymptotically stable, while, for n > 3, we are able to give some asymptotic results. As an application, we then introduce a proportional tax or subsidy to the model, and discuss the influence of such policies on the positive equilibrium. Furthermore, we briefly discuss a generalization of the results to non-iso-elastic demand functions. Comments on possible areas of future work are given.