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Continuous-time dynamic games for the Cournot adjustment process for competing oligopolists. (English) Zbl 1284.91057

Summary: 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.

MSC:

91A25 Dynamic games
91B54 Special types of economic markets (including Cournot, Bertrand)
91A80 Applications of game theory
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