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Analytic solutions of nonlinear Cournot duopoly game. (English) Zbl 1186.91041
Summary: We construct a Cournot duopoly model with production externality in which reaction functions are unimodal. We consider the case of a Cournot model which has a stable equilibrium point. Then we show the existence of analytic solutions of the model. Moreover, we seek general solutions of the model in the form of nonlinear second-order difference equation.

MSC:
91A25 Dynamic games
91A50 Discrete-time games
39A10 Additive difference equations
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