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The dynamics of a tripoly Cournot game. (English) Zbl 0998.91035
The Cournot oligopoly is extended to three economic agents. The marginal cost of production is constant, the demand function is iso-elastic. The gents react upon market’s situation independently and instantly, without gap and rational expectation. It is assumed discrete time in the model. Therefore, repeated noncooperative game with given function of changing of output for each agent is under consideration. In fact, stepwise transformations of the game are defined as finite difference equations. The paper analyses whether this game converges to its Nash equilibrium, which is obtained explicitly; it is a fixed point of the transformation. So, the question is whether a trajectory starting from some initial point converges to the fixed point. The authors examine various parameters of the original economic problem, which determine an initial point of the trajectory. The unstability of the trajectory corresponds to some bifurcation, relevant 3D bifurcations and associated domains of parameters are carefully studied.

MSC:
91B54 Special types of economic markets (including Cournot, Bertrand)
91A10 Noncooperative games
91A70 Spaces of games
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