Complex dynamics and synchronization of a duopoly game with bounded rationality. (English) Zbl 1002.91010

Consider a symmetric Cournot duopoly with a unique Nash equilibrium. Specify the out-of-equilibrium dynamics as a system of first-order nonlinear difference equations as described by Cournot, with speed of adjustment parameter \(\alpha\). The paper shows that the boundaries of the problem are an unstable rest point. For small values of \(\alpha\), the Nash equilibrium is stable, while larger values of a lead to complex dynamics.


91A50 Discrete-time games
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