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Zbl 1002.91010
Agiza, H.N.; Hegazi, A.S.; Elsadany, A.A.
Complex dynamics and synchronization of a duopoly game with bounded rationality.
(English)
[J] Math. Comput. Simul. 58, No.2, 133-146 (2002). ISSN 0378-4754

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.
[Roy Gardner (Bloomington)]
MSC 2000:
*91A50 Discrete-time games

Keywords: bounded rationality; symmetric Cournot duopoly; unique Nash equilibrium; out-of-equilibrium dynamics; first-order nonlinear difference equations; complex dynamics

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