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

Agiza, H. N.; Hegazi, A. S.; Elsadany, A. A.

Math. Comput. Simul. 58, No. 2, 133-146 (2002).

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.

Reviewer: Roy Gardner (Bloomington)

MSC:

91A50

Discrete-time games

Keywords:

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

References:

[2]	Agiza, H. N.; Bischi, G. I.; Kopel, M., Multistability in a dynamic Cournot game with three oligopolists, Math. Comput. Simul., 51, 63-90 (1999)
[4]	Ahmed, E.; Agiza, H. N.; Hassan, S. Z., On modification of Puu’s dynamical duopoly, Chaos, Solitons & Fraclals, 11, 7, 1025-1028 (2000) · Zbl 0955.91045
[5]	Aicardi, F.; Invernizzi, S., Memory effects in discrete dynamical systems, Int. J. Bifu. Chaos, 2, 4, 815-830 (1992) · Zbl 0870.58016
[7]	Bischi, G. I.; Stefanini, L.; Gardini, L., Synchronization intermittency and critical curves in a duopoly game, Math. Comput. Simul., 44, 559-585 (1998) · Zbl 1017.91500
[10]	Gardini, L.; Abrahem, R.; Record, R.; Fournier-Prunaret, Di, A double logistic map, Int. J. Bifu. Chaos, 4, 1, 145-176 (1994) · Zbl 0870.58020
[16]	Maistermko, Y.; Kapitanaiak, T., Different types of chaos synchronization in two coup1ed picewise linear maps, Phys. Rev. E, 54, 3285 (1996)