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Zbl 1102.91021
Yassen, M. T.; Agiza, H. N.
Analysis of a duopoly game with delayed bounded rationality. (English)
[J] Appl. Math. Comput. 138, No. 2-3, 387-402 (2003). ISSN 0096-3003

A dynamic of Cournot duopoly game is analyzed, where players use different production methods and choose their quantities with bounded rationality. A dynamic of nonlinear Cournot duopoly game is analyzed, where players choose quantities with delayed bounded rationality and similar methods production. The equilibria of the corresponding discrete dynamic systems are investigated. The stability conditions of Nash equilibrium under a local adjustment process are studied. The stability od Nash equilibrium, as some parameters of the model are varied, gives rise to complex dynamics such as cycles of higher order and chaos. We show that firms using delayed bounded rationality have a higher chance of reaching Nash equilibrium. Numerical simulations are used to show bifurcations diagrams, stability regions and chaos.
[Tadeusz Radzik (Jelenia Góra)]

MSC 2000:: *91A26 Rationality, learning
90C33 Complementarity problems

Keywords: duopoly game; delayed bounded rationality; Nash equilibrium; stability; bifurcation; chaos

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