Analysis of a duopoly game with delayed bounded rationality

Authors:
M. T. Yassen;H. N. Agiza
Affiliations:
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt;Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
Venue:
Applied Mathematics and Computation
Year:
2003

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Abstract

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 of production. The equilibria of the corresponding discrete dynamical systems are investigated. The stability conditions of Nash equilibrium under a local adjustment process are studied. The stability of 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.