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Analysis of a duopoly game with delayed bounded rationality. (English) Zbl 1102.91021
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.
MSC:
91A26Rationality, learning (game theory)
90C33Complementarity and equilibrium problems; variational inequalities (finite dimensions)