Nonlinear dynamics of a duopoly game with adjusting, heterogeneous players, facing increasing marginal costs

Abstract

A repeated, discrete time, nonlinear Cournot duopoly game with adjusting heterogeneous players, i.e. bounded rational and adaptive, is subject of investigation. The game is modeled by a system of two nonlinear difference equations. The evolution of outputs over time is obtained by iteration of a two dimensional noninvertible map. Existing equilibria and their stability are analyzed. Complex behavior is examined by means of numerical analysis. Dynamics of the region of stability is demonstrated. Period doubling route to chaos is presented. Periodic window is identified. Bifurcations, Lyapunov exponents, parameter basin of periodic cycles are computed. Intermittency and crisis are shown. Strange chaotic attractors are displayed and their fractal dimensions are calculated. Sensitive dependence on initial conditions is tested.