Qualitative study of a bounded rationality duopoly game with exponential demand function

A bounded rationality duopoly game with exponential demand function is introduced. Local stability analysis of duopoly game is carried out. The stability of Nash equilibrium point is lost through period-doubling bifurcation as some parameters varied. Numerical simulations are used to show bifurcation diagrams, maximal Lyapunov exponents and sensitive dependence on initial conditions. The chaotic behavior of the model has been stabilized on the Nash equilibrium point, by the use of the Pyragas delay feedback control method.