The dynamics of Bowleyʹs model with bounded rationality

A nonlinear dynamical system which describe the time evolution of n-competitors in a Cournot game (Bowleyʹs model) with bounded rationality is analyzed. The existence and stability of the equilibria of this system is studied. The stability conditions of the steady states for two and three players are explicitly computed. Complex behavior such as cycles and chaotic behavior are observed by numerical simulation. Delayed Bowleyʹs with bounded rationality in monopoly is studied. We show that firms using bounded rationality with delay has a higher chance of reaching Nash equilibrium.