Controlling Chaos Through Local Knowledge

We propose an duopoly game where quantity-setting firms have incomplete information about the demand function. In each time step, they solve a profit maximization problem assuming a linear local approximation of the demand function. In particular, we construct an example using the well known duopoly Puu's model with isoelastic demand function and constant marginal costs. An explicit form of the dynamical system that describes the time evolution of the duopoly game with boundedly rational players is given. The main result is the global stability of the system.