Equilibrium stability of a nonlinear heterogeneous duopoly game with extrapolative foresight

We make a further attempt to investigate equilibrium stability of a nonlinear Cournot duopoly game with adaptive adjustment toward best reply by assuming heterogeneous firms where one firm only uses naive expectations whereas the other employs a simple forecast technology to form sophisticated expectations. More precisely, based on the knowledge of actual production of the competitor and its actual rate of change, the clever firm is able to evaluate its opponent's output in the near future by virtue of straightforward extrapolative foresight. We finally arrive at a conclusion that this seemingly rational mechanism takes a positive effect on convergence to equilibrium behavior. Inconsistent with common intuition, we demonstrate that stronger foresight ability is not always better to stabilize the equilibrium. Particularly, perfect foresight dose not give rise to the best stabilizing factor.