Equilibrium stability of a nonlinear heterogeneous duopoly game with extrapolative foresight

Equilibrium stability of a nonlinear heterogeneous duopoly game with extrapolative foresight

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Article ID: iaor20125182
Volume: 82
Issue: 11
Start Page Number: 2069
End Page Number: 2078
Publication Date: Jul 2012
Journal: Mathematics and Computers in Simulation
Authors: , ,
Keywords: duopoly, Nash equilibrium
Abstract:

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.

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