Duopoly Output Game with Bounded Rationality and Limiter Control

Abstract

Based on the bounded rationality strategy, a duopoly output game model is constructed in this paper. The local stability conditions of Nash equilibrium point of the model are also analyzed by employing the well-known Jury’s criteria. The results show that the model has three boundary fixed points and a local stable Nash equilibrium point. When the combination values of the two firms’ adjustment speed are out of the local stability region, some more complex dynamic phenomena will be caused such as bifurcation and chaos. In order to eliminate chaos and improve the profit level, a limiter control scheme is designed. Numerical simulations further verify that the designed limiter control scheme is feasible and effective to eliminate chaos and improve profit level.

Key words: Duopoly game; Bounded rationality; Limiter control; Chaos