The stability and duality of dynamic Cournot and Bertrand duopoly model with comprehensive preference

作者：

Highlights：

• The Cournot and Bertrand model with comprehensive preference are discussed.

• A proportion parameter ε which classifies three competition conditions is introduced.

• The logistic mapping is applied to studying the dynamics of models on invariant axes.

• The critical curves help us observe the basin of attraction with “holes”.

• The duality of Cournot and Bertrand model with comprehensive preference still exists.

摘要

•The Cournot and Bertrand model with comprehensive preference are discussed.•A proportion parameter ε which classifies three competition conditions is introduced.•The logistic mapping is applied to studying the dynamics of models on invariant axes.•The critical curves help us observe the basin of attraction with “holes”.•The duality of Cournot and Bertrand model with comprehensive preference still exists.

论文关键词：Dynamic game,Chaos,Global stability,Comprehensive preference

论文评审过程：Received 4 November 2020, Revised 27 November 2020, Accepted 29 November 2020, Available online 19 December 2020, Version of Record 19 December 2020.

论文官网地址：https://doi.org/10.1016/j.amc.2020.125852