Complexity study on the Cournot-Bertrand mixed duopoly game model with market share preference

Junhai Ma; Lijian Sun; Shunqi Hou; Xueli Zhan

doi:10.1063/1.5001353

Complexity study on the Cournot-Bertrand mixed duopoly game model with market share preference

Chaos. 2018 Feb;28(2):023101. doi: 10.1063/1.5001353.

Authors

Junhai Ma¹, Lijian Sun¹, Shunqi Hou¹, Xueli Zhan²

Affiliations

¹ Group of Nonlinear Dynamics and Chaos, College of Management and Economics, Tianjin University, Tianjin 300072, China.
² School of Economics, Beijing Wuzi University, Beijing 10114, China.

PMID: 29495671
DOI: 10.1063/1.5001353

Abstract

In this paper, a Cournot-Bertrand duopoly model with market share preference is established. Assume that there is a degree of product difference between the two firms, where one firm takes the price as a decision variable and the other takes the quantity. Both firms are bounded rational, with linear cost functions and demand functions. The stability of the equilibrium points is analyzed, and the effects of some parameters (α, β, d and v₁) on the model stability are studied. Basins of attraction are investigated and the evolution process is shown with the increase in the output adjustment speed. The simulation results show that instability will lead to the increase in the average utility of the firm that determines the quantity and reduce the average utility of the firm that determines price.