Research on a Cournot–Bertrand Game Model with Relative Profit Maximization

Abstract EN

This paper considers a Cournot–Bertrand game model based on the relative profit maximization with bounded rational players.

The existence and stability of the Nash equilibrium of the dynamic model are investigated.

The influence of product differentiation degree and the adjustment speed on the stability of the dynamic system is discussed.

Furthermore, some complex properties and global stability of the dynamic system are explored.

The results find that the higher degree of product differentiation enlarges the stable range of the dynamic system, while the higher unit product cost decreases the stable range of price adjustment and increases the one of output adjustment; period cycles and aperiodic oscillation (quasi-period and chaos) occur via period-doubling or Neimark–Sacker bifurcation, and the attraction domain shrinks with the increase of adjustment speed values.

By selecting appropriate control parameters, the chaotic system can return to the stable state.

The research of this paper is of great significance to the decision-makers’ price decision and quantity decision.