Study and Simulation on Discrete Dynamics of Bertrand Triopoly Team-Game

Abstract EN

A Bertrand Triopoly team-game model is considered in which two firms with bounded rational expectations make up a cooperative team and allocate common profits proportionate to their marketing strength.

The existence and three-dimensional stable regions of the fixed points are investigated.

Complex effects of ( α , β , v ) on bifurcation scenarios and profits are displayed by parameter basin plots and average profits charts.

Impact of assigning weight w on stable regions, 2D-bifurcation phase portraits, and the average profits is investigated.

We find ( α , β , v ) and w can cause chaos; chaos resulting from adjustment speed is harmful to all the players as for profits, while chaos resulting from w is conducive to firm 3.

Basins of attraction are investigated and we find that the attraction domain will become smaller with increase of price modification speed.