Study and simulation on discrete dynamics of Bertrand Triopoly team-game

Abstract

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 ω can cause chaos; chaos resulting from adjustment speed is harmful to all the players as for profits, while chaos resulting from ω 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.