Dynamic outcome of coopetition duopoly with implicit collusion. (July 2022)

• Record Type: Journal Article
• Authors: Ding, Shasha; Sun, Hao; Sun, Panfei; Han, Weibin
• Is Part Of: Chaos, solitons and fractals. Volume 160(2022)
• Publication Date: 2022-07
• Subjects: Dynamics -- Coopetition duopoly -- Implicit collusion -- chaos; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2022.112236
• Languages: English
• ISSNs: 0960-0779

Abstract

Abstract: This paper mainly explores the influence of implicit collusion on the dynamic outcome of enterprises in coopetitive duopoly market. We construct a coopetitive duopoly model with implicit collusion, in which the narrowing price difference could be regarded as implicit collusion to drive the price up and avoid the risk of price wars brought by cutthroat competition. The dynamic coopetition duopoly model demonstrates the effect of implicit collusion on interior stable point. The equilibrium price of coopetitive balance with implicit collusion is higher than the Bertrand equilibrium price since implicit collusion maintains the prices at a high level. Furthermore, our model reveals that implicit collusion could bring back the enterprise, which has been dislodged from duopoly market on boundary stable point under certain parameter conditions. Besides, numerical simulations show a series of chaotic behaviors and present that the size of stability region is related to the values of parameters. Highlights: A coopetitive duopoly model with implicit collusion is constructed. The implicit collusion could be expressed as the narrowing of price difference. The equilibrium price of coopetitive balance is higher than the Bertrand equilibrium price. The analysis on bifurcation behaviors and stability of equilibrium price had been studied.