On complex dynamics of Cournot-Bertrand game with asymmetric market information

• Published in: Applied mathematics and computation Vol. 393; p. 125823
• Main Author: Askar, S.S.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15.03.2021
• Subjects: Bifurcation; Bounded rational firms; Cournot-Bertrand game; Critical curves; Noninvertible map; Noninvertible map; Bifurcation; Cournot-Bertrand game; Bounded rational firms; Critical curves
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2020.125823

•A Cournot-Bertrand duopoly game that is characterized as bounded rational firms is introduced by a discrete dynamical map.•The second firm in the game is characterized by knowing some information about the next time production of its opponent.•The game’s equilibrium points are calculated and their stability conditions are obtained.•The stability of Nash point gives rise to periodic and chaotic attractors.•The structure of basins of attraction for some attracting set changes from simple to complex.•The critical curves of the map’s game show that it is noninvertible. A Cournot-Bertrand duopoly game that is characterized as bounded rational firms is introduced by a discrete dynamical map. The second firm in the game is characterized by knowing some information about the next time production of its opponent. The game’s equilibrium points are calculated and their conditions which ensuring stability are obtained for the boundary points. Due to the complex form of Nash point its stability loss is analyzed under varying some of the game’s parameters. The numerical simulation of Nash equilibrium point gives rise to periodic and chaotic attractors. Using some parameters’ values the structure of basins of attraction for some attracting set that changes that structure from simple to complex is determined. We also calculate the critical curves of the map’s game and show that it is noninvertible.