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

Abstract

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.