Competition analysis of a triopoly game with bounded rationality

A dynamic Cournot game characterized by three boundedly rational players is modeled by three nonlinear difference equations. The stability of the equilibria of the discrete dynamical system is analyzed. As some parameters of the model are varied, the stability of Nash equilibrium is lost and a complex chaotic behavior occurs. Numerical simulation results show that complex dynamics, such as, bifurcations and chaos are displayed when the value of speed of adjustment is high. The global complexity analysis can help players to take some measures and avoid the collapse of the output dynamic competition game.

► We model a Cournot triopoly game with three boundedly rational players.
► The equilibrium points of the model and their local stability are investigated.
► We study the dynamics of this model as varying the parameters.
► The stability of Nash equilibrium is lost and a chaotic behaviors occur.