Nonlinear Dynamics in a Cournot Duopoly with Different Attitudes towards Strategic Uncertainty

Figure 2

Critical curves are represented for the parameter set: 𝛼=0.3, 𝑎=7.2, 𝑏=0.22, 𝑐=0.4, and 𝛾=0.9. The blue lines LC^(𝑎)₋₁ and LC^(𝑏)₋₁ are the two branches of the LC₋₁ set. The portion of the plane that lies between the axes and LC^(𝑎) defines region 𝑍₄; the portion of the plane that lies between the black lines LC^(𝑎) and LC^(𝑏) defines region 𝑍₂; the portion of the plane beyond LC^(𝑏) defines region 𝑍₀. In addition, 𝑂 and its preimages define the quadrilateral 𝑂𝐴𝐵𝐶 that delimitates the (grey) region of bounded trajectories. The blue line 𝑝=0 represents points in which the market price equals zero. The white region below the line 𝑝=0 represents initial conditions with respect to which trajectories lead to the invariant axes for map 𝑀^∗₁.