Describing the Dynamics and Complexity of Matsumoto-Nonaka's Duopoly Model

Table 1

We compute average profits for the initial conditions considered in Figure 11 and following the iteration processes we make there we check that both firms should produce starting from the initial conditions on the basis of the attractor (𝑓). Note that the profits in the fixed point (Cournot equilibrium) are 0.0140236 for firm 1 and 0.148848 for firm 2, and therefore, the only firm interested in stabilizing the Cournot point will be firm 2.

Initial conditions	Firm 1	Firm 2
𝑥0=1/𝛽,𝑦0=0	0.0179073	0.0175666
𝑥0=1/𝛽,𝑦0=0.001	0.0145578	0.0161027
𝑥0=1/𝛽,𝑦0=1	−0.00460741	0.052774
𝑥0=1/𝛽,𝑦0=𝐺(1)	−0.00459554	0.0527484
𝑥0=1/𝛽1−1−1/𝛼,𝑦0=1	0.00177609	0.125768
𝑥0=1/𝛽1−1−1/𝛼,𝑦0=0.999	0.00190711	0.12623