Evolutionary game theory

replicator equation

Warning

The implementation of mathematics might be wrong due to my lack of knowledge.

import matplotlib.pyplot as plt
import numpy as np
from mpltern.datasets import get_triangular_grid

x = np.array(get_triangular_grid(25))

payoff_matrix = [
    [0.0, -1.0, 1.0],
    [1.0, 0.0, -1.0],
    [-1.0, 1.0, 0.0],
]

fitness = payoff_matrix @ x
d = (fitness - np.sum(fitness * x, axis=0)) * x
norm = np.linalg.norm(d, axis=0)

ax = plt.subplot(projection="ternary")

ax.tripcolor(*x, norm, cmap="turbo", shading="gouraud", rasterized=True)

ax.quiver(*x, *d, scale=5, clip_on=False)

ax.set_tlabel("$x_0$")
ax.set_llabel("$x_1$")
ax.set_rlabel("$x_2$")

plt.show()