Use replicator dynamics with mutation

Given a matrix \(Q\) such that \(Q_{ij}\) gives the probability that an individual of type i mutates to an individual of type j, the replicator dynamics equation with mutation can be solved using the following:

>>> import nashpy as nash
>>> import numpy as np
>>> A = np.array([[3, 2], [4, 2]])
>>> Q = np.array([[9 / 10,  1 / 10], [1 / 5, 4 / 5]])
>>> game = nash.Game(A)
>>> game.replicator_dynamics(mutation_matrix=Q)
array([[0.5       , 0.5       ],
       [0.50049813, 0.49950187],
       [0.50099155, 0.49900845],
       ...,
       [0.55278206, 0.44721794],
       [0.5527821 , 0.4472179 ],
       [0.55278214, 0.44721786]])