Stochastic_fictitious_play fails for large valued payoff matrices

[katiemcgoldrick]

In #100 stochastic fictitious play is implemented but it fails for large values pay off matrices due to an overflow error when computing the exponential of large numbers.

>>> import nashpy as nash
>>> import numpy as np
>>> A = np.array([[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]])
>>> B = A + 71
>>> game=nash.Game(A,B)
>>> tuple(game.stochastic_fictitious_play(iterations=10))
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-6-867513ac063a> in <module>
----> 1 x = tuple(game.stochastic_fictitious_play(iterations=10))

c:\users\kathr\desktop\nashpy\src\nashpy\learning\stochastic_fictitious_play.py in stochastic_fictitious_play(A, B, iterations, etha, epsilon_bar, play_counts)
     44         ]
     45 
---> 46         plays = [
     47             np.random.choice(range(len(distribution)), p=distribution)
     48             for distribution in distributions

c:\users\kathr\desktop\nashpy\src\nashpy\learning\stochastic_fictitious_play.py in <listcomp>(.0)
     45 
     46         plays = [
---> 47             np.random.choice(range(len(distribution)), p=distribution)
     48             for distribution in distributions
     49         ]

mtrand.pyx in numpy.random.mtrand.RandomState.choice()

ValueError: probabilities contain NaN

This breaks down because of :

>>> np.exp(700)
1.0142320547350045e+304
>>> np.exp(710)
inf

Speaking with @drvinceknight and @11michalis11 , two possible solutions are 1) catch the error and provide a better error message or 2) rescale the matrix automatically