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fictitious_play.py
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fictitious_play.py
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import numpy
import math
from scipy import stats
def RandomizedFictitiousPlay(A, Epsilon):
n = len(A[0])
m = len(A)
X = numpy.matrix(numpy.zeros((m, 1), dtype=int))
Y = numpy.matrix(numpy.zeros((n, 1), dtype=int))
X[0] = 1
Y[0] = 1
numpy.random.shuffle(X)
numpy.random.shuffle(Y)
t = int(round(6*math.log(2*n*m)/pow(Epsilon, 2)))
for i in range(t):
Ax = numpy.array(numpy.transpose(A) * X).tolist()
#print Ax
Ay = numpy.array(A * Y).tolist()
#print Ay
values = Ay
probabilities = []
for item in Ay:
probabilities.append(pow(math.e, Epsilon*item[0]/2))
while True:
try:
theprobabilities = []
temp = sum(probabilities)
theprobabilities[:] = [x / temp for x in probabilities]
distrib = stats.rv_discrete(values=(values, theprobabilities))
xchoice = Ay.index(distrib.rvs(size=1)[0])
break
except:
pass
values = Ax
probabilities = []
for item in Ax:
probabilities.append(pow(math.e, -Epsilon*item[0]/2))
while True:
try:
theprobabilities = []
temp = sum(probabilities)
theprobabilities[:] = [x / temp for x in probabilities]
distrib = stats.rv_discrete(values=(values, theprobabilities))
ychoice = Ax.index(distrib.rvs(size=1)[0])
break
except:
pass
#print xchoice
X[xchoice] += 1
#print X
#print ychoice
Y[ychoice] += 1
#print Y
return X/float(t+1), Y/float(t+1)
def FictitiousPlay(A, t):
n = len(A[0])
m = len(A)
X = numpy.matrix(numpy.zeros((m, 1), dtype=int))
Y = numpy.matrix(numpy.zeros((n, 1), dtype=int))
X[0] = 1
Y[0] = 1
numpy.random.shuffle(X)
numpy.random.shuffle(Y)
for i in range(t):
Ax = numpy.array(numpy.transpose(A) * X).tolist()
Ay = numpy.array(A * Y).tolist()
xchoice = Ax.index(min(Ax))
ychoice = Ay.index(max(Ay))
#print xchoice
X[ychoice] += 1
#print X
#print ychoice
Y[xchoice] += 1
#print Y
return X/float(t+1), Y/float(t+1)
#The payoff Matrix
A = numpy.identity(5, dtype=int)
#A = numpy.array([[1, 0, 2, -2], [-1, 1, -1, 0]])
print FictitiousPlay(A, 10000)
print RandomizedFictitiousPlay(A, 0.1)
#r = 1
#while r >= 0.3:
# temp1, temp = RandomizedFictitiousPlay(A, 0.1)
# Ax = numpy.array(numpy.transpose(A) * temp1).tolist()
# Ay = numpy.array(A * temp).tolist()
# r = abs(max(Ay)[0] - min(Ax)[0])
# print r
#print temp1, temp
#while temp
#print RandomizedFictitiousPlay(A, 0.1)
#print FictitiousPlay(A, 1700)