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June 7, 2014 10:52
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Zero determinant strategie
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# -*- coding: utf-8 -*- | |
import numpy as np | |
import matplotlib.pyplot as plt | |
# Define gain matrix | |
T,R,P,S = 5,3,1,0 | |
G = np.array([[[R,R],[S,T]],[[T,S],[P,P]]]) | |
# X chooses to unilaterally set Y score | |
p1 = 0.9 | |
p4 = 0.1 | |
p2 = (p1*(T-P)-(1+p4)*(T-R))/(R-P) | |
p3 = ((1-p1)*(P-S)+p4*(R-S))/(R-P) | |
sY = ((1-p1)*P+p4*R)/(1-p1+p4) | |
## X chooses to extortionate | |
#chi = 4 | |
#phi = 0.5 * (P-S)/((P-S)+chi*(T-P)) | |
#p1 = 1-phi*(chi-1)*(R-P)/(P-S) | |
#p2 = 1-phi*(1+chi*(T-P)/(P-S)) | |
#p3 = phi*(chi+(T-P)/(P-S)) | |
#p4 = 0 | |
# Q stratetey | |
q1,q2,q3,q4 = 0.9,0.1,0.1,0.2 | |
# Define strategy matrices and gain matrix | |
M1 = np.array([[p1,p2],[p3,p4]]) | |
M2 = np.array([[q1,q2],[q3,q4]]) | |
prevDefect = [False,False] # True if player defected | |
curDefect = [False,False] | |
total1, total2 = 0, 0 | |
tx = [] | |
ty = [] | |
N = 10000 | |
for n in range(N): | |
x1,x2 = np.random.random(size=2) | |
curDefect[0] = x1 > M1[prevDefect[0],prevDefect[1]] | |
curDefect[1] = x2 > M2[prevDefect[1],prevDefect[0]] | |
total1 = total1 + G[curDefect[0],curDefect[1],0] | |
total2 = total2 + G[curDefect[0],curDefect[1],1] | |
prevDefect = curDefect | |
tx.append(total1/(n+1)) | |
ty.append(total2/(n+1)) | |
print(total1/(N+1),total2/(N+1)) | |
plt.plot(tx) | |
plt.plot(ty) | |
plt.show() |
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