Zero determinant strategie

gistfile1.py

# -*- 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()