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Mixed-Nash-Equilibrium.py
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Mixed-Nash-Equilibrium.py
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import math
import numpy as np
from math import inf
class LPSolver(object):
EPS = 1e-9
NEG_INF = -inf
def __init__(self, A, b, c):
self.m = len(b)
self.n = len(c)
self.N = [0] * (self.n + 1)
self.B = [0] * self.m
self.D = [[0 for i in range(self.n + 2)] for j in range(self.m + 2)]
self.D = np.array(self.D, dtype=np.float64)
for i in range(self.m):
for j in range(self.n):
self.D[i][j] = A[i][j]
for i in range(self.m):
self.B[i] = self.n + i
self.D[i][self.n] = -1
self.D[i][self.n + 1] = b[i]
for j in range(self.n):
self.N[j] = j
self.D[self.m][j] = -c[j]
self.N[self.n] = -1
self.D[self.m + 1][self.n] = 1
def pivot(self, r, s):
D = self.D
B = self.B
N = self.N
inv = 1.0 / D[r][s]
dec_mat = np.matmul(D[:, s:s + 1], D[r:r + 1, :]) * inv
dec_mat[r, :] = 0
dec_mat[:, s] = 0
self.D -= dec_mat
self.D[r, :s] *= inv
self.D[r, s + 1:] *= inv
self.D[:r, s] *= -inv
self.D[r + 1:, s] *= -inv
self.D[r][s] = inv
B[r], N[s] = N[s], B[r]
def simplex(self, phase):
m = self.m
n = self.n
D = self.D
B = self.B
N = self.N
x = m + 1 if phase == 1 else m
while True:
s = -1
for j in range(n + 1):
if phase == 2 and N[j] == -1:
continue
if s == -1 or D[x][j] < D[x][s] or D[x][j] == D[x][s] and N[j] < N[s]:
s = j
if D[x][s] > -self.EPS:
return True
r = -1
for i in range(m):
if D[i][s] < self.EPS:
continue
if r == -1 or D[i][n + 1] / D[i][s] < D[r][n + 1] / D[r][s] or (D[i][n + 1] / D[i][s]) == (
D[r][n + 1] / D[r][s]) and B[i] < B[r]:
r = i
if r == -1:
return False
self.pivot(r, s)
def solve(self):
m = self.m
n = self.n
D = self.D
B = self.B
N = self.N
r = 0
for i in range(1, m):
if D[i][n + 1] < D[r][n + 1]:
r = i
if D[r][n + 1] < -self.EPS:
self.pivot(r, n)
if not self.simplex(1) or D[m + 1][n + 1] < -self.EPS:
return self.NEG_INF, None
for i in range(m):
if B[i] == -1:
s = -1
for j in range(n + 1):
if s == -1 or D[i][j] < D[i][s] or D[i][j] == D[i][s] and N[j] < N[s]:
s = j
self.pivot(i, s)
if not self.simplex(2):
return self.NEG_INF, None
x = [0] * self.n
for i in range(m):
if B[i] < n:
x[B[i]] = round(D[i][n + 1], 6)
return round(D[m][n + 1], 6), x
def main():
N, M = list(map(int, input().split()))
utility_1 = []
utility_2 = []
for i in range(N):
utility_1.append([int(j) for j in input().split()])
for i in range(N):
utility_2.append([int(j) for j in input().split()])
utility_1 = np.array(utility_1)
utility_2 = np.array(utility_2)
count = 0
for i in range(2 ** N):
if count != 0:
break
for j in range(2 ** M):
if count != 0:
break
index1 = [k for k in range(N) if i & (1 << k)]
A = []
c = [0] * N + [0] * M
c += [1, 1]
index2 = [k for k in range(M) if j & (1 << k)]
b = []
if len(index2) == len(index1):
list1 = [0] * (N + M + 2)
for eee in range(N):
list1[eee] = 1
new_list = []
for x in list1:
new_list.append(-x)
A.append(new_list)
b.append(-1)
A.append(list1)
b.append(1)
list1 = [0] * (N + M + 2)
t = 0
for www in range(N):
if www not in index1:
list1[t] = 1
else:
list1[t] = 0
t += 1
A.append(list1)
b.append(0)
for k in range(N):
list1 = [0] * (2 + N + M)
list1[N + M] = -1
for q in range(M):
if q in index2:
list1[N + q] = utility_1[k][q]
if k in index1:
new_list = []
for x in list1:
new_list.append(-x)
A.append(new_list)
b.append(50)
A.append(list1)
b.append(-50)
list1 = [0] * (N + M + 2)
for aaaa in range(N, M + N):
list1[aaaa] = 1
A.append(list1)
b.append(1)
new_list = []
for x in list1:
new_list.append(-x)
A.append(new_list)
b.append(-1)
list1 = [0] * (N + M + 2)
t = 0
for www in range(M):
if www not in index2:
list1[t + N] = 1
else:
list1[t + N] = 0
t += 1
A.append(list1)
b.append(0)
for k in range(M):
list1 = [0] * (2 + N + M)
for q in range(N):
if q in index1:
list1[q] = utility_2[q][k]
list1[N + M + 1] = -1
if k in index2:
new_list = []
for x in list1:
new_list.append(-x)
A.append(new_list)
b.append(50)
A.append(list1)
b.append(-50)
s = LPSolver(A, b, c)
answer = s.solve()
if answer[1] is not None:
for t in range(N):
print("{:.6f}".format(answer[1][t]), end=" ")
print()
for t in range(M):
print("{:.6f}".format(answer[1][N + t]), end=" ")
print()
count += 1
else:
continue
main()