for i in range(1, N+1): #行動１→行動０への変更
m_i = i / N #行動 1 をとっているプレイヤーとマッチする確率,行動１の人が選ばれる確率
ratio = np.array([1-m_i, m_i])
exp = np.dot(profit_A, ratio)
if exp[0] > exp[1]: #行動０が最適反応のとき
p[i][i-1] = m_i*((1.0-epsilon) + epsilon*0.5) # p[i][i-1] x_0が１減少するマスの確率
else:
p[i][i-1] = m_i*(epsilon*0.5)
for i in range(N): #行動０→行動１への変更
m_i = i / N
ratio = np.array([1-m_i, m_i])
exp = np.dot(profit_A, ratio)
if exp[0] < exp[1]:
p[i][i+1] = (1-m_i)*((1-epsilon) + epsilon*0.5)
else:
p[i][i+1] = (1-m_i)*(epsilon*0.5)
for i in range(1, N): #行動を変えない
p[i][i] = 1 - p[i][i-1] - p[i][i+1]
#上からもれたマス
p[0][0] = 1 - p[0][1]
p[N][N] = 1 - p[N][N-1]
X = mc_sample_path(p, x_0, times) #マルコフ連鎖
plt.plot(X)
plt.show()
P[i, i - 1] = (i/N)*((1 - ep) + ep*0.5)
P[i, i] = (1 - i/N)*ep*0.5 + (i/N)*ep*0.5
P[i, i + 1] = (1 - i/N)*((1 - ep) + ep*0.5)
else:
P[i, i - 1] = (i/N)*ep*0.5
P[i, i] = (1 - i/N)*ep*0.5 + (i/N)*((1 - ep) + ep*0.5)
P[i, i + 1] = (1 - i/N)*((1 - ep) + ep*0.5)
return P
P = kmr(N, ep, p)
x_t = mc_sample_path(P, x_0, sample_size=t)
plt.plot(x_t)
plt.show()
payoff_0 = np.array([[payoff[0, 0, 0], payoff[0, 1, 0]], [payoff[1, 0, 0], payoff[1, 1, 0]]]) # payoff matrix for player 0
# setting up transitive matrix A
A = np.zeros([N+1, N+1])
A[0, 0] = 1 - epsilon*0.5
A[0, 1] = epsilon*0.5
A[N, N-1] = epsilon*0.5
A[N, N] = 1 - epsilon*0.5
for i in range(1, N):
x_i = i / N
ratio = np.array([1- x_i, x_i]) # the ratio b/w action0 and action1
exp = np.dot(payoff_0, ratio)
if exp[0] > exp[1]:
A[i, i -1] = x_i * (1-epsilon*0.5)
A[i, i+1] = (1-x_i) * epsilon*0.5
A[i, i] = 1- A[i, i-1] - A[i, i+1]
elif exp[0] < exp[1]:
A[i, i -1] = x_i * epsilon*0.5
A[i, i+1] = (1 - x_i) * (1 - epsilon * 0.5)
A[i, i] = 1- A[i, i-1] - A[i, i+1]
else:
A[i, i -1] = x_i * 0.5
A[i, i+1] = x_i * 0.5
A[i, i] = 0.5
y = mc_sample_path(A, x_0, times)
fig, ax = plt.subplots()
ax.plot(y)
plt.show()
def set_P(self):
if self.move == 'sequential':
self.P = KMR_2x2_P_sequential(self.N, self.p, self._epsilon)
else:
self.P = KMR_2x2_P_simultaneous(self.N, self.p, self._epsilon)
def simulate(self, T=100000, x0=0):
"""
Generates a NumPy array containing a sample path of length T
with initial state x0 = 0
"""
self.s = mc_sample_path(self.P, x0, T)
def get_sample_path(self):
return self.s
def plot_sample_path(self, ax=None, show=True):
if show:
fig, ax = plt.subplots()
ax.plot(self.s, alpha=0.5)
ax.set_ylim(0, self.N)
ax.set_title(r'Sample path: $\\varepsilon = {0}$'.format(self._epsilon))
ax.set_xlabel('time')
ax.set_ylabel('state space')
if show:
X[k][k]=(k/n)*epsilon*0.5
elif expay1[0]==expay1[1]:
X[k][k-1]=(k/n)*0.5
X[k][k]=(k/n)*0.5
else:
X[k][k-1]= (k/n)*epsilon*0.5
X[k][k] = (k/n)*((1-epsilon)+epsilon*0.5)
if expay0[1]>expay0[0]:
X[k][k+1]=((n-k)/n)*((1-epsilon)+epsilon*0.5) #k人からk+1人になる確率
X[k][k] += ((n-k)/n)*epsilon*0.5 #X[k][k]は上でも定めているので上書きでなく加えている
elif expay0[1]==expay0[0]:
X[k][k+1] = ((n-k)/n)*0.5
X[k][k] += ((n-k)/n)*0.5
else:
X[k][k+1] = ((n-k)/n)*epsilon*0.5
X[k][k] += ((n-k)/n)*((1-epsilon)+epsilon*0.5)
X[0][0] = (1-epsilon)+epsilon*0.5
X[0][1] = epsilon*0.5
X[n][n-1] = epsilon*0.5
X[n][n] = (1-epsilon)+epsilon*0.5
x_0 = np.random.binomial(n,p) # determine X_0
xs=mc_sample_path(X,init=x_0,sample_size=t)
"""
確率分布を入れる場合は長さn+1のリストを入れなければいけないらしく
面倒なので各人が確率pで行動1を選択するという二項分布を作って整数値で代入
"""
plt.plot(xs, 'b-', label='X_t')
plt.legend()
plt.show()
elif exp[0] < exp[1]:
P[i][i] = num*(1-epsilon*0.5)+(1-num)*epsilon*0.5
else:
P[i][i] = 0.5
for i in range(1, n+1):
num = fractions.Fraction(i, n)
pr = np.array([1-num, num])
exp = np.dot(pay0, pr)
if exp[0] > exp[1]:
P[i][i-1] = num*(1-epsilon*0.5)
elif exp[0] < exp[1]:
P[i][i-1] = num*epsilon*0.5
else:
P[i][i-1] = num*0.5
for i in range(n):
num = fractions.Fraction(i, n)
pr = np.array([1-num, num])
exp = np.dot(pay0, pr)
if exp[0] > exp[1]:
P[i][i+1] = (1-num)*epsilon*0.5
elif exp[0] < exp[1]:
P[i][i+1] = (1-num)*(1-epsilon*0.5)
else:
P[i][i+1] = (1-num)*0.5
X = mc_sample_path(P, psi, t)
fig, ax = plt.subplots()
ax.plot(X)
plt.show()
N = 6
t = 10000
epsilon = 0.1
x_0 = 0
p = 1/3
A = np.zeros([N+1, N+1])
A[0,0] = 1 - epsilon*0.5
A[0,1] = epsilon*0.5
A[N,N-1] = epsilon*0.5
A[N,N] = 1 - epsilon*0.5
for i in range(1,N):
x_i = i / N
if x_i < p:
A[i, i-1] = x_i * (1 - epsilon*0.5)
A[i, i+1] = (1 - x_i) * epsilon*0.5
A[i, i] = 1 - A[i, i-1] - A[i, i+1]
elif x_i > p:
A[i, i -1] = x_i * epsilon*0.5
A[i, i+1] = (1 - x_i) * (1 - epsilon * 0.5)
A[i, i] = 1- A[i, i-1] - A[i, i+1]
else:
A[i, i -1] = x_i * 0.5
A[i, i+1] = x_i * 0.5
A[i, i] = 0.5
y = mc_sample_path(A, x_0, t)
fig, ax = plt.subplots()
ax.plot(y)
plt.show()
if expay[0] == expay[1]:
P[n, n+1] += (1 - n/N) * 0.5
P[n, n-1] += n/N * 0.5
elif expay[0] > expay[1]:
P[n, n+1] += (1 - n/N) * epsilon * 0.5
P[n, n-1] += n/N * (1 - epsilon * 0.5)
else:
P[n, n+1] += (1 - n/N) * (1 - epsilon * 0.5)
P[n, n-1] += n/N * epsilon * 0.5
P[n,n] = 1 - sum(P[n])
# Derive a path of x with mc_tools
x = mc_sample_path(P, default, trials)
# Plot a path of x
fig, ax = plt.subplots()
xaxis = range(trials)
ax.plot(xaxis, x, 'b-',label = 'Num. of people taking action 1')
ax.legend(loc = 4)
plt.title('Num. of players = ' + str(N) + ', '+ 'Trials = '+ str(trials) + ', ' + 'epsilon = ' + str(epsilon), color='k')
plt.savefig(gamename + str(N) + str(trials) + str(epsilon) + '.png',transparent=True, bbox_inches='tight', pad_inches=0)
plt.close()
epsilon = 0.2
r = random.uniform(0, 1)
psi = (r, 1 - r)
P = np.zeros([n + 1, n + 1])
for i in range(1, n + 1): #行動１をとっている人が選ばれて行動０に変更する
num0 = fractions.Fraction(i - 1, n - 1)
num1 = fractions.Fraction(i, n)
ratio = np.array([1.0 - num0, num0])
exp = np.dot(p_0, ratio)
if exp[0] > exp[1]:
P[i][i - 1] = num1 * ((1.0 - epsilon) + epsilon * 0.5)
else:
P[i][i - 1] = num1 * (epsilon * 0.5)
for i in range(n): #行動0をとっている人が選ばれて行動1に変更する
num0 = fractions.Fraction(i, n - 1)
num1 = fractions.Fraction(i, n)
ratio = np.array([1 - num0, num0])
exp = np.dot(p_0, ratio)
if exp[0] < exp[1]:
P[i][i + 1] = (1 - num1) * ((1 - epsilon) + epsilon * 0.5)
else:
P[i][i + 1] = (1 - num1) * (epsilon * 0.5)
for i in range(1, n): #行動を変えない
P[i][i] = 1 - P[i][i - 1] - P[i][i + 1]
P[0][0] = 1 - P[0][1]
P[n][n] = 1 - P[n][n - 1]
X = mc_sample_path(P, psi, t)
plt.plot(X)
plt.show()
def path(self, t):
self.set_move()
self.set_x0()
self.xs = mc_sample_path(self.X,init=self.x_0,sample_size=t)
