def w(beta, N, delta, r, threshold, epsilon_draw):
w_next = numpy.empty(N + 1)
w_now = numpy.ones(N + 1) # initial value
distance = 1
while distance > threshold: # loop until convergence
for x in range(N + 1): # calculate for each state
val = numpy.empty(epsilon_draw) # values for different epsilon draws
epsilon = numpy.random.gumbel(0, 1, epsilon_draw) # Random Type 1 Extreme Values
for i in range(epsilon_draw): # Monte Carlo simulation
choice_specific_val = numpy.empty(2)
for j in [0,1]: # calculate choice specific value for each action
cont_val = beta * sum(w_now[x_prime] * f(x_prime, x, j, N) for x_prime in range(N + 1))
choice_specific_val[j] = util(x, j, delta, N, r) + epsilon[i] + cont_val
val[i] = choice_specific_val.max()
w_next[x] = val.mean() # Take average of values for each epsilon
distance = numpy.linalg.norm(w_next - w_now) # calculate distance between w(n+1) and w(n)
w_now = w_next # move on to the next step
return w_now
def vj(beta, N, delta, r, threshold, epsilon_draw):
v = numpy.empty(2 * (N + 1))
v.shape = (N + 1, 2)
for j in range(2): # calculate choice specific value for each action
for x in range(N + 1): # calculate for each state
emax_w = w(beta, N, delta, r, threshold, epsilon_draw) # emax function
cont_val = beta * sum(emax_w[x_prime] * f(x_prime, x, j, N) for x_prime in range(N + 1))
v[x,j] = util(x, j, delta, N, r) + cont_val
return v