def policy_diff(r = 10, R_max = 100, a = 1000, b1 = 1, b2 = 1, q = -0.5, c = 0.05,
d = 100, k = 2, p = 3, h = 0.06, g = 0.01, m = 0.3,
W_min = 0, dt = 0.08):
'''
Loop through several different caps to see if policies have any effect. Takes in
usual parameters, returns whether or not any of the policies led to a different
outcome
'''
num_points = 50
np.random.seed(0)
initial_points = doe.lhs(3, samples = num_points)
# Scale points ([R, U, W])
R_0 = initial_points[:,0] * 100
U_0 = initial_points[:,1] * 45
W_0 = initial_points[:,2] * 20
amount = 500
caps = np.linspace(1.5, 31.5, 11)
caps = np.append(caps, 100)
res = np.zeros(len(caps))
for i, cap in enumerate(caps):
for j in range(num_points):
ts = simulate_SES(r, R_max, a, b1, b2, q, c, d, k, p, h, g, m,
W_min, dt, R_0[j], W_0[j], U_0[j], cap, amount)
R, E, U, S, W, P, L, convergence = ts.run()
if R[-1] < 90 and U[-1] > 1:
res[i] += 1
return res/num_points
def resource_from_extraction(R_0, trajectory):
R = np.zeros(len(trajectory) + 1)
R[0] = R_0
# set resource parameters
r = 10
R_max = 100 # aquifer capacity
# Set industrial payoff parameters
a = 1000 # profit cap
b1 = 1
b2 = 1
q = -0.5
c = 0.05 # extraction cost parameter
d = 100
# Set domestic user parameters
k = 2 # water access parameter (how steeply benefit of water rises)
p = 3 # out-of-system wellbeing/payoff
h = 0.06 # rate at which wage declines with excess labor
g = 0.01 # rate at which wage increases with marginal benefit of more labor
m = 0.8 # responsiveness of population to wellbeing (h*p > 1 with dt=1)
W_min = 0
dt = 0.08
W_0 = 0
U_0 = 0
for i, E in enumerate(trajectory):
ts = simulate_SES(r, R_max, a, b1, b2, q, c, d, k, p, h, g, m, W_min,
dt, R_0, W_0, U_0)
R[i + 1] = ts.resource(R[i], E)
return R
def bifurcation(r=10,
R_max=100,
a=1000,
b1=1,
b2=1,
q=-0.5,
c=0.05,
d=100,
k=2,
p=3,
h=0.06,
g=0.01,
m=0.3,
W_min=0,
dt=0.08):
'''
Loop through several different caps to see if policies have any effect. Takes in
usual parameters, returns whether or not any of the policies led to a different
outcome
'''
num_points = 10
np.random.seed(0)
initial_points = doe.lhs(3, samples=num_points)
# Scale points ([R, U, W])
R_0 = initial_points[:, 0] * 100
U_0 = initial_points[:, 1] * 45
W_0 = initial_points[:, 2] * 20
eq_R = np.zeros([num_points])
eq_U = np.zeros([num_points])
eq_W = np.zeros([num_points])
for i in range(num_points):
ts = simulate_SES(r, R_max, a, b1, b2, q, c, d, k, p, h, g, m, W_min,
dt, R_0[i], U_0[i], W_0[i])
R, E, U, S, W, P, L, convergence = ts.run()
eq_R[i] = R[-1]
eq_U[i] = U[-1]
eq_W[i] = W[-1]
return eq_R, eq_U, eq_W
def wellbeing(resource_data, wage_data, pop_data, labor_data, num_points):
"""
calculates wellbeing trajectories for each policy
"""
# set resource parameters
r = 10
R_max = 100 # aquifer capacity
# Set industrial payoff parameters
a = 1000 # profit cap
b1 = 1
b2 = 1
q = -0.5
c = 0.05 # extraction cost parameter
d = 100
# Set domestic user parameters
k = 2 # water access parameter (how steeply benefit of water rises)
p = 3 # out-of-system wellbeing/payoff
h = 0.06 # rate at which wage declines with excess labor
g = 0.01 # rate at which wage increases with marginal benefit of more labor
m = 0.3 # responsiveness of population to wellbeing (h*p > 1 with dt=1)
W_min = 0
dt = 0.08
W_0 = 0
U_0 = 0
R_0 = 0
wellbeing_trajectories = [0]*num_points
ts = simulate_SES(r, R_max, a, b1, b2, q, c, d, k, p, h, g, m,
W_min, dt, R_0, W_0, U_0)
for i in range(num_points):
water_access_data = np.array(ts.water_access(np.array(resource_data[i])))[1:]
wage_data[i] = np.array(wage_data[i][1:])
wellbeing_trajectories[i] = water_access_data*wage_data[i]*labor_data[i]
return wellbeing_trajectories
W_min = 0
dt = 1
N = 10
U_arr = np.linspace(1, 55, N)
W_arr = np.linspace(1, 30, N)
dU = np.zeros((N, N))
dW = np.zeros((N, N))
dR = np.zeros((N, N))
for j, U_0 in enumerate(U_arr):
for l, W_0 in enumerate(W_arr):
pp = simulate_SES(r, R_max, a, b1, b2, q, c, d, k, p, h, g, m, W_min,
dt, 100, W_0, U_0)
R, E, U, S, W, P, L, convergence = pp.run()
dU[j, l] = U[-1] - U_0
if U[-1] < 0.1:
dW[j, l] = 0 - W_0
else:
dW[j, l] = (L[-1] / U[-1]) * W[-1] - W_0
U, W = np.meshgrid(U_arr, W_arr)
plt.figure()
ax = plt.axes()
ax.quiver(U, W, dU, dW)
ax.set_xlabel('Population (U)')
ax.set_ylabel('Wage (W)')
p = 3 # out-of-system wellbeing/payoff
h = 0.06 # rate at which wage declines with excess labor
g = 0.01 # rate at which wage increases with marginal benefit of more labor
m = 0.8 # responsiveness of population to wellbeing (h*p > 1 with dt=1)
W_min = 0
# Step size
dt = 0.08
R_0 = 100
U_0 = 10
W_0 = 4
W_min = 0
ts = simulate_SES(r, R_max, a, b1, b2, q, c, d, k, p, h, g, m, W_min, dt, R_0,
W_0, U_0)
R, E, U, S, W, P, L, convergence = ts.run()
R = np.array(R)
n = len(R)
T = n * dt
fig, axarr = plt.subplots(3)
axarr[0].plot(np.arange(n) * dt, R, color='k')
axarr[0].set_ylim([0, R_max])
axarr[0].set_title('Resource')
axarr[1].plot(np.arange(n) / (n / T), U, color='k')
axarr[1].set_title('Population')
axarr[1].set_ylim([0, 30])
eff_W = W[1:] * (np.array(L) / np.array(U[1:]))
axarr[2].plot(np.arange(n - 1) / (n / T), eff_W, color='k')
axarr[2].set_title('Effective Wage')
def make_policy_cm(fines, fine_caps, fees, fee_caps, r, R_max, a, b1, b2, q, c,
d, k, p, h, g, m, W_min, dt, processor_num,
cells_per_processor):
"""
Produces a colormap for various combinations of fines and thresholds.
For each policy, runs simulation over 100 different trajectories and averages
the payoff and population and keeps track of the proportion sustainable equilibrium.
"""
# check which policy is an array
if hasattr(fines, "__len__"):
amounts = fines
caps = fine_caps
policy = 'fine'
else:
amounts = fees
caps = fee_caps
policy = 'fee'
# set initial conditions to loop over
np.random.seed(1)
num_points = 80
initial_points = doe.lhs(3, samples=num_points)
# Scale points ([R, U, W])
initial_points[:, 0] = initial_points[:, 0] * 100
initial_points[:, 1] = initial_points[:, 1] * 45
initial_points[:, 2] = initial_points[:, 2] * 20
print('running')
#
# Es = create_2d_list(len(amounts), len(caps))
# Us = create_2d_list(len(amounts), len(caps))
# Ps = create_2d_list(len(amounts), len(caps))
# Ws = create_2d_list(len(amounts), len(caps))
for i, cap in enumerate(caps):
for j, amount in enumerate(amounts):
R_trajectories = [0] * num_points
U_trajectories = [0] * num_points
P_trajectories = [0] * num_points
W_trajectories = [0] * num_points
L_trajectories = [0] * num_points
for n, point in enumerate(initial_points):
R_0 = point[0]
U_0 = point[1]
W_0 = point[2]
if policy == 'fee':
pp = simulate_SES(r,
R_max,
a,
b1,
b2,
q,
c,
d,
k,
p,
h,
g,
m,
W_min,
dt,
R_0,
W_0,
U_0,
fee_cap=cap,
fee=amount)
else:
pp = simulate_SES(r,
R_max,
a,
b1,
b2,
q,
c,
d,
k,
p,
h,
g,
m,
W_min,
dt,
R_0,
W_0,
U_0,
fine_cap=cap,
fine=amount)
R, E, U, S, W, P, L, converged = pp.run()
# save trajectories
R_trajectories[n] = R
U_trajectories[n] = U
P_trajectories[n] = P
W_trajectories[n] = W
L_trajectories[n] = L
# Save compressed colormap data
p_row = processor_num // 8
p_column = processor_num % 8
piece_number = 200 * p_row + 5 * p_column + 40 * j + i #cells_per_processor*processor_num + i # goes from 0 to 1599
with bz2.BZ2File("labor_%s.p" % (piece_number), 'w') as f:
pickle.dump(L_trajectories, f)
with bz2.BZ2File("pop_%s.p" % (piece_number), 'w') as f:
pickle.dump(U_trajectories, f)
with bz2.BZ2File("payoff_%s.p" % (piece_number), 'w') as f:
pickle.dump(P_trajectories, f)
with bz2.BZ2File("wage_%s.p" % (piece_number), 'w') as f:
pickle.dump(W_trajectories, f)
def plot_equilibrium_basins(r, R_max, a, b1, b2, q, c, d, fine_cap, fine, fee_cap,
fee, k, p, h, g, m, W_min, dt, policy, num_points):
"""
Produce scatterplot of randomly sampled initial conditions color coded by the
equilibrium that they end up at. Saves a file with the equilibrium (whether it
is a sustainable or collapse outcome) for each point.
"""
# generate initial points using latin hypercube sampling
np.random.seed(0)
initial_points = doe.lhs(3, samples = num_points)
# Scale points ([R, U, W])
initial_points[:,0] = initial_points[:,0] * 100
initial_points[:,1] = initial_points[:,1] * 45
initial_points[:,2] = initial_points[:,2] * 20
sust_eq = 0
# initialize matrix recording whether initial point leads to good or bad eq
eq_condition = np.zeros(len(initial_points))
# matrix for recording sustainable eq
eq = []
ax = plt.axes(projection='3d')
for i, point in enumerate(initial_points):
R_0 = point[0]
U_0 = point[1]
W_0 = point[2]
pp = simulate_SES(r, R_max, a, b1, b2, q, c, d, k, p, h, g, m,
W_min, dt, R_0, W_0, U_0, fine_cap, fine, fee_cap, fee)
R, E, U, S, W, P, L, convergence = pp.run()
if R[-1] > 90 and U[-1] < 1:
eq_condition[i] = 0
ax.scatter(R[0], U[0], W[0], s = (30,), marker = 'o', color = 'red', alpha = 0.3)
else:
ax.scatter(R[0], U[0], W[0], s = (30,), marker = 'o', color = 'blue', alpha = 0.3)
ax.scatter(R[-1], U[-1], W[-1], s = (60,), marker = '*', color = 'b')
eq_condition[i] = 1
sust_eq += 1
eq.append((R[-1],U[-1],W[-1]))
ax.scatter(100, 0, 0, s = (60,), marker = 'X', color = 'red')
ax.set_xlabel('Resource (R)')
ax.set_ylabel('Population (U)')
ax.set_zlabel('Wage (W)')
if policy == 'fine':
filename = 'scatterplot_data\\fine_eq_basins_c%s_%s_%s.csv'%(c, fine_cap, int(fine))
else:
filename = 'scatterplot_data\\fee_eq_basins_c2_%s_%s.csv'%(fee_cap, int(fee))
with open(filename, 'w+') as f:
csvwriter = csv.writer(f)
csvwriter.writerows(np.transpose([initial_points[:,0], initial_points[:,1], initial_points[:,2], eq_condition]))
csvwriter.writerows(eq)
sust_eq /= len(initial_points)
return sust_eq, eq_condition, eq