def test_noninteractive(self):
"Test case for when agents don't interact with each other"
# Copied these values from test_lqcontrol
a = np.array([[.95, 0.], [0, .95]])
b1 = np.array([.95, 0.])
b2 = np.array([0., .95])
r1 = np.array([[-.25, 0.], [0., 0.]])
r2 = np.array([[0., 0.], [0., -.25]])
q1 = np.array([[-.15]])
q2 = np.array([[-.15]])
f1, f2, p1, p2 = nnash(a, b1, b2, r1, r2, q1, q2, 0, 0, 0, 0, 0, 0,
tol=1e-8, max_iter=10000)
alq = a[:1, :1]
blq = b1[:1].reshape((1, 1))
rlq = r1[:1, :1]
qlq = q1
lq_obj = LQ(qlq, rlq, alq, blq, beta=1.)
p, f, d = lq_obj.stationary_values()
assert_allclose(f1, f2[:, ::-1])
assert_allclose(f1[0, 0], f[0])
assert_allclose(p1[0, 0], p2[1, 1])
assert_allclose(p1[0, 0], p[0, 0])
def test_noninteractive(self):
"Test case for when agents don't interact with each other"
# Copied these values from test_lqcontrol
a = np.array([[.95, 0.], [0, .95]])
b1 = np.array([.95, 0.])
b2 = np.array([0., .95])
r1 = np.array([[-.25, 0.], [0., 0.]])
r2 = np.array([[0., 0.], [0., -.25]])
q1 = np.array([[-.15]])
q2 = np.array([[-.15]])
f1, f2, p1, p2 = nnash(a, b1, b2, r1, r2, q1, q2, 0, 0, 0, 0, 0, 0,
tol=1e-8, max_iter=10000)
alq = a[:1, :1]
blq = b1[:1].reshape((1, 1))
rlq = r1[:1, :1]
qlq = q1
lq_obj = LQ(qlq, rlq, alq, blq, beta=1.)
p, f, d = lq_obj.stationary_values()
assert_allclose(f1, f2[:, ::-1])
assert_allclose(f1[0, 0], f[0])
assert_allclose(p1[0, 0], p2[1, 1])
assert_allclose(p1[0, 0], p[0, 0])
# Remember state is x_t = [1, y_{1, t}, y_{2, t}] and
# control is u_{i, t} = [y_{i, t+1} - y_{i, t}]
# ---------------------------------------------------------------------#
a0 = 10.
a1 = 1.
beta = 1.
d = .5
a = eye(3)
b1 = array([[0.], [1.], [0.]])
b2 = array([[0.], [0.], [1.]])
r1 = array([[a0, 0., 0.],
[0., -a1, -a1/2.],
[0, -a1/2., 0.]])
r2 = array([[a0, 0., 0.],
[0., 0., -a1/2.],
[0, -a1/2., -a1]])
q1 = array([[-.5*d]])
q2 = array([[-.5*d]])
# ---------------------------------------------------------------------#
# Solve using QE's nnash function
# ---------------------------------------------------------------------#
f1, f2, p1, p2 = nnash(a, b1, b2, r1, r2, q1, q2, 0., 0., 0., 0., 0., 0.,
tol=1e-8, max_iter=1000)
a = eye(3)
b1 = array([[0.], [1.], [0.]])
b2 = array([[0.], [0.], [1.]])
r1 = array([[a0, 0., 0.], [0., -a1, -a1 / 2.], [0, -a1 / 2., 0.]])
r2 = array([[a0, 0., 0.], [0., 0., -a1 / 2.], [0, -a1 / 2., -a1]])
q1 = array([[-.5 * d]])
q2 = array([[-.5 * d]])
#---------------------------------------------------------------------#
# Solve using QE's nnash function
#---------------------------------------------------------------------#
f1, f2, p1, p2 = nnash(a,
b1,
b2,
r1,
r2,
q1,
q2,
0.,
0.,
0.,
0.,
0.,
0.,
tol=1e-8,
max_iter=1000)
def test_nnash():
"Use judd test case for nnash. Follows judd.m"
# Define Parameters
delta = 0.02
d = np.array([[-1, 0.5], [0.5, -1]])
B = np.array([25, 25])
c1 = np.array([1, -2, 1])
c2 = np.array([1, -2, 1])
e1 = np.array([10, 10, 3])
e2 = np.array([10, 10, 3])
delta_1 = 1 - delta
## Define matrices
a = np.array([[delta_1, 0, -delta_1 * B[0]], [0, delta_1, -delta_1 * B[1]],
[0, 0, 1]])
b1 = delta_1 * np.array([[1, -d[0, 0]], [0, -d[1, 0]], [0, 0]])
b2 = delta_1 * np.array([[0, -d[0, 1]], [1, -d[1, 1]], [0, 0]])
r1 = -np.array([[0.5 * c1[2], 0, 0.5 * c1[1]], [0, 0, 0],
[0.5 * c1[1], 0, c1[0]]])
r2 = -np.array([[0, 0, 0], [0, 0.5 * c2[2], 0.5 * c2[1]],
[0, 0.5 * c2[1], c2[0]]])
q1 = np.array([[-0.5 * e1[2], 0], [0, d[0, 0]]])
q2 = np.array([[-0.5 * e2[2], 0], [0, d[1, 1]]])
s1 = np.zeros((2, 2))
s2 = np.copy(s1)
w1 = np.array([[0, 0], [0, 0], [-0.5 * e1[1], B[0] / 2.]])
w2 = np.array([[0, 0], [0, 0], [-0.5 * e2[1], B[1] / 2.]])
m1 = np.array([[0, 0], [0, d[0, 1] / 2.]])
m2 = np.copy(m1)
# build model and solve it
f1, f2, p1, p2 = nnash(a, b1, b2, r1, r2, q1, q2, s1, s2, w1, w2, m1, m2)
aaa = a - b1.dot(f1) - b2.dot(f2)
aa = aaa[:2, :2]
tf = np.eye(2) - aa
tfi = np.linalg.inv(tf)
xbar = tfi.dot(aaa[:2, 2])
# Define answers from matlab. TODO: this is ghetto
f1_ml = np.asarray(
np.matrix("""\
0.243666582208565, 0.027236062661951, -6.827882928738190;
0.392370733875639, 0.139696450885998, -37.734107291009138"""))
f2_ml = np.asarray(
np.matrix("""\
0.027236062661951, 0.243666582208565, -6.827882928738186;
0.139696450885998, 0.392370733875639, -37.734107291009131"""))
xbar_ml = np.array([1.246871007582702, 1.246871007582685])
assert_allclose(f1, f1_ml)
assert_allclose(f2, f2_ml)
assert_allclose(xbar, xbar_ml)
def test_nnash(self):
"Use judd test case for nnash. Follows judd.m"
# Define Parameters
delta = 0.02
d = np.array([[-1, 0.5], [0.5, -1]])
B = np.array([25, 25])
c1 = np.array([1, -2, 1])
c2 = np.array([1, -2, 1])
e1 = np.array([10, 10, 3])
e2 = np.array([10, 10, 3])
delta_1 = 1 - delta
## Define matrices
a = np.array([[delta_1, 0, -delta_1*B[0]],
[0, delta_1, -delta_1*B[1]],
[0, 0, 1]])
b1 = delta_1 * np.array([[1, -d[0, 0]],
[0, -d[1, 0]],
[0, 0]])
b2 = delta_1 * np.array([[0, -d[0, 1]],
[1, -d[1, 1]],
[0, 0]])
r1 = -np.array([[0.5*c1[2], 0, 0.5*c1[1]],
[0, 0, 0],
[0.5*c1[1], 0, c1[0]]])
r2 = -np.array([[0, 0, 0],
[0, 0.5*c2[2], 0.5*c2[1]],
[0, 0.5*c2[1], c2[0]]])
q1 = np.array([[-0.5*e1[2], 0], [0, d[0, 0]]])
q2 = np.array([[-0.5*e2[2], 0], [0, d[1, 1]]])
s1 = np.zeros((2, 2))
s2 = np.copy(s1)
w1 = np.array([[0, 0],
[0, 0],
[-0.5*e1[1], B[0]/2.]])
w2 = np.array([[0, 0],
[0, 0],
[-0.5*e2[1], B[1]/2.]])
m1 = np.array([[0, 0], [0, d[0, 1] / 2.]])
m2 = np.copy(m1)
# build model and solve it
f1, f2, p1, p2 = nnash(a, b1, b2, r1, r2, q1, q2, s1, s2, w1, w2, m1,
m2)
aaa = a - b1.dot(f1) - b2.dot(f2)
aa = aaa[:2, :2]
tf = np.eye(2)-aa
tfi = np.linalg.inv(tf)
xbar = tfi.dot(aaa[:2, 2])
# Define answers from matlab. TODO: this is ghetto
f1_ml = np.asarray(np.matrix("""\
0.243666582208565, 0.027236062661951, -6.827882928738190;
0.392370733875639, 0.139696450885998, -37.734107291009138"""))
f2_ml = np.asarray(np.matrix("""\
0.027236062661951, 0.243666582208565, -6.827882928738186;
0.139696450885998, 0.392370733875639, -37.734107291009131"""))
xbar_ml = np.array([1.246871007582702, 1.246871007582685])
assert_allclose(f1, f1_ml)
assert_allclose(f2, f2_ml)
assert_allclose(xbar, xbar_ml)
