def classic_pd(R=None, tf=None, xini=None):
"""Plays a classic prisoner's dilemma between two players"""
# Two connected players
A = np.zeros([2, 2])
A[0, 1] = 1
A[1, 0] = 1
# Classic positive prisoner's dilemma
B = np.zeros([2, 2])
B[0, 0] = 3 # R
B[0, 1] = 1 # S
B[1, 0] = 4 # T
B[1, 1] = 2 # P
# Relationship matrix
if R is None or R.shape != (2, 2):
R = np.zeros([2, 2], dtype='double')
R[0, 0] = 2 / 3 + 0.05
R[0, 1] = 1 / 3 - 0.05
R[1, 1] = 2 / 3 - 0.05
R[1, 0] = 1 / 3 + 0.05
# Initial Condition, 0.5 in all strategies for all players
if xini is None or xini.shape != (6, 2):
xini = np.divide(np.ones([2, 2], dtype='double'), 2)
# Time interval and number of steps
t0 = 0
if tf is None:
tf = 150
n = (tf - t0) * 10
h = (tf - t0) / n
x = hrg.hr_game(t0, tf, n, A, B, R, xini)
# Plot results
xaxis = np.arange(t0, tf + h, h)
plt.plot(xaxis, x[0, 0, :], 'r', label='Player 1')
plt.plot(xaxis, x[1, 0, :], 'b', label='Player 2', alpha=0.7)
plt.ylim([-0.05, 1.05])
plt.legend(['Player 1', 'Player 2'])
plt.title("Cooperation probability")
plt.show()
plt.close()
return None
def hinge_love_triangle(R=None, tf=None, xini=None):
"""Plays a love triangle game in a 'hinge' graph, a path with 3 nodes"""
# A hinge, path with 3 nodes
A = np.zeros([3, 3])
A[0, 1] = 1
A[1, 0] = 1
A[1, 2] = 1
A[2, 1] = 1
# Payoff matrices
# Person 1 wants to play s1 against Person 2
# Person 2 only benefits when playing s2 against Person 1
# Person 2 has no benefit from playing with Person 3
B = np.zeros([2, 2, 3])
# Player 1 payoff matrix
B[0, 0, 0] = 0
B[0, 1, 0] = 1
B[1, 0, 0] = 0
B[1, 1, 0] = 0
# Player 2 payoff matrix
B[0, 0, 1] = 0
B[0, 1, 1] = 0
B[1, 0, 1] = 1
B[1, 1, 1] = 0
# Player 3 payoff matrix
B[0, 0, 2] = 1
B[0, 1, 2] = 0
B[1, 0, 2] = 0
B[1, 1, 2] = 0
# Relationship matrix
if R is None or R.shape != (3, 3):
R = np.zeros([3, 3], dtype='double')
# Person 1 cares equally about itself and it's partner
R[0, 0] = 1 / 2
R[0, 1] = 1 / 2
# Person 2 cares about itself and Person 3
R[1, 1] = 1 / 2 + 0.05
R[1, 2] = 1 / 2 - 0.05
# Person cares only about itself
R[2, 2] = 1
# Initial Condition, 0.5 in all strategies for all players
if xini is None or xini.shape != (3, 2):
xini = np.divide(np.ones([3, 2], dtype='double'), 2)
# Time interval and number of steps
t0 = 0
if tf is None:
tf = 150
n = (tf - t0) * 10
h = (tf - t0) / n
x = hrg.hr_game(t0, tf, n, A, B, R, xini)
# Plot results
xaxis = np.arange(t0, tf + h, h)
plt.plot(xaxis, x[0, 0, :], 'r', label='Player 1')
plt.plot(xaxis, x[1, 0, :], 'b', label='Player 2', alpha=0.7)
plt.plot(xaxis, x[2, 0, :], 'g', label='Player 2', alpha=0.7)
plt.ylim([-0.05, 1.05])
plt.legend(['Player 1', 'Player 2', 'Player 3'])
plt.title("Probability of using strategy 1")
plt.show()
plt.close()
return None
def simulations_madeo_mocenni():
"""
Runs the same simulations found in Madeo and Mocennis article
but with hyper-rational agents instead of standard replicators.
There will be some code rewriting because I want all functions
to be standalone examples and not reusable functions.
"""
# Lists for iterations
ini_cond = ['external', 'central', 'ext_cent']
graph = ['open_star', 'closed_star', 'asym_weighted']
# Graph definitions
open_star = np.zeros([6, 6])
open_star[0, 1] = 1
open_star[1, 0] = 1
open_star[0, 2] = 1
open_star[2, 0] = 1
open_star[0, 3] = 1
open_star[3, 0] = 1
open_star[0, 4] = 1
open_star[4, 0] = 1
open_star[0, 5] = 1
open_star[5, 0] = 1
closed_star = np.subtract(np.ones([6, 6]), np.eye(6))
closed_star[1, 3] = 0
closed_star[1, 4] = 0
closed_star[2, 4] = 0
closed_star[2, 5] = 0
closed_star[3, 5] = 0
closed_star[3, 1] = 0
closed_star[4, 1] = 0
closed_star[4, 2] = 0
closed_star[5, 2] = 0
closed_star[5, 3] = 0
asym_weighted = np.zeros([6, 6])
asym_weighted[0, 1] = 1
asym_weighted[0, 2] = 1
asym_weighted[0, 4] = 3
asym_weighted[0, 5] = 1
asym_weighted[1, 0] = 1
asym_weighted[1, 5] = 3
asym_weighted[2, 0] = 1
asym_weighted[2, 3] = 3
asym_weighted[3, 2] = 3
asym_weighted[3, 4] = 1
asym_weighted[4, 3] = 1
asym_weighted[4, 0] = 3
asym_weighted[5, 0] = 1
asym_weighted[5, 1] = 3
# Save graph matrices
for i in range(3):
np.savetxt(graph[i] + '.txt', locals()[graph[i]])
# Payoffs
bistability = np.zeros([2, 2])
bistability[0, 0] = 1
bistability[1, 1] = 1
prisoners_dilemma = np.zeros([2, 2])
prisoners_dilemma[0, 0] = 1
prisoners_dilemma[1, 0] = 1.5
coexistence = np.zeros([2, 2])
coexistence[0, 1] = 1
coexistence[1, 0] = 1
# Initial conditions
external = np.zeros([6, 2], dtype="double")
for v in range(6):
if v == 1:
external[v, :] = np.array([0.01, 0.99])
else:
external[v, :] = np.array([0.99, 0.01])
central = np.zeros([6, 2], dtype="double")
for v in range(6):
if v == 0:
central[v, :] = np.array([0.01, 0.99])
else:
central[v, :] = np.array([0.99, 0.01])
ext_cent = np.zeros([6, 2], dtype="double")
for v in range(6):
if v == 0 or v == 1:
ext_cent[v, :] = np.array([0.01, 0.99])
else:
ext_cent[v, :] = np.array([0.99, 0.01])
# Relationship matrices
R_eye = np.eye(6)
R_open_star = rel_matrix_builder(open_star)
R_closed_star = rel_matrix_builder(closed_star)
R_asym_weighted = rel_matrix_builder(asym_weighted)
# Do simulation and print final state do text file
# Bistability
for i in range(3):
for j in range(3):
x = hrg.hr_game(0, 50, 500,
locals()[graph[j]], bistability,
locals()['R_' + graph[j]],
locals()[ini_cond[i]])
np.savetxt('bi-' + ini_cond[i] + '-' + graph[j] + '.txt', x[:, :,
500])
# Prisoner's Dilemma
for i in range(3):
for j in range(3):
x = hrg.hr_game(0, 100, 1000,
locals()[graph[j]], prisoners_dilemma,
locals()['R_' + graph[j]],
locals()[ini_cond[i]])
np.savetxt('pd-' + ini_cond[i] + '-' + graph[j] + '.txt', x[:, :,
1000])
# Coexistance
for i in range(3):
for j in range(3):
x = hrg.hr_game(0, 50, 500,
locals()[graph[j]], coexistence,
locals()['R_' + graph[j]],
locals()[ini_cond[i]])
np.savetxt('co-' + ini_cond[i] + '-' + graph[j] + '.txt', x[:, :,
500])
return None
def closed_star_coex(R=None, tf=None, xini=None):
"""Plays a coexistance game on a closed star with 6 vertices"""
# Closed star, it's easier to erase connections
A = np.subtract(np.ones([6, 6]), np.eye(6))
A[1, 3] = 0
A[1, 4] = 0
A[2, 4] = 0
A[2, 5] = 0
A[3, 5] = 0
A[3, 1] = 0
A[4, 1] = 0
A[4, 2] = 0
A[5, 2] = 0
A[5, 3] = 0
# Basic coexistance game
B = np.zeros([2, 2])
B[0, 0] = 0
B[0, 1] = 1
B[1, 0] = 0
B[1, 1] = 1
# Relationship matrix, everyone's selfish
if R is None or R.shape != (6, 6):
R = np.eye(6)
# Initial Condition
if xini is None or xini.shape != (6, 2):
xini = np.zeros([6, 2], dtype='double')
# Almost 1
xini[0, 0] = 0.99
xini[1, 0] = 0.99
xini[3, 0] = 0.99
xini[5, 0] = 0.99
# Almost 0
xini[2, 0] = 0.01
xini[4, 0] = 0.01
# Iterate to complete assignments
for i in range(6):
xini[i, 1] = np.subtract(1, xini[i, 0])
# Time interval and number of steps
t0 = 0
if tf is None:
tf = 150
n = (tf - t0) * 10
h = (tf - t0) / n
x = hrg.hr_game(t0, tf, n, A, B, R, xini)
# Plot results
xaxis = np.arange(t0, tf + h, h)
labels = ["Player " + str(i) for i in range(1, 7)]
for i in range(6):
plt.plot(xaxis, x[i, 0, :], label=labels[i], alpha=0.7)
plt.ylim([-0.05, 1.05])
plt.legend(labels)
plt.title("Cooperation probability")
plt.show()
plt.close()
return None