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english-iterated-prisoners-dilemma.py
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english-iterated-prisoners-dilemma.py
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# ======================================================== #
# ======================================================== #
# ===================== Game Theory ====================== #
# ======================================================== #
# ======================================================== #
# Confrontation de stratégies pour le Dilemme du Prisonnier
# dans sa version Itérée
# Étude des équilibres et des stratégies Zero Determinant de
# Press & Dyson
# Créé par Ewen Quimerc'h, 2018
# ========================================================= #
import random
import numpy as np
import matplotlib.pyplot as plt
import xlsxwriter
# ========================================================= #
# ===================== Transposition ===================== #
# ========================================================= #
def transpose(A):
(n, p) = np.shape(A)
B = np.zeros((p, n))
for i in range(n):
for j in range(p):
B[j][i] = A[i][j]
return B
# ========================================================= #
# ===================== Modelisation ====================== #
# ========================================================= #
initial_game = (0, 0)
(S,P,R,T) = (0,1,3,5)
utility_matrix = np.array([[[R, R], [S, T]],
[[T, S], [P, P]]])
# These are global variables
# ================================================ #
# ================== STRATEGIES ================== #
# ================================================ #
# ============ Strategies independant from the opponent ============ #
all_c = {"strat" : np.array([[1,1],
[1,1]]),
"first" : 1,
"name" : "Naive (all_c)"}
all_d = {"strat" : np.array([[0,0],
[0,0]]),
"first" : 0,
"name" : "Thief (all_d)"}
random_strat = {"strat" : np.array([[0.5,0.5],
[0.5,0.5]]),
"first" : 0.5,
"name" : "Random"}
strat_indecis = {"strat" : np.array([[0,0],
[1,1]]),
"first" : 1,
"name" : "Irresolute"}
# ================== Deterministic (pure) strategies ================== #
tit_for_tat = {"strat" : np.array([[1,0],
[1,0]]),
"first" : 1,
"name" : "Copycat (tit for tat)"}
resentful = {"strat" : np.array([[1,0],
[0,0]]),
"first" : 1,
"name" : "Resentful"}
strat_inverse = {"strat" : np.array([[0,1],
[0,1]]),
"first" : 1,
"name" : "Inverse tit-for-tat"}
# ================== Mixed strategies ================== #
strat_conciliant = {"strat" : np.array([[1, 0.1],
[1, 0.1]]),
"first" : 1,
"name" : "Accommodating"}
strat_prudent = {"strat" : np.array([[0.99, 0.5],
[0.9, 0.1]]),
"first" : 1,
"name" : "Cautious"}
strat_inspiree = {"strat" : np.array([[0.9,0.1],
[0.1,0.2]]),
"first" : 1,
"name" : "Inspired"}
# ================== Stratégies Zero Determinant (ZD) ================== #
# Ces stratégies sont le fruit du travail des informaticiens Press & Dyson
# Pour plus d'information, consultez
# https://sciencetonnante.wordpress.com/2017/03/03/la-theorie-des-jeux/ (simple)
# http://www.pnas.org/content/109/26/10409.full (très technique)
p1 = 0.9 # 0.9 pour gain de 2 / 0.0 pour un gain de 1
p4 = 0.1 # 0.1 pour un gain de 2 / 0.0 pour un gain de 1
p2 = (p1*(T-P)-(1+p4)*(T-R))/(R-P)
p3 = ((1-p1)*(P-S)+p4*(R-S))/(R-P)
gain_moyen = ((1-p1)*P+p4*R)/(1-p1+p4)
# = 2 pour (0,1,3,5)
print("Control", int(gain_moyen*100)/100)
print("p1", p1, "p2", p2, "p3", p3, "p4", p4)
strat_maitrise = {"strat" : np.array([[p1,p2],
[p3,p4]]),
"first" : 1,
"name" : "Control 2 (ZD)"}
# La stratégie "extorque" impose un rapport fixe entre le gain du
# joueur et celui de l'adversaire (pour 10 000 itérations)
chi = 2
phi = 0.5 * (P-S)/((P-S) + chi*(T-P))
print(phi, chi)
q1 = 1 - phi*(chi-1)*(R-P)/(P-S)
q2 = 1 - phi*(1 + chi*(T-P)/(P-S))
q3 = phi*(chi+ (T-P)/(P-S) )
q4 = 0
print("Extortion", chi)
print("q1", q1, "q2", q2, "q3", q3, "q4 0")
strat_extorque = {"strat" : np.array([[q1,q2],
[q3,q4]]),
"first" : 1,
"name" : "Extortion 2 (ZD)"}
# ================ List of strategies ================ #
# dans le but de se les faire affronter entre elles
# on les considère comme des variables globales
liste_strat = [all_c, all_d, random_strat, strat_indecis,
tit_for_tat, resentful,
strat_conciliant, strat_prudent,
strat_maitrise, strat_extorque]
# Non inclus : inverse, inspiree qui n'ont que peu d'interêt
# ========================================================= #
# ======================= Simulation ====================== #
# ========================================================= #
# ========= Iterated game for 2 strategies ========= #
def iterated_game(nb_of_games, strat_a, strat_b, display=False, utility_matrix=utility_matrix):
if random.random() < strat_a["first"]:
a = 0
else:
a = 1
if random.random() < strat_b["first"]:
b = 0
else:
b = 1
gain_a = utility_matrix[a][b][0]
gain_b = utility_matrix[a][b][1]
if display:
A = np.zeros(nb_of_games)
B = np.zeros(nb_of_games)
A[0] = gain_a
B[0] = gain_b
for i in range(1, nb_of_games):
if random.random() < strat_a["strat"][a][b]:
new_choice_of_A = 0
else:
new_choice_of_A = 1
if random.random() < strat_b["strat"][b][a]:
new_choice_of_B = 0
else:
new_choice_of_B = 1
(a, b) = (new_choice_of_A, new_choice_of_B)
gain_a += utility_matrix[a][b][0]
gain_b += utility_matrix[a][b][1]
if display:
A[i] = gain_a / (i+1)
B[i] = gain_b / (i+1)
if display:
plt.plot(A, "r")
plt.plot(B, "b")
plt.plot(np.ones(nb_of_games), "g")
plt.xlabel("Red : "+strat_a["name"]+" - Blue : "+strat_b["name"])
plt.ylabel("Mean score")
plt.show()
mean_score_a = int(100*gain_a/nb_of_games)/100
mean_score_b = int(100*gain_b/nb_of_games)/100
return (mean_score_a, mean_score_b)
#iterated_game(10000, strat_prudent, strat_alea_total, display = True)
#iterated_game(5000, strat_vol, strat_alea_total, display = True)
iterated_game(10000, strat_maitrise, strat_extorque, display = True)
# ================== For a Strategy ================== #
def results_strategies(strat, nb_of_games, opponents = liste_strat):
n = len(opponents)
M = np.zeros((n,2))
for i in range(n):
M[i] = iterated_game(nb_of_games, strat, opponents[i])
return M
# ================== Affichage sous forme d'histogramme ================== #
# !!! xlsxwriter required !!!
# Get it here : https://github.com/jmcnamara/XlsxWriter
# Or just `pip install xlsxwriter`
def create_sheets(list_strategies, list_opponents, nb_of_rounds):
nb_opponents = len(list_opponents)
liste_noms_adv = [adv["name"] for adv in list_opponents]
for strat in list_strategies:
# Get the results
res = results_strategies(strat, nb_of_rounds, opponents = list_opponents)
tab = transpose(res)
# Export data
workbook = xlsxwriter.Workbook("strat_"+strat["name"]+".xlsx")
worksheet = workbook.add_worksheet()
bold = workbook.add_format({'bold': 1})
headings = ['name adv', 'Score', 'Opp score']
worksheet.write_row('A1', ["Made by E. Quimerc'h"], bold)
worksheet.write_row('A3', headings, bold)
worksheet.write_column('A4', liste_noms_adv)
worksheet.write_column('B4', tab[0])
worksheet.write_column('C4', tab[1])
# Créer le graphique
chart1 = workbook.add_chart({'type': 'column'})
chart1.add_series({
'name': '=Sheet1!$B$3',
'categories': '=Sheet1!$A$4:$A$'+str(nb_opponents+3),
'values': '=Sheet1!$B$4:$B$'+str(nb_opponents+3),
})
chart1.add_series({
'name': '=Sheet1!$C$3',
'categories': '=Sheet1!$A$4:$A$'+str(nb_opponents+3),
'values': '=Sheet1!$C$4:$C$'+str(nb_opponents+3),
})
chart1.set_title({'name': 'Results of strategy '+strat["name"]+" for "+str(nb_of_rounds)+" rounds"})
chart1.set_y_axis({'name': 'Mean score'})
chart1.set_table({'show_keys': True})
chart1.set_legend({'position': 'none'})
worksheet.insert_chart('D18', chart1, {'x_offset': 15, 'y_offset': 5})
workbook.close()
print("Strategy "+strat["name"]+": printing")
print("\Everything printed\n\n\n")
return
create_sheets(liste_strat, liste_strat, 10000)