統計学者（もう演奏していません）
import random
import collections
R, P, S = moves = range(3)
move_idx = {"R": R, "P": P, "S": S}
name = "RPS"
beat = (P, S, R)
beaten = (S, R, P)
def react(_0, _1, _2, _3, _4, opp_history):
if not opp_history:
return random.randrange(0, 3)
return beat[opp_history[-1]]
def anti_react(_0, _1, _2, _3, _4, opp_history):
if not opp_history:
return random.randrange(0, 3)
return beaten[opp_history[-1]]
def random_max(scores):
scores = [s + random.normalvariate(0, 1) for s in scores]
return scores.index(max(scores))
def greedy_margin(my_points, opp_points, my_loaded, opp_loaded, my_history, opp_history):
scores = [my_loaded[move] - opp_loaded[beat[move]] for move in moves]
return random_max(scores)
def anti_greedy(my_points, opp_pints, my_loaded, opp_loaded, my_history, opp_history):
scores = [-my_loaded[move] for move in moves]
return random_max(scores)
def recent_stats(my_points, opp_points, my_loaded, opp_loaded, my_history, opp_history):
opp_history = opp_history[-10:-1]
counts = collections.Counter(opp_history)
scores = [(counts[beaten[move]] + 1) * my_loaded[move] -
(counts[beat[move]] + 1) * opp_loaded[move] for move in moves]
return random_max(scores)
def statistician(_0, _1, _2, _3, my_history, opp_history):
m1 = []
o1 = []
my_loaded = [0] * 3
opp_loaded = [0] * 3
my_points = 0
opp_points = 0
strategies = [react, anti_react, greedy_margin, anti_greedy, recent_stats]
strategy_scores = [0 for _ in strategies]
for i, (mx, ox) in enumerate(zip(my_history, opp_history)):
mx = move_idx[mx]
ox = move_idx[ox]
for j, strategy in enumerate(strategies):
strategy_scores[j] *= 0.98
move = strategy(my_points, opp_points, my_loaded, opp_loaded, m1, o1)
if move == beat[ox]:
strategy_scores[j] += my_loaded[move]
elif move == beaten[ox]:
strategy_scores[j] -= opp_loaded[ox]
m1.append(mx)
o1.append(ox)
if mx == beat[ox]:
opp_loaded[ox] += 1
my_points += my_loaded[mx]
elif mx == beaten[ox]:
my_loaded[mx] += 1
opp_points += opp_loaded[ox]
else:
my_loaded[mx] += 0.5
opp_loaded[ox] += 0.5
strategy = strategies[random_max(strategy_scores)]
return name[strategy(my_points, opp_points, my_loaded, opp_loaded, m1, o1)]
予想される過去のパフォーマンスに基づいて、いくつかの単純な戦略を切り替える
統計学者2
import random
import collections
import numpy as np
R, P, S = moves = range(3)
move_idx = {"R": R, "P": P, "S": S}
names = "RPS"
beat = (P, S, R)
beaten = (S, R, P)
def react(my_loaded, opp_loaded, my_history, opp_history):
if not opp_history:
return random.randrange(0, 3)
counts = [0, 0, 0]
counts[beat[opp_history[-1]]] += 1
return counts
def random_max(scores):
scores = [s + random.normalvariate(0, 1) for s in scores]
return scores.index(max(scores))
def argmax(scores):
m = max(scores)
return [s == m for s in scores]
def greedy_margin(my_loaded, opp_loaded, my_history, opp_history):
scores = [my_loaded[move] - opp_loaded[beat[move]] for move in moves]
return argmax(scores)
recent_counts = None
def best_move(counts, my_loaded, opp_loaded):
scores = [(counts[beaten[move]] + 0.5) * my_loaded[move] -
(counts[beat[move]] + 0.5) * opp_loaded[move] for move in moves]
return argmax(scores)
def recent_stats(my_loaded, opp_loaded, my_history, opp_history):
if len(opp_history) >= 10:
recent_counts[opp_history[-10]] -= 1
recent_counts[opp_history[-1]] += 1
return best_move(recent_counts, my_loaded, opp_loaded)
order2_counts = None
def order2(my_loaded, opp_loaded, my_history, opp_history):
if len(my_history) >= 2:
base0 = 9 * my_history[-2] + 3 * opp_history[-2]
order2_counts[base0 + opp_history[-1]] += 1
base1 = 9 * my_history[-1] + 3 * opp_history[-1]
counts = [order2_counts[base1 + move] for move in moves]
return best_move(counts, my_loaded, opp_loaded)
def nash(my_loaded, opp_loaded, my_history, opp_history):
third = 1.0 / 3
p = np.full(3, third)
q = np.full(3, third)
u = np.array(my_loaded)
v = np.array(opp_loaded)
m0 = np.zeros(3)
m1 = np.zeros(3)
lr = 0.2
for _ in range(10):
de0 = u * np.roll(q, 1) - np.roll(v * q, 2)
de1 = v * np.roll(p, 1) - np.roll(u * p, 2)
m0 = 0.9 * m0 + 0.1 * de0
m1 = 0.9 * m1 + 0.1 * de1
p += lr * m0
q += lr * m1
p[p < 0] = 0
q[q < 0] = 0
tp, tq = np.sum(p), np.sum(q)
if tp == 0 or tq == 0:
return np.full(3, third)
p /= tp
q /= tq
lr *= 0.9
return p
strategies = [react, greedy_margin, recent_stats, order2, nash]
predictions = strategy_scores = mh = oh = None
def statistician2func(my_points, opp_points, my_loaded, opp_loaded, my_history, opp_history):
global strategy_scores, history, recent_counts, mh, oh, predictions, order2_counts
if not opp_history:
strategy_scores = [0 for _ in strategies]
recent_counts = collections.Counter()
order2_counts = collections.Counter()
mh, oh = [], []
predictions = None
return random.choice(names)
my_move = move_idx[my_history[-1]]
opp_move = move_idx[opp_history[-1]]
if predictions is not None:
for j, p in enumerate(predictions):
good = beat[opp_move]
bad = beaten[opp_move]
strategy_scores[j] += (my_loaded[good] * p[good] - opp_loaded[opp_move] * p[bad]) / sum(p)
mh.append(my_move)
oh.append(opp_move)
predictions = [strategy(my_loaded, opp_loaded, mh, oh) for strategy in strategies]
strategy = random_max(strategy_scores)
p = predictions[strategy]
r = random.random()
for i, pi in enumerate(p):
r -= pi
if r <= 0:
break
return names[i]
ナッシュ
import numpy as np
import random
def nashfunc(my_points, opp_points, my_loaded, opp_loaded, my_history, opp_history):
third = 1.0 / 3
p = np.full(3, third)
q = np.full(3, third)
u = np.array(my_loaded)
v = np.array(opp_loaded)
m0 = np.zeros(3)
m1 = np.zeros(3)
lr = 0.2
for _ in range(10):
de0 = u * np.roll(q, 1) - np.roll(v * q, 2)
de1 = v * np.roll(p, 1) - np.roll(u * p, 2)
m0 = 0.9 * m0 + 0.1 * de0
m1 = 0.9 * m1 + 0.1 * de1
p += lr * m0
q += lr * m1
p[p < 0] = 0
q[q < 0] = 0
tp, tq = np.sum(p), np.sum(q)
if tp == 0 or tq == 0:
return random.choice("RPS")
p /= tp
q /= tq
lr *= 0.9
r = random.random()
for i, pi in enumerate(p):
r -= pi
if r <= 0:
break
return "RPS"[i]
勾配降下法により、おおよそのナッシュ平衡を計算します。