前言：當演算法遇見海洋智慧
在臺灣周圍的海域中，珊瑚與藻類進行著一場古老的合作遊戲。牠們面臨著一個經典的選擇：是要無私地分享資源，還是自私地獨占養分？這個看似簡單的生態互動，實際上蘊含著深刻的遊戲理論智慧——囚徒困境（Prisoner's Dilemma）。
今天，我們將用 Python 來模擬這個經典的哲學問題，從海洋生態的角度重新審視合作與競爭的本質，並探討其背後的哲學意涵。
第一章：囚徒困境的核心邏輯
1.1 經典囚徒困境
囚徒困境是博弈論中的經典案例。兩名囚犯被分別審訊，他們可以選擇「合作」（保持沉默）或「背叛」（指證對方）。每個人的最佳策略取決於對方的選擇，但理性的個體決策往往導致雙輸的結果。
讓我們用 Python 來建立基本的囚徒困境模型：
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
from collections import defaultdict
import random
class PrisonersDilemma:
"""囚徒困境遊戲類別"""
def __init__(self):
# 收益矩陣：(玩家1收益, 玩家2收益)
# 策略：0=合作(C), 1=背叛(D)
self.payoff_matrix = {
(0, 0): (3, 3), # 雙方合作：中等收益
(0, 1): (0, 5), # 自己合作，對方背叛：自己受損
(1, 0): (5, 0), # 自己背叛，對方合作：自己得利
(1, 1): (1, 1) # 雙方背叛：雙輸
}
def play_round(self, strategy1, strategy2):
"""進行一輪遊戲"""
return self.payoff_matrix[(strategy1, strategy2)]
def get_payoff_description(self, s1, s2):
"""取得策略組合的描述"""
strategies = {0: "合作", 1: "背叛"}
return f"玩家1: {strategies[s1]}, 玩家2: {strategies[s2]}"
# 示例：基本遊戲
game = PrisonersDilemma()
print("囚徒困境收益矩陣：")
print("=" * 40)
for (s1, s2), (p1, p2) in game.payoff_matrix.items():
desc = game.get_payoff_description(s1, s2)
print(f"{desc} -> 收益: ({p1}, {p2})")
1.2 海洋生態中的囚徒困境
在海洋生態系統中，我們可以觀察到許多類似囚徒困境的現象：
清潔魚與宿主魚的互動：
- 合作：清潔魚專心清除寄生蟲，宿主魚保持靜止
- 背叛：清潔魚咬食宿主的健康組織，或宿主魚突然游走
珊瑚與共生藻的關係：
- 合作：珊瑚提供庇護，共生藻進行光合作用分享養分
- 背叛：任一方過度消耗資源而不給予回報
第二章：Python 實作海洋生態囚徒困境
2.1 海洋生物策略模擬
讓我們創建一個模擬海洋生物互動的進階模型：
class MarineCreature:
"""海洋生物基類"""
def __init__(self, name, strategy_type="random"):
self.name = name
self.strategy_type = strategy_type
self.total_payoff = 0
self.interaction_history = []
self.reputation = 0.5 # 信譽值：0-1之間
def choose_strategy(self, opponent_history, current_round):
"""根據策略類型選擇行動"""
if self.strategy_type == "always_cooperate":
return 0 # 總是合作
elif self.strategy_type == "always_defect":
return 1 # 總是背叛
elif self.strategy_type == "tit_for_tat":
# 以牙還牙：第一輪合作，之後模仿對手上一輪行為
if current_round == 0 or len(opponent_history) == 0:
return 0
return opponent_history[-1]
elif self.strategy_type == "tit_for_two_tats":
# 雙重以牙還牙：對手連續背叛兩次才報復
if len(opponent_history) < 2:
return 0
if opponent_history[-1] == 1 and opponent_history[-2] == 1:
return 1
return 0
elif self.strategy_type == "generous_tit_for_tat":
# 寬容的以牙還牙：有機率原諒對手的背叛
if current_round == 0 or len(opponent_history) == 0:
return 0
if opponent_history[-1] == 1:
return 1 if random.random() > 0.1 else 0 # 90%機率報復
return 0
else: # random
return random.choice([0, 1])
def update_reputation(self, own_action, opponent_action):
"""更新信譽值"""
if own_action == 0: # 合作
self.reputation = min(1.0, self.reputation + 0.01)
else: # 背叛
self.reputation = max(0.0, self.reputation - 0.02)
class MarineEcosystemSimulation:
"""海洋生態系統模擬"""
def __init__(self):
self.game = PrisonersDilemma()
self.creatures = []
self.simulation_history = []
def add_creature(self, creature):
"""添加海洋生物"""
self.creatures.append(creature)
def simulate_interaction(self, creature1, creature2, rounds=100):
"""模擬兩個生物之間的互動"""
history1, history2 = [], []
payoffs1, payoffs2 = [], []
for round_num in range(rounds):
# 選擇策略
action1 = creature1.choose_strategy(history2, round_num)
action2 = creature2.choose_strategy(history1, round_num)
# 計算收益
payoff1, payoff2 = self.game.play_round(action1, action2)
# 更新記錄
history1.append(action1)
history2.append(action2)
payoffs1.append(payoff1)
payoffs2.append(payoff2)
# 更新總收益和信譽
creature1.total_payoff += payoff1
creature2.total_payoff += payoff2
creature1.update_reputation(action1, action2)
creature2.update_reputation(action2, action1)
# 儲存互動歷史
interaction_record = {
'creature1': creature1.name,
'creature2': creature2.name,
'strategy1': creature1.strategy_type,
'strategy2': creature2.strategy_type,
'history1': history1,
'history2': history2,
'payoffs1': payoffs1,
'payoffs2': payoffs2,
'cooperation_rate1': history1.count(0) / len(history1),
'cooperation_rate2': history2.count(0) / len(history2),
'total_payoff1': sum(payoffs1),
'total_payoff2': sum(payoffs2),
'final_reputation1': creature1.reputation,
'final_reputation2': creature2.reputation
}
self.simulation_history.append(interaction_record)
return interaction_record
# 創建海洋生態系統模擬
ecosystem = MarineEcosystemSimulation()
# 創建不同策略的海洋生物
creatures = [
MarineCreature("善良珊瑚", "always_cooperate"),
MarineCreature("自私海葵", "always_defect"),
MarineCreature("聰明清潔魚", "tit_for_tat"),
MarineCreature("寬容海龜", "generous_tit_for_tat"),
MarineCreature("謹慎小丑魚", "tit_for_two_tats"),
MarineCreature("隨機水母", "random")
]
for creature in creatures:
ecosystem.add_creature(creature)
print("海洋生態系統中的生物：")
for creature in creatures:
print(f"- {creature.name} ({creature.strategy_type})")
2.2 大規模生態競賽模擬
def run_ecosystem_tournament(ecosystem, rounds_per_match=100):
"""執行生態系統錦標賽"""
print(f"\n開始海洋生態錦標賽（每場對戰 {rounds_per_match} 輪）...")
print("=" * 60)
# 重置所有生物的總收益
for creature in ecosystem.creatures:
creature.total_payoff = 0
creature.reputation = 0.5
# 每對生物都進行對戰
match_count = 0
for i in range(len(ecosystem.creatures)):
for j in range(i + 1, len(ecosystem.creatures)):
creature1 = ecosystem.creatures[i]
creature2 = ecosystem.creatures[j]
print(f"對戰 {match_count + 1}: {creature1.name} vs {creature2.name}")
interaction = ecosystem.simulate_interaction(
creature1, creature2, rounds_per_match
)
print(f" 合作率: {creature1.name} {interaction['cooperation_rate1']:.2%}, "
f"{creature2.name} {interaction['cooperation_rate2']:.2%}")
print(f" 總收益: {creature1.name} {interaction['total_payoff1']}, "
f"{creature2.name} {interaction['total_payoff2']}")
print(f" 最終信譽: {creature1.name} {interaction['final_reputation1']:.3f}, "
f"{creature2.name} {interaction['final_reputation2']:.3f}")
print()
match_count += 1
return ecosystem.simulation_history
# 執行錦標賽
tournament_results = run_ecosystem_tournament(ecosystem, 200)
# 分析結果
print("錦標賽最終排名：")
print("=" * 40)
sorted_creatures = sorted(ecosystem.creatures,
key=lambda x: x.total_payoff, reverse=True)
for rank, creature in enumerate(sorted_creatures, 1):
avg_payoff = creature.total_payoff / (len(ecosystem.creatures) - 1)
print(f"{rank}. {creature.name:12} | "
f"總收益: {creature.total_payoff:4d} | "
f"平均: {avg_payoff:6.1f} | "
f"信譽: {creature.reputation:.3f} | "
f"策略: {creature.strategy_type}")
第三章：資料視覺化與分析
3.1 合作率與收益的視覺化分析
import matplotlib.pyplot as plt
import seaborn as sns
# 設定中文字體
plt.rcParams['font.sans-serif'] = ['Arial Unicode MS', 'Microsoft JhengHei']
plt.rcParams['axes.unicode_minus'] = False
def analyze_tournament_results(ecosystem, tournament_results):
"""分析錦標賽結果"""
# 創建分析資料
analysis_data = []
for creature in ecosystem.creatures:
creature_matches = [r for r in tournament_results
if r['creature1'] == creature.name or r['creature2'] == creature.name]
cooperation_rates = []
payoffs = []
for match in creature_matches:
if match['creature1'] == creature.name:
cooperation_rates.append(match['cooperation_rate1'])
payoffs.extend(match['payoffs1'])
else:
cooperation_rates.append(match['cooperation_rate2'])
payoffs.extend(match['payoffs2'])
analysis_data.append({
'name': creature.name,
'strategy': creature.strategy_type,
'avg_cooperation_rate': np.mean(cooperation_rates),
'total_payoff': creature.total_payoff,
'avg_payoff_per_match': creature.total_payoff / len(creature_matches),
'reputation': creature.reputation,
'payoff_variance': np.var(payoffs)
})
df = pd.DataFrame(analysis_data)
# 創建視覺化圖表
fig, axes = plt.subplots(2, 2, figsize=(15, 12))
fig.suptitle('海洋生態囚徒困境錦標賽分析', fontsize=16, fontweight='bold')
# 1. 合作率 vs 總收益
ax1 = axes[0, 0]
scatter = ax1.scatter(df['avg_cooperation_rate'], df['total_payoff'],
c=df['reputation'], s=100, alpha=0.7, cmap='viridis')
ax1.set_xlabel('平均合作率')
ax1.set_ylabel('總收益')
ax1.set_title('合作率與收益關係')
plt.colorbar(scatter, ax=ax1, label='最終信譽')
# 添加生物名稱標籤
for i, row in df.iterrows():
ax1.annotate(row['name'], (row['avg_cooperation_rate'], row['total_payoff']),
xytext=(5, 5), textcoords='offset points', fontsize=8)
# 2. 策略比較柱狀圖
ax2 = axes[0, 1]
strategy_colors = plt.cm.Set3(np.linspace(0, 1, len(df)))
bars = ax2.bar(range(len(df)), df['total_payoff'], color=strategy_colors)
ax2.set_xlabel('海洋生物')
ax2.set_ylabel('總收益')
ax2.set_title('各生物收益比較')
ax2.set_xticks(range(len(df)))
ax2.set_xticklabels([f"{row['name']}\n({row['strategy']})"
for _, row in df.iterrows()], rotation=45, ha='right')
# 3. 信譽分佈
ax3 = axes[1, 0]
ax3.hist(df['reputation'], bins=10, alpha=0.7, color='skyblue', edgecolor='black')
ax3.set_xlabel('最終信譽值')
ax3.set_ylabel('頻次')
ax3.set_title('信譽值分佈')
ax3.axvline(df['reputation'].mean(), color='red', linestyle='--',
label=f'平均信譽: {df["reputation"].mean():.3f}')
ax3.legend()
# 4. 收益變異性
ax4 = axes[1, 1]
ax4.scatter(df['avg_cooperation_rate'], df['payoff_variance'],
c=df['total_payoff'], s=100, alpha=0.7, cmap='plasma')
ax4.set_xlabel('平均合作率')
ax4.set_ylabel('收益變異性')
ax4.set_title('合作率與收益穩定性')
plt.tight_layout()
plt.show()
return df
# 執行分析
results_df = analyze_tournament_results(ecosystem, tournament_results)
# 顯示詳細統計
print("\n詳細統計分析：")
print("=" * 50)
print(results_df.round(3))
本章節我們先建立了python的整體觀念，以及相關的數據統計分析，下篇章節，我們再繼續針對哲學層面進行更深入的探討。
