遗传算法求解纳什均衡点的python代码

遗传算法可以用于求解纳什均衡点，以下是一个简单的Python代码示例：

import random

# 设置博弈的参数
num_players = 2
num_strategies = 3
max_iterations = 100
population_size = 50
mutation_rate = 0.1
crossover_rate = 0.5

# 定义博弈矩阵
game_matrix = [[(1, 1), (-1, 2)],
               [(2, -1), (0, 0)],
               [(0, 0), (-1, -1)]]

# 定义个体编码方式
def encode_strategy(strategy):
    return ''.join(str(s) for s in strategy)

def decode_strategy(encoded_strategy):
    return [int(s) for s in encoded_strategy]

# 定义适应度函数
def fitness_function(strategy):
    total_payoff = [0] * num_players
    for i in range(num_players):
        player_strategy = decode_strategy(strategy[i])
        for j in range(num_strategies):
            opponent_strategy = decode_strategy(strategy[(i + 1) % num_players])
            payoff = game_matrix[player_strategy][opponent_strategy][i]
            total_payoff[i] += payoff
    return sum(total_payoff)

# 定义选择函数
def selection(population):
    fitness_scores = [fitness_function(strategy) for strategy in population]
    total_fitness = sum(fitness_scores)
    probabilities = [fitness / total_fitness for fitness in fitness_scores]
    selected_indices = random.choices(range(population_size), weights=probabilities, k=population_size)
    return [population[i] for i in selected_indices]

# 定义交叉函数
def crossover(parent1, parent2):
    if random.random() < crossover_rate:
        crossover_point = random.randint(1, len(parent1) - 1)
        child1 = parent1[:crossover_point] + parent2[crossover_point:]
        child2 = parent2[:crossover_point] + parent1[crossover_point:]
        return child1, child2
    else:
        return parent1, parent2

# 定义变异函数
def mutation(child):
    mutated_child = ''
    for bit in child:
        if random.random() < mutation_rate:
            mutated_child += '0' if bit == '1' else '1'
        else:
            mutated_child += bit
    return mutated_child

# 初始化种群
population = [''.join(str(random.randint(0, 1)) for _ in range(num_strategies)) for _ in range(population_size)]

# 迭代
for iteration in range(max_iterations):
    # 选择
    selected_population = selection(population)
    # 交叉
    children = []
    for i in range(0, population_size, 2):
        child1, child2 = crossover(selected_population[i], selected_population[i+1])
        children.append(mutation(child1))
        children.append(mutation(child2))
    # 替换
    population = children

# 输出结果
fitness_scores = [fitness_function(strategy) for strategy in population]
best_strategy_index = fitness_scores.index(max(fitness_scores))
best_strategy = decode_strategy(population[best_strategy_index])
print('Best strategy:', best_strategy)

上述代码中，我们定义了一个2人3策略的博弈矩阵，然后使用遗传算法求解纳什均衡点。在适应度函数中，我们计算了每个个体的总收益，并以此作为适应度的度量。在选择函数中，我们使用轮盘赌选择法选择下一代种群。在交叉函数中，我们使用单点交叉法进行交叉操作。在变异函数中，我们使用随机位翻转法进行变异操作。最后，我们输出了得到的最优策略。