基于Python实现计算纳什均衡的示例详解

import nashpy as nash
import numpy as np

A = np.array([[1, -1], [-1, 1]])
game = nash.Game(A)
equilibrium = game.vertex_enumeration()
print("纳什均衡是: ", next(equilibrium))

import numpy as np
from scipy.optimize import linprog


def nash_equilibrium(payoff_matrix_a, payoff_matrix_b):
    """
    计算二人非合作博弈的纳什均衡。
    """
    num_actions_a = payoff_matrix_a.shape[1]
    num_actions_b = payoff_matrix_b.shape[1]

    # 定义优化问题
    c = -np.ones(num_actions_a + num_actions_b)
    A = np.zeros((num_actions_b, num_actions_a + num_actions_b))
    for j in range(num_actions_b):
        A[j, :num_actions_a] = -payoff_matrix_b[:, j]
        A[j, num_actions_a:] = np.ones(num_actions_b)

    b = np.zeros(num_actions_b)
    bounds = [(0, None) for _ in range(num_actions_a + num_actions_b)]

    # 解决优化问题
    res = linprog(c, A_ub=A, b_ub=b, bounds=bounds, method='simplex')

    # 提取混合策略
    mixed_strategy_a = res.x[:num_actions_a]
    mixed_strategy_b = res.x[num_actions_a:]

    return mixed_strategy_a, mixed_strategy_b



payoff_matrix_a = np.array([[1, 5], [0, 5]])
payoff_matrix_b = np.array([[3, 7], [2, 3]])
mixed_strategy_a, mixed_strategy_b = nash_equilibrium(payoff_matrix_a, payoff_matrix_b)

print("混合策略 A:", mixed_strategy_a)
print("混合策略 B:", mixed_strategy_b)

from pulp import *

# 创建一个线性规划模型
prob = LpProblem("纳什均衡", LpMaximize)

# 创建玩家1的策略变量
p1 = LpVariable("p1", 0, 1)

# 创建玩家2的策略变量
p2 = LpVariable("p2", 0, 1)

# 设置目标函数
prob += 5 * p1 + 4 * p2, "Total Utility"

# 设置约束条件
prob += p1 + 2 * p2 <= 1, "玩家 1 约束条件"
prob += 3 * p1 + 2 * p2 <= 2, "玩家 2 约束条件"

# 解决问题
prob.solve()

# 输出结果
print("玩家1策略: ", value(p1))
print("玩家2策略: ", value(p2))