【原创】纳什均衡寻找器

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功能：寻找博弈的纳什均衡点，适用于所有类型矩阵博弈，包括不可解的三人以上博弈

下载地址：https://github.com/lansiz/nash-finder

使用要求：Python及其numpy、matplotlib包

用法举例一、 寻找双人博弈的均衡点

下面是经典的双人博弈的收益矩阵，每个玩家使用三个策略。


对照收益矩阵可以很直观转化为Python代码：

import grm  # 主程序，就一个文件，10多K，很小巧
game = grm.Game()
# two playeys, and each player uses THREE pure strategies
game.player_join(grm.Player(3))
game.player_join(grm.Player(3))
game.player_init_mixed_strategies()
# assign the payoff (define the payoff function)
# player 1
game.player_assign_payoff(1, "11", -231)
game.player_assign_payoff(1, "12", -505)
game.player_assign_payoff(1, "13", 525)
game.player_assign_payoff(1, "21", -552)
game.player_assign_payoff(1, "22", 831)
game.player_assign_payoff(1, "23", -928)
game.player_assign_payoff(1, "31", -74)
game.player_assign_payoff(1, "32", -96)
game.player_assign_payoff(1, "33", -604)
# player 2
game.player_assign_payoff(2, "11", 175)
game.player_assign_payoff(2, "12", -350)
game.player_assign_payoff(2, "13", -770)
game.player_assign_payoff(2, "21", -641)
game.player_assign_payoff(2, "22", -222)
game.player_assign_payoff(2, "23", -189)
game.player_assign_payoff(2, "31", 302)
game.player_assign_payoff(2, "32", 504)
game.player_assign_payoff(2, "33", 767)
# run the iterations to approximate Nash equilibrium
game.run(iterations=10**5)

运行上面代码可以看到输出。输出包括均衡点逼近值；Deviation表示精度，越小越好。



还可以对逼近过程进行可视化


用法举例二、 寻找三人博弈的均衡点



转化为Python代码：

# assign the payoff (define the payoff function)
# player 1
# left matrix
game.player_assign_payoff(1, "111", 4)
game.player_assign_payoff(1, "121", 3)
game.player_assign_payoff(1, "211", 5)
game.player_assign_payoff(1, "221", 5)
# right matrix
game.player_assign_payoff(1, "112", 4)
game.player_assign_payoff(1, "122", 5)
game.player_assign_payoff(1, "212", 8)
game.player_assign_payoff(1, "222", 4)
# player 2
# left matrix
game.player_assign_payoff(2, "111", 5)
game.player_assign_payoff(2, "121", 2)
game.player_assign_payoff(2, "211", 3)
game.player_assign_payoff(2, "221", 4)
# right matrix
game.player_assign_payoff(2, "112", 6)
game.player_assign_payoff(2, "122", 3)
game.player_assign_payoff(2, "212", 2)
game.player_assign_payoff(2, "222", 3)
# player 3
# left matrix
game.player_assign_payoff(3, "111", 3)
game.player_assign_payoff(3, "121", 5)
game.player_assign_payoff(3, "211", 2)
game.player_assign_payoff(3, "221", 4)
# right matrix
game.player_assign_payoff(3, "112", 2)
game.player_assign_payoff(3, "122", 4)
game.player_assign_payoff(3, "212", 6)
game.player_assign_payoff(3, "222", 5)

运行结果及可视化：




用法举例三、 寻找任意博弈的均衡点
上述两个举例针对常见的博弈，目的是提供直观的了解。但本工具主要特点是，（理论上）适用于任意博弈，也就是任意数量玩家、任意策略个数的博弈。下面的例子中，有四个玩家，分别使用二、三、四、五个策略。

import grm
game = grm.Game()
# four palyers, and each uses two, three, four and five pure strategies
game.player_join(grm.Player(2))
game.player_join(grm.Player(3))
game.player_join(grm.Player(4))
game.player_join(grm.Player(5))
game.player_init_mixed_strategies()
# assign the payoff (define the payoff function)
game.player_assign_random_payoff()  # 120个设置，一个个写太冗长了，因此本例子统一随机设置
game.run()

输出结果：



关于此工具的更多具体介绍和不足，有兴趣的可以去“下载地址”网页看看。

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关键词：纳什均衡 equilibrium Approximate Strategies iterations

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