Matrix games, mixed strategies, and statistical mechanics
Matrix games, mixed strategies, and statistical mechanics
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DOI：
10.1103/physrevlett.81.4999
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发表时间：
1998-11-30
影响因子：
8.6
通讯作者：
Engel, A
中科院分区：
文献类型：
--
作者：
Berg, J;Engel, A
矩阵博弈构成了博弈论的一个基本问题，描述了两个利益完全冲突的博弈者的情况。我们展示了如何使用统计力学的方法来研究具有随机支付矩阵的大型矩阵博弈的最优混合策略的统计特性，并导出博弈价值和策略强度分布的分析表达式。特别是计算对玩家的最佳混合策略没有贡献的纯策略的分数。考虑支付矩阵的独立分布和相关元素，并将结果与数值模拟进行比较。 [S0031-9007(98)07803-X]。
Matrix games constitute a fundamental problem of game theory and describe a situation of two players with completely conflicting interests. We show how methods from statistical mechanics can be used to investigate the statistical properties of optimal mixed strategies of large matrix games with random payoff matrices and derive analytical expressions for the value of the game and the distribution of strategy strengths. In particular the fraction of pure strategies not contributing to the optimal mixed strategy of a player is calculated. Both independently distributed as well as correlated elements of the payoff matrix are considered and the results are compared with numerical simulations. [S0031-9007(98)07803-X].