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n人0-1理性博弈的严格纯Nash均衡和期望均衡求解法与期望均衡分析

Solution Method for Expected Equilibrium and Strictly Pure Nash Equilibirium and Analysis of Expecte Equilibrium in an n-person 0-1 Rational Game
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摘要 为了解决每个参与人恰有两个行动且极大熵准则以及每个参与人都完全不知道其他参与人的行动信息是全体参与人的共同知识的多人策略博弈的可能出现局势,给出了严格纯Nash均衡和期望均衡的求解法和最可能局势的分析法及其用应例子。以二进制和十进制数为基本工具,证明了严格纯Nash均衡的一个求解算法,基于全体参与人上述共同知识系统,给出了一个明显的期望均衡求解公式。通过设定参与人的效用为未知参数并根据期望均衡求解公式,由解不等式组的方法提出了期望均衡分析法。研究表明,此类常用博弈的特殊性致使两种均衡和期望均衡分析计算简洁。实例分析表明,此法可快速计算出博弈的严格纯Nash均衡和期望均衡,由期望均衡分析法给出的结论由传统方法无法得到且更加符合实际。 In order to find the most probable situation in an n-person strategy game that every player has exactly two actions and that principle of maximum entropy is all players' common knowledge when every player knows nothing about decisions of other ones, the method of solving strictly pure Nash equilibria and expected equilibria and the methods of finding the most probable situation with applications are given in this paper. By using the systems of binary numbers and decimal numbers, the algorithm of solving strictly pure Nash equilibria is proven. Basic on the above-mentioned common knowledge system, an evident formula of solving expected equilibria is given. By letting players' utilities be parameters, solving inequalities, and by formula of solving expected equilibria, an analysis method of equilibria is put forward. The study results show that simplicity of the formulas and methods come from the character of this form of games. Empirical results show that strictly pure Nash equilibria and expected equilbria can be quickly obtained by our methods and the conclusion obtained through the method of expected equilibrium analysis is more consist with practice, which is unlikely to be drawn from classical game theory.
作者 姜殿玉
出处 《系统工程》 CSSCI CSCD 北大核心 2010年第1期64-67,共4页 Systems Engineering
基金 国家自然科学基金资助项目(70871051)
关键词 0-1博弈 理性博弈 严格纯Nash均衡 期望均衡 极大嫡原理 期望均衡分析 0-1 Game Rational Game Strictly Pure Nash Equilibrium Expected Equilibrium Principle of Maximum Entropy Expected Equilibrium Analysis
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