基于连续同伦的多方对策之Nash均衡点的机械化求解方法  

A Mechanical Method for Computing the Nash Mixed Equilibrium via Continuous Homotopy

作　　者：熊贝贝 杨争峰[2] 武斌 曾振柄[4] XIONG Beibei;YANG Zhengfeng;WU Bin;ZENG Zhenbing(School of Mathematics and Computer Science,Hubei University,Wuhan 430062;School of Software Engineering,East China Normal University,Shanghai 200062;Zhejiang University of Finance and Economics,Jinhua 321013;Chengdu Institute of Computer Applications,Chinese Academy of Sciences,Chengdu 610213)

机构地区：[1]湖北大学数学与统计学学院,武汉430062 [2]华东师范大学软件工程学院,上海200062 [3]上海财经大学浙江学院,金华321013 [4]中国科学院成都计算机应用研究所,成都610213

出　　处：《系统科学与数学》2023年第3期780-796,共17页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(12171159)资助课题。

摘　　要：Nash定理证明非合作n人矩阵对策一定有混合平衡解,现有文献多讨论n=2时混合平衡解的求法,一般用优化或逼近的方法.文章给出了一种机械化求解方法,通过构造非合作多人矩阵对策的混合平衡局势所满足的多项式方程组,应用方程组求解软件由此可直接求出多人对策的问题的各种混合平衡解.Applying the Brouwer fixed theorems Nash proved that there exists at least one mixed equilibrium point for any n-player non-cooperative game.For solving the mixed equilibrium of given games,most of previous works in literatures as we know are designed for 2-player zero-sum or non-zero-sum cases,and the methods are mainly based on numerical optimization or approximate computation.In this paper,we present an innovative mechanical method to construct polynomial equations for Nash mixed equilibrium points,therefore combining the continuous homotopy method one can find all mixed equilibria directly.

关 键 词：Nash定理 混合平衡策略 数学机械化 多项式方程 连续同伦方法 

分 类 号：O175[理学—数学]