基于蜉蝣算法的非合作博弈Nash均衡求解
Solving Nash Equilibrium for N-Persons'Non-Cooperative Game Based on Mayfly Algorithm
胡作鹏 1杨彦龙 1贾文生1
作者信息
- 1. 贵州大学数学与统计学院,贵州 贵阳 550025
- 折叠
摘要
鉴于凸优化问题算法在非合作博弈Nash均衡的求解中具有一定的局限性,N人非合作博弈Nash均衡求解是NP 问题,提出一种N人非合作博弈Nash均衡求解问题的改进仿生算法-蜉蝣算法(MA).算法中蜉蝣通过个体最优位置及全体最优位置调整位置来搜索最优解,同时引入高斯变异算子提高算法搜素能力.根据Nash均衡的解空间为单纯形的特性,采用固定初始化点和随机初始化点相结合的方式,提高搜索速度且结果不局限于纯策略.实验表明,蜉蝣算法求解Nash均衡效果优于烟花算法、免疫粒子群算法,特别地,对于高维博弈问题也有很好的效果.
Abstract
In view of the limitation of the convex optimization algorithm in solving the Nash equilibrium of a non-cooperative game,the Nash equilibrium of an N-person non-cooperative game is an NP problem,an improved bionic algorithm for solving the Nash equilibrium of an N-person non-cooperative game,Mayfly algorithm(MA),is pro-posed.In this algorithm,Mayfly searches for the optimal solution by adjusting the position through the individual opti-mal position and the overall optimal position,and introduces the Gaussian mutation operator to improve the search a-bility of the algorithm.According to the characteristics that the solution space of Nash equilibrium is simplex,the fixed initialization point and random initialization point are combined to improve the search speed and the results are not limited to pure strategy.Experiments show that the Mayfly algorithm is better than the fireworks algorithm and im-mune particle swarm algorithm in solving Nash equilibrium,especially for high dimensional game problems.
关键词
非合作博弈/均衡求解/蜉蝣算法Key words
Non-cooperative game/Equilibrium Solving/Mayfly Algorithm引用本文复制引用
基金项目
国家自然科学基金(12061020)
国家自然科学基金(黔科合LH字[2017]7223)
国家自然科学基金(贵大人基合字201949)
出版年
2024
NETL
NSTL
万方数据