Differential evolution particle swarm optimization algorithm based on good point set for computing Nash equilibrium of finite noncooperative game

• Published in: AIMS mathematics Vol. 6; no. 2; pp. 1309 - 1323
• Main Authors: Li, Huimin, Xiang, Shuwen, Yang, Yanlong, Liu, Chenwei
• Format: Journal Article
• Language: English
• Published: AIMS Press 01.01.2021
• Subjects: differential evolution particle swarm optimization algorithm; good point set; high-dimensional payoff matrix; nash equilibrium; non-cooperative game
• ISSN: 2473-6988; 2473-6988
• DOI: 10.3934/math.2021081

In this paper, a hybrid differential evolution particle swarm optimization (PSO) method based on a good point set (GPDEPSO) is proposed to compute a finite noncooperative game among N people. Stochastic functional analysis is used to prove the convergence of this algorithm. First, an ergodic initial population is generated by using a good point set. Second, PSO is proposed and utilized as the variation operator to perform variation crossover selection with differential evolution (DE). Finally, the experimental results show that the proposed algorithm has a better convergence speed, accuracy, and global optimization ability than other existing algorithms in computing the Nash equilibrium of noncooperative games among N people. In particular, the efficiency of the algorithm is higher for determining the Nash equilibrium of a high-dimensional payoff matrix game.