An Intelligent Algorithm for Solving the Efficient Nash Equilibrium of a Single-Leader Multi-Follower Game

Lu-Ping Liu and Wen-Sheng Jia
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Lu-Ping Liu: School of Mathematics and Statistic, Guizhou University, Huaxidadao, Guiyang 550025, China
Wen-Sheng Jia: School of Mathematics and Statistic, Guizhou University, Huaxidadao, Guiyang 550025, China

Mathematics, 2021, vol. 9, issue 5, 1-14

Abstract: This aim of this paper is to provide the immune particle swarm optimization (IPSO) algorithm for solving the single-leader–multi-follower game (SLMFG). Through cooperating with the particle swarm optimization (PSO) algorithm and an immune memory mechanism, the IPSO algorithm is designed. Furthermore, we define the efficient Nash equilibrium from the perspective of mathematical economics, which maximizes social welfare and further refines the number of Nash equilibria. In the end, numerical experiments show that the IPSO algorithm has fast convergence speed and high effectiveness.

Keywords: single-leader–multi-follower game; immune particle swarm optimization (IPSO) algorithm; probability density selection function; efficient Nash equilibrium (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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