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Article

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

by and *,†
School of Mathematics and Statistic, Guizhou University, Huaxidadao, Guiyang 550025, China
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Academic Editor: Vladimir Mazalov
Mathematics 2021, 9(5), 454; https://doi.org/10.3390/math9050454
Received: 19 January 2021 / Revised: 18 February 2021 / Accepted: 19 February 2021 / Published: 24 February 2021
(This article belongs to the Special Issue Mathematical Game Theory 2021)
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. View Full-Text
Keywords: single-leader–multi-follower game; immune particle swarm optimization (IPSO) algorithm; probability density selection function; efficient Nash equilibrium single-leader–multi-follower game; immune particle swarm optimization (IPSO) algorithm; probability density selection function; efficient Nash equilibrium
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MDPI and ACS Style

Liu, L.-P.; Jia, W.-S. An Intelligent Algorithm for Solving the Efficient Nash Equilibrium of a Single-Leader Multi-Follower Game. Mathematics 2021, 9, 454. https://doi.org/10.3390/math9050454

AMA Style

Liu L-P, Jia W-S. An Intelligent Algorithm for Solving the Efficient Nash Equilibrium of a Single-Leader Multi-Follower Game. Mathematics. 2021; 9(5):454. https://doi.org/10.3390/math9050454

Chicago/Turabian Style

Liu, Lu-Ping, and Wen-Sheng Jia. 2021. "An Intelligent Algorithm for Solving the Efficient Nash Equilibrium of a Single-Leader Multi-Follower Game" Mathematics 9, no. 5: 454. https://doi.org/10.3390/math9050454

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