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

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