An new swarm intelligent algorithm to solve the efficiency Nash
equilibrium of single-leader-multi-follower game
This paper presents the particle swarm optimization algorithm and immune
particle swarm optimization algorithm (PSO-IPSO) to solve the
single-leader-multi-follower game (SLMFG). The PSO-IPSO algorithm is
designed by combining particle swarm algorithm and immune memory
mechanism, and the diversity of the population is maintained by using
probability density selection function. Meanwhile, we define the
efficiency Nash equilibrium by using the idea of efficiency, which is
more beneficial to all players and greatly refine Nash equilibrium.
Finally, numerical experiments show that this algorithm not only does
not rely on the choice of an initial point, but also increases the
diversity of swarm to keep global convergence, and the PSO-IPSO
algorithm is fast convergence speed and effective.