One Swarm per Queen: A Particle Swarm Learning for Stochastic Games

This article examines a particle swarm collaborative model-free learning algorithm for approximating equilibria of stochastic games with continuous action spaces. The results support the argument that a simple learning algorithm which consists to explore the continuous action set by means of multi-population of particles can provide a satisfactory solution. A collaborative learning between the particles of the same player takes place during the interactions of the game, in which the players and the particles have no direct knowledge of the payoff model. Each particle is allowed to observe her own payoff and has only one-step memory. The existing results linking the outcomes to stationary satisfactory set do not apply to this situation because of continuous action space and non-convex local response. We provide a different approach to stochastic differential inclusion for arbitrary number of agents.