A statistical property of multiagent learning based on Markov decision process

We exhibit an important property called the asymptotic equipartition property (AEP) on empirical sequences in an ergodic multiagent Markov decision process (MDP). Using the AEP which facilitates the analysis of multiagent learning, we give a statistical property of multiagent learning, such as reinforcement learning (RL), near the end of the learning process. We examine the effect of the conditions among the agents on the achievement of a cooperative policy in three different cases: blind, visible, and communicable. Also, we derive a bound on the speed with which the empirical sequence converges to the best sequence in probability, so that the multiagent learning yields the best cooperative result.