A mathematical model for learning agents on a multi-agent system

A term "the learning agent" on the multi-agent system has appeared in the beginning of 1990\´s [LJ Lin, 1991]. Since then, a number of researches have been studied some applications of the learning agents on the basis of reinforcement learning such as SLA and Q-learning incorporated with the automation, as well as [Michiko Watanabe et al., 2001]. However, in designing the learning agents, there are questions; what stands on the state and action model, and the state and action evaluate function? How is the reward designed? This paper aims at developing a mathematical model for the learning agents of the multi-agent system to answer these questions. The learning agent is derived from the introduced formulation. Also, the relation of reward between the multi-agents is analyzed using mathematical model as well.