Two Person Zero-sum Markov Games with Partial Information on Action Spaces

摘要

In everyday life we sometimes encounter the conflicts in which we cannot know what the other sides do or what they can do. If several stages are played in the conflicts, every person tries to gain exact information about the other sides' intentions or their abilities by observing their behavior. To research these conflicts, we introduce a new mathematical model and define "two-person zero-sum Markov games with partial information on action spaces". Each player in the game observes his opponent's actions carefully to obtain some information about the opponent's action space, which means the ability of him. The more information he obtains, the more payoff he will gain. Thus the player tries to get more information about the opponent and try to reveal less information about himself. By the Nash's theorem of game theory, we prove the existence of a mixed-strategy equilibrium and do the existence of the optimal random strategies for both players.