Security Strategies of Both Players in Asymmetric Information Zero-Sum Stochastic Games with an Informed Controller

This paper considers a zero-sum two-player asymmetric information stochastic game where only one player knows the system state, and the transition law is controlled by the informed player only. For the informed player, it has been shown that the security strategy only depends on the belief and the current stage. We provide LP formulations whose size is only linear in the size of the uninformed player’s action set to compute both history based and belief based security strategies. For the uninformed player, we focus on the regret, the difference between 0 and the future payoff guaranteed by the uninformed player in every possible state. Regret is a real vector of the same size as the belief, and depends only on the action of the informed player and the strategy of the uninformed player. This paper shows that the uninformed player has a security strategy that only depends on the regret and the current stage. LP formulations are then given to compute the history based security strategy, the regret at every stage, and the regret based security strategy. The size of the LP formulations are again linear in the size of the uninformed player action set. Finally, an intrusion detection problem is studied to demonstrate the main results in this paper.