Efficient computation of discounted asymmetric information zero-sum stochastic games

In asymmetric information zero-sum games, one player has superior information about the game over the other. Asymmetric information games are particularly relevant for security problems, e.g., where an attacker knows its own skill set or alternatively a system administrator knows the state of its resources. In such settings, the informed player is faced with the tradeoff of exploiting its superior information at the cost of revealing its superior information. This tradeoff is typically addressed through randomization, in an effort to keep the uninformed player informationally off balance. A lingering issue is the explicit computation of such strategies. This paper, building on prior work for repeated games, presents an LP formulation to compute suboptimal strategies for the informed player in discounted asymmetric information stochastic games in which state transitions are not affected by the uninformed player. Furthermore, the paper presents bounds between the security level guaranteed by the sub-optimal strategy and the optimal value. The results are illustrated on a stochastic intrusion detection problem.