Sufficient Statistic Based Suboptimal Strategies in Infinite Horizon Two-Player Zero-Sum Stochastic Bayesian Games

This paper considers two-player zero-sum stochastic Bayesian games with infinite horizon time frame where each player’s dynamic state is unknown to the others. Based on our previous work in finite horizon games [1], we provide a sufficient statistic based suboptimal strategy in the infinite horizon games using the receding horizon idea. In this sub-optimal strategy, both the strategy and the sufficient statistic can be updated using linear programming (LP) formulations. The performance analysis of the suboptimal strategy provides an upper bound on the performance difference between the suboptimal strategy and the optimal one. It is shown that the upper bound decreases exponentially with respect to the window size. The performance of the suboptimal strategies is demonstrated in an underwater jamming problem.