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This paper studies two-player zero-sum stochastic Bayesian games where eachplayer has its own dynamic state that is unknown to the other player. Usingtypical techniques, we provide the recursive formulas and sufficient statisticsin both the primal game and its dual games. It's also shown that with aspecific initial parameter, the optimal strategy of one player in a dual gameis also the optimal strategy of the player in the primal game. To deal with thelong finite Bayesian game we have provided an algorithm to compute thesub-optimal strategies of the players step by step to avoid the LP complexity.For this, we computed LPs to find the special initial parameters in the dualgames and update the sufficient statistics of the dual games. The performanceanalysis has provided an upper bound on the performance difference between theoptimal and suboptimal strategies. The main results are demonstrated in asecurity problem of underwater sensor networks.

LP Formulations of sufficient statistic based strategies in Finite Horizon Two-Player Zero-Sum Stochastic Bayesian games