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

This paper studies two-player zero-sum stochastic Bayesian games where each player has its own dynamic state that is unknown to the other player. Using typical techniques, we provide the recursive formulas and sufficient statistics in both the primal game and its dual games. It's also shown that with a specific initial parameter, the optimal strategy of one player in a dual game is also the optimal strategy of the player in the primal game. To deal with the long finite Bayesian game we have provided an algorithm to compute the sub-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 dual games and update the sufficient statistics of the dual games. The performance analysis has provided an upper bound on the performance difference between the optimal and suboptimal strategies. The main results are demonstrated in a security problem of underwater sensor networks.