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.

翻译：本文研究了两个玩家零和随机贝叶西亚游戏, 每个玩家都有自己的动态状态, 而另一个玩家不知道。 我们使用典型的技巧, 在原始游戏及其双向游戏中提供循环公式和足够的统计数据。 它还显示, 使用一个特定的初始参数, 一个玩家在双向游戏中的最佳策略也是玩家在原始游戏中的最佳策略。 为了处理长期有限的巴伊西亚游戏, 我们提供了一个算法, 以一步步计算玩家的亚最佳策略, 以避免 LP 复杂程度 。 为此, 我们计算LP 以在双向游戏中找到特殊的初始参数, 并更新双向游戏的充足统计数据 。 性能分析为最佳策略和亚最佳策略之间的性能差异提供了一个上限 。 主要结果表现在水下传感器网络的安全问题中 。