Common Information Belief based Dynamic Programs for Stochastic Zero-sum Games with Competing Teams
Common Information Belief based Dynamic Programs for Stochastic Zero-sum Games with Competing Teams
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DOI：
10.23919/acc53348.2022.9867399
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发表时间：
2021-02
期刊：
影响因子：
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通讯作者：
D. Kartik;A. Nayyar;U. Mitra
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文献类型：
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作者：
D. Kartik;A. Nayyar;U. Mitra
人们对去中心化团队问题进行了积极研究，其中参与者对底层随机系统状态的信息不对称，但对此类团队之间的游戏了解较少。我们考虑两个竞争团队之间零和随机博弈的一般模型。该模型包含了许多先前考虑的团队和零和博弈模型。对于这个通用模型，我们提供了游戏的上限（最小-最大）和下限（最大-最小）值的界限。此外，如果游戏的上限和下限相同（即，如果游戏有一个值），则我们的边界与游戏的值一致。我们的界限是使用两个动态程序获得的，该程序基于称为公共信息信念（CIB）的充分统计量。我们还确定了某些信息结构，其中只有最小化团队控制 CIB 的演变。在这些情况下，我们展示了基于 CIB 的动态程序之一可用于查找最小-最大策略（除了最小-最大值之外）。我们提出了一种近似动态规划方法来计算值（以及适用时的策略），并通过示例说明了我们的结果。
Decentralized team problems where players have asymmetric information about the state of the underlying stochastic system have been actively studied, but games between such teams are less understood. We consider a general model of zero-sum stochastic games between two competing teams. This model subsumes many previously considered team and zero-sum game models. For this general model, we provide bounds on the upper (min-max) and lower (max-min) values of the game. Furthermore, if the upper and lower values of the game are identical (i.e., if the game has a value), our bounds coincide with the value of the game. Our bounds are obtained using two dynamic programs based on a sufficient statistic known as the common information belief (CIB). We also identify certain information structures in which only the minimizing team controls the evolution of the CIB. In these cases, we show that one of our CIB based dynamic programs can be used to find the min-max strategy (in addition to the min-max value). We propose an approximate dynamic programming approach for computing the values (and the strategy when applicable) and illustrate our results with the help of an example.