We analyze a class of stochastic dynamic games among teams with asymmetric information, where members of a team share their observations internally with a delay of $d$. Each team is associated with a controlled Markov Chain, whose dynamics are coupled through the players' actions. These games exhibit challenges in both theory and practice due to the presence of signaling and the increasing domain of information over time. We develop a general approach to characterize a subset of Nash Equilibria where the agents can use a compressed version of their information, instead of the full information, to choose their actions. We identify two subclasses of strategies: Sufficient Private Information Based (SPIB) strategies, which only compress private information, and Compressed Information Based (CIB) strategies, which compress both common and private information. We show that while SPIB-strategy-based equilibria always exist, the same is not true for CIB-strategy-based equilibria. We develop a backward inductive sequential procedure, whose solution (if it exists) provides a CIB strategy-based equilibrium. We identify some instances where we can guarantee the existence of a solution to the above procedure. Our results highlight the tension among compression of information, existence of (compression based) equilibria, and backward inductive sequential computation of such equilibria in stochastic dynamic games with asymmetric information.

中文翻译：

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团队内部信息共享被延迟的团队之间的动态游戏

我们分析了具有不对称信息的团队之间的一类随机动态博弈，其中团队成员在内部共享他们的观察结果，延迟时间为$ d $。每个团队都与一个受控的马尔可夫链相关联，该马尔可夫链的动态性通过玩家的行动而耦合。由于信号的存在和信息范围的不断扩大，这些游戏在理论和实践上均面临挑战。我们开发了一种通用方法来表征Nash均衡的子集，在该子集中，代理可以使用其信息的压缩版本而不是完整的信息来选择其操作。我们确定了策略的两个子类：充分压缩基于私有信息（SPIB）的策略（仅压缩私有信息）和基于压缩信息的基于CIB的策略，压缩公共和私人信息。我们表明，尽管基于SPIB策略的均衡始终存在，但对于基于CIB策略的均衡却并非如此。我们开发了一种反向归纳顺序程序，其解决方案（如果存在）提供了基于CIB策略的均衡。我们确定了一些可以保证上述程序有解决方案的情况。我们的结果突出了信息压缩，基于平衡的（基于压缩的）平衡的存在以及在具有非对称信息的随机动态博弈中这种平衡的反向归纳顺序计算之间的张力。其解决方案（如果存在）提供了基于CIB策略的均衡。我们确定了一些可以保证上述程序有解决方案的情况。我们的结果突出了信息压缩，基于平衡的（基于压缩的）平衡的存在以及在具有非对称信息的随机动态博弈中这种平衡的反向归纳顺序计算之间的张力。其解决方案（如果存在）提供了基于CIB策略的均衡。我们确定了一些可以保证上述程序有解决方案的情况。我们的结果突出了信息压缩，基于平衡的（基于压缩的）平衡的存在以及在具有非对称信息的随机动态博弈中这种平衡的反向归纳顺序计算之间的张力。