A fundamental problem in noncooperative dynamic game theory is the computation of Nash equilibria under different information structures, which specify the information available to each agent during decision-making. Prior work has extensively studied equilibrium solutions for two canonical information structures: feedback, where agents observe the current state at each time, and open-loop, where agents only observe the initial state. However, these paradigms are often too restrictive to capture realistic settings exhibiting interleaved information structures, in which each agent observes only a subset of other agents at every timestep. To date, there is no systematic framework for modeling and solving dynamic games under arbitrary interleaved information structures. To this end, we make two main contributions. First, we introduce a method to model deterministic dynamic games with arbitrary interleaved information structures as Mathematical Program Networks (MPNs), where the network structure encodes the informational dependencies between agents. Second, for linear-quadratic (LQ) dynamic games, we leverage the MPN formulation to develop a systematic procedure for deriving Riccati-like equations that characterize Nash equilibria. Finally, we illustrate our approach through an example involving three agents exhibiting a cyclic information structure.

翻译：非合作动态博弈论中的一个基本问题是在不同信息结构下计算纳什均衡。信息结构规定了每个智能体在决策时可获取的信息。已有研究广泛探讨了两种经典信息结构下的均衡解：反馈式（智能体在每一时刻观测当前状态）和开环式（智能体仅观测初始状态）。然而，这些范式往往过于严格，无法刻画具有交错信息结构的现实场景——其中每个智能体在每个时间步仅能观测到其他智能体的子集。迄今为止，尚无系统性框架可用于建模和求解任意交错信息结构下的动态博弈。为此，我们做出两项主要贡献。首先，我们提出了一种将具有任意交错信息结构的确定性动态博弈建模为数学规划网络（MPN）的方法，其中网络结构编码了智能体之间的信息依赖关系。其次，针对线性二次型（LQ）动态博弈，我们利用MPN表述开发了一套系统化流程，用于推导刻画纳什均衡的类Riccati方程。最后，我们通过一个包含三个智能体且呈现循环信息结构的案例对所提方法进行了说明。