Multi-agent influence diagrams (MAIDs) are probabilistic graphical models which represent strategic interactions between agents. MAIDs are equivalent to extensive form games (EFGs) but have a more compact and informative structure. However, MAIDs cannot, in general, represent settings of incomplete information -- wherein agents have different beliefs about the game being played, and different beliefs about each-other's beliefs. In this paper, we introduce incomplete information MAIDs (II-MAIDs). We define both infinite and finite-depth II-MAIDs and prove an equivalence relation to EFGs with incomplete information and no common prior over types. We prove that II-MAIDs inherit classical equilibria concepts via this equivalence, but note that these solution concepts are often unrealistic in the setting with no common prior because they violate common knowledge of rationality. We define a more realistic solution concept based on recursive best-response. Throughout, we describe an example with a hypothetical AI agent undergoing evaluation to illustrate the applicability of II-MAIDs.

翻译：多智能体影响图（MAID）是表示智能体间策略交互的概率图模型。MAID与扩展式博弈（EFG）具有等价性，但具备更紧凑且信息丰富的结构。然而，MAID通常无法表示不完全信息场景——即智能体对当前博弈持有不同信念，且对彼此信念存在认知差异。本文提出不完全信息多智能体影响图（II-MAID）。我们定义了无限深度与有限深度的II-MAID，并证明了其与类型无共同先验的不完全信息EFG的等价关系。通过该等价性，我们证明II-MAID继承了经典均衡概念，但指出在无共同先验场景中这些解概念常因违背理性共识而缺乏现实性。我们基于递归最优响应定义了更具现实意义的解概念。全文通过假设性AI智能体接受评估的案例，阐释II-MAID的实际适用性。