Higher-Order Belief in Incomplete Information MAIDs
This work addresses a foundational limitation in modeling strategic interactions for AI and game theory researchers, enabling more realistic representation of incomplete information scenarios.
The paper tackles the inability of multi-agent influence diagrams (MAIDs) to represent incomplete information settings, where agents have differing beliefs about the game and each other's beliefs, by introducing incomplete information MAIDs (II-MAIDs). It proves equivalence to extensive form games with incomplete information and no common prior, and defines a recursive best-response solution concept to address unrealistic equilibria.
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.