Higher-Order Belief in Incomplete Information MAIDs

2025-03-08

AI Summary

Existing multi-agent influence diagrams (MAIDs) cannot represent heterogeneous and nested higher-order beliefs under incomplete information. Method: We propose incomplete-information multi-agent influence diagrams (II-MAIDs), the first formal framework supporting both finite- and infinite-depth belief hierarchies. II-MAIDs integrate probabilistic graphical models with game-theoretic reasoning, enabling higher-order belief modeling and recursive rational inference without assuming a common prior. Contribution/Results: We rigorously prove that II-MAIDs are expressively equivalent to and complete for extensive-form games with incomplete information (EFGs). Theoretically, we reformulate solution concepts—including Nash equilibrium—within this framework and introduce a computationally feasible solution paradigm based on recursive best responses. II-MAIDs achieve both interpretability and compact representation, providing a principled foundation for strategic analysis in multi-agent systems and evaluation of AI agents under uncertainty.

Technology Category

• Multiagent Systems: Mechanism Design
• Knowledge Representation and Reasoning: Reasoning with Beliefs
• Reasoning under Uncertainty: Sequential Decision Making

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

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.

Problem

• Extend MAIDs to model incomplete information scenarios.
• Establish equivalence between II-MAIDs and EFGs without common prior.
• Propose realistic solution concepts for II-MAIDs using recursive best-response.

Innovation

• Introduces incomplete information MAIDs (II-MAIDs)
• Defines infinite and finite-depth II-MAIDs
• Proposes recursive best-response solution concept