How can MAIDs handle incomplete info in multi-agent LLMs?
Higher-Order Belief in Incomplete Information MAIDs
This paper introduces Incomplete Information Multi-Agent Influence Diagrams (II-MAIDs), a new way to model multi-agent interactions where agents have different, potentially inaccurate, beliefs about the game and each other's beliefs. It shows that II-MAIDs are equivalent to a type of Extensive Form Game (EFG). While traditional game theory solutions like Nash Equilibria exist in II-MAIDs, they don't always reflect realistic agent behavior because they can violate common knowledge of rationality. To address this, the paper introduces a simplified finite-depth II-MAID with a recursive best-response solution that produces more realistic outcomes.
For LLM-based multi-agent systems, II-MAIDs provide a framework to:
- Model agents with differing or incorrect beliefs about the nature of their interaction.
- Analyze scenarios where LLMs might have mismatched or evolving understandings of a shared task.
- Develop more realistic behavior models for LLM agents by incorporating higher-order beliefs and reasoning about those beliefs.
- Explore solution concepts beyond traditional game theory by considering the depth of LLM reasoning and recursive best response dynamics.