Strategic Use of Common Knowledge in Multi-Agent LLM Interactions

Successful coordination depends on what agents know and what they know about each other's knowledge. Human coordination often depends on creating common knowledge, knowledge that everyone knows and everyone knows that everyone knows it. Yet how LLM agents use such higher-order knowledge in strategic multi-agent interaction remains poorly understood. We introduce CK-Games, a controlled framework that gives each agent the same payoff-relevant information while varying its epistemic status from private knowledge, higher order levels of mutual knowledge, and ultimately common knowledge. Across multiple games, we evaluate eight model configurations across different knowledge levels, group sizes, communication networks, and a shared message board. We find agent coordination is sensitive to nuances in the level of knowledge each agent receives or can create. Agents starting from private knowledge can build shared knowledge through communication or a shared message board, but coordination degrades when the channel is unreliable or when a single agent is sparsely connected to others. We also find instances of misalignment. Communication does not always produce reliable shared knowledge: agents sometimes break their commitments, send messages that intend to deceive. Together, our results show that coordination among LLM agents depends less on what each agent knows than on what it knows about who knows what.