Do Agents Develop Tacit Understanding? From Repeated Collaboration to Partner-Specific Coordination

In long-term agent collaboration, fixed partners gradually accumulate relational knowledge about each other's response patterns and coordination habits. Human long-term partners transform such knowledge into tacit understanding, thereby reducing repeated negotiation in similar situations. Prior work shows that LLM agents can coordinate implicitly, form conventions, and adapt to partner history, yet it remains unclear what behavioral evidence distinguishes genuine dyadic tacit understanding from coordination explained by current task structure, generic experience, partner predictability, or memorization. To address this gap, we formalize Dyadic Tacit Understanding (DTU) as a directional, history-induced shift from a history-neutral coordination-response law, and define Genuine Dyadic Tacit Understanding (GTU) by the joint requirements of Formation, Interaction Specificity, and Cross-Instance Generalization. We further propose a decentralized online relational learning framework that enables each agent to independently learn its partner's coordination-response patterns and transform them into private distributional guidance for its own decisions under limited explicit communication. We validate the proposed theory and framework on multiple collaborative benchmarks, showing that agents can develop reusable partner-specific coordination knowledge from shared experience while maintaining collaboration quality with reduced explicit communication. Code is available at https://anonymous.4open.science/r/tact-agents-F45C.