Abstract
Grounding is the collaborative process of establishing mutual belief sufficient for the current communicative purpose. While static grounding maps language to a shared, externally observable context, dynamic grounding is a joint activity where meaning is negotiated through interaction. Current multi-agent Large Language Model (LLM) benchmarks focus on static, one-shot tasks, overlooking the ability to repair grounding breakdowns across turns. We introduce an iterated, multi-turn negotiation game in which two agents allocate shared resources toward private projects with verifiable jointly optimal outcomes. While individual agents can identify Pareto-optimal allocations in isolation, agent dyads consistently fail to reach them across open- and closed-source models. Our investigation reveals four failure modes: (1) coordination degrades when shared interaction history is absent; (2) yet accumulated context can itself become a liability thro