Observe, Share, or Predict? Disentangling Partner Information in Embodied Multi-Agent Collaboration

LLMs are used as high-level controllers for embodied agents, but it remains unclear whether they support collaborative reasoning, such as anticipating a collaborator's actions in real-time teamwork without dialogue. We ask if observing the partner's state, exchanging object knowledge, and predicting the partner's next action, shape task outcomes and coordination when agents can share percepts but never intentions, plans, or task-level messages, and whether the two agents occupy symmetric roles. Using the Habitat-based PARTNR benchmark, we introduce a Decoupled Partial Observability regime that enforces strictly individual perception, and we augment decentralized zero-shot ReAct planners with Other Agent's State (OAS) observation, object Knowledge Exchange (KE) between co-located agents, and Other Agent's Next Action (OANA) prediction, evaluated on the full 2 x 2 x 2 grid with four planners on 1,000 validation tasks. OAS observation improves task quality, reducing extraneous effort for every planner, whereas KE primarily improves execution efficiency, cutting simulation steps by up to 25% with little change in success. The two are largely redundant for strong planners but complementary for the weakest, for which KE without the OAS is the worst configuration. OANA prediction lowers the success rate in 15 of 16 model x context pairs while raising explicit partner mentions to 55-100%, and its accuracy gains lie mainly in the coarse action type, partly because agents recognize the action the partner is already performing. The robot retrieves objects sooner and completes its tasks earlier than the simulated human. Shared context reduces total task time by shortening the remaining duration that the human works alone. Also, coordination benefits arise from responding to shared context, especially the OAS, rather than explicit anticipation, yielding shallow, planner-dependent partner modeling.