Bayes-Sufficient Compression Is Not Enough: How Communication Helps in Multi-Agent Systems?

Multi-agent LLM systems often split work between a main agent with broad context and an executor subagent with limited local context. Communication can help recover missing information, but it can also add parsing burden, distract from the local decision, or induce protocol failures. We ask when the main agent should send a short message rather than raw context or no message, and when upgrading the main agent pays off. We formalize this as receiver-relative bounded coordination, where a message's value is the executor's next-step gain minus its protocol tax. This view yields four findings. First, compressed messages can outperform raw context when tax savings exceed losses from omitted information or decoder mismatch. Second, Bayes-sufficient compression, which preserves all information needed for the optimal decision, can still be worse than raw context when a bounded executor cannot decode or operationalize its surface form. Third, post-message failures can be localized into externalization, absorption, and action closure, with residual error concentrating in closure even after the right content reaches the executor. Fourth, a stronger upstream agent helps only when the executor's local view is weak enough for the added gain to exceed the added tax. Across six benchmarks, these regimes recur: the same multi-agent protocol raises ContextBench joint accuracy from 0.633 to 0.775 but lowers ToolSandbox from 0.889 to 0.653, helping in context-heavy regimes and hurting in locally sufficient ones. The same quantities drive an inference-time selector over communication actions, improving the accuracy-cost frontier on the two benchmarks where the full action set is evaluated. Code and results at https://anonymous.4open.science/r/Communication/