The Shape of Cooperation Across Tasks

When should a team of agents communicate through a hub, through groups or directly? We characterize these choices by two fitted summaries of evidence demand, the traffic outside the best hub and the smallest modular detour. Under a faithful transport model that preserves evidence delivery, this signature and the ratio of channel overhead to traffic cost determine the cheapest pattern within the declared family. Identical hub concentration can require different patterns, so concentration alone is insufficient. We derive exact decision boundaries and a confidence bound that charges for learning before authorizing a change. Controlled transport experiments show that matching connectivity to persistent demand can lower total modeled cost after paying to learn it. A direct ablation shows that access to modular patterns improves future cost for concentrated demand but adds no benefit for diffuse demand. More observations improve prediction but can reduce net savings, while replacing future demand reverses the benefit. The resulting characterization explains when fitting a richer communication pattern is useful and when its learning expense or changing demand defeats the gain.