arXiv:2508.12683v1 Announce Type: cross Abstract: Hierarchical multi-agent systems (HMAS) organize collections of agents into layered structures that help manage complexity and scale. These hierarchies can simplify coordination, but they also can introduce trade-offs that are not always obvious. This paper proposes a multi-dimensional taxonomy for HMAS along five axes: control hierarchy, information flow, role and task delegation, temporal layering, and communication structure. The intent is not to prescribe a single "best" design but to provide a lens for comparing different approaches. Rather than treating these dimensions in isolation, the taxonomy is connected to concrete coordination mechanisms - from the long-standing contract-net protocol for task allocation to more recent work in hierarchical reinforcement learning. Industrial contexts illustrate the framework, including power grids and oilfield operations, where agents at production, maintenance, and supply levels coordinate to diagnose well issues or balance energy demand. These cases suggest that hierarchical structures may achieve global efficiency while preserving local autonomy, though the balance is delicate. The paper closes by identifying open challenges: making hierarchical decisions explainable to human operators, scaling to very large agent populations, and assessing whether learning-based agents such as large language models can be safely integrated into layered frameworks. This paper presents what appears to be the first taxonomy that unifies structural, temporal, and communication dimensions of hierarchical MAS into a single design framework, bridging classical coordination mechanisms with modern reinforcement learning and large language model agents.