Emergence of Hierarchies in Multi-Agent Self-Organizing Systems Pursuing a Joint Objective

Multi-agent self-organizing systems (MASOS) exhibit key characteristics including scalability, adaptability, flexibility, and robustness, which have contributed to their extensive application across various fields. However, the self-organizing nature of MASOS also introduces elements of unpredictability in their emergent behaviors. This paper focuses on the emergence of dependency hierarchies during task execution, aiming to understand how such hierarchies arise from agents' collective pursuit of the joint objective, how they evolve dynamically, and what factors govern their development. To investigate this phenomenon, multi-agent reinforcement learning (MARL) is employed to train MASOS for a collaborative box-pushing task. By calculating the gradients of each agent's actions in relation to the states of other agents, the inter-agent dependencies are quantified, and the emergence of hierarchies is analyzed through the aggregation of these dependencies. Our results demonstrate that hierarchies emerge dynamically as agents work towards a joint objective, with these hierarchies evolving in response to changing task requirements. Notably, these dependency hierarchies emerge organically in response to the shared objective, rather than being a consequence of pre-configured rules or parameters that can be fine-tuned to achieve specific results. Furthermore, the emergence of hierarchies is influenced by the task environment and network initialization conditions. Additionally, hierarchies in MASOS emerge from the dynamic interplay between agents' "Talent" and "Effort" within the "Environment." "Talent" determines an agent's initial influence on collective decision-making, while continuous "Effort" within the "Environment" enables agents to shift their roles and positions within the system.