Emergence of Secondary Norm from Distributed Interaction of Autonomous Agents

Abstract # ↰

Secondary (contrary-to-duty) norms specify what should happen when a primary norm is violated; their design and collective acceptance remain challenging in decentralized multi-agent systems. In this work, we present a minimal yet expressive simulation framework to study the bottom-up emergence of secondary norms from distributed interaction. We consider a toroidal multi-agent system where a primary norm prescribes collision avoidance, violations occur with non-zero probability, and a secondary norm specifies a fine whose magnitude is collectively determined through voting driven by agents’ frustration. Our results show that the system achieves the intended safety–efficiency trade-off and that a non-trivial secondary norm emerges as a stable and meaningful equilibrium without central coordination. We further show that the secondary norm must influence agents’ violation probability in order to be effective, as punishment alone is insufficient. Finally, we show that the emergence phenomenon is robust across different voting mechanisms and design choices. These results operationalize contrary-to-duty reasoning as an emergent coordination process and provide a foundation for richer logic-grounded normative mechanisms in responsible AI systems.