Self-organized institutions in evolutionary dynamical-systems games.

Social institutions are systems of shared norms and rules that regulate people's behaviors, often emerging without external enforcement. They provide criteria to distinguish cooperation from defection and establish rules to sustain cooperation, shaped through long-term trial and error. While principles for successful institutions have been proposed, the mechanisms underlying their emergence remain poorly understood. To address this, we introduce the evolutionary dynamical-systems game theory that couples game actions with environmental dynamics and explores the evolution of cognitive frameworks for decision-making. We analyze a minimal model of common-pool resource management, where resources grow naturally and are harvested. Players use decision-making functions to determine whether to harvest at each step, based on environmental and peer monitoring. After evolution, decision-making functions enable players to detect selfish harvesting and punish it by overharvesting, which degrades the environment. This process leads to the self-organization of norms that classify harvesting actions as cooperative, defective, or punitive. The emergent norms for "cooperativeness" and rules of punishment serve as institutions. The environmental and players' states converge to distinct modes characterized by limit-cycle attractors, representing temporal regularities in socio-ecological systems. These modes remain stable despite slight variations in individual decision-making, illustrating the stability of institutions. We measure evolutionary robustness of decision-making functions, defined as the capacity to keep dominance against invasion. It is revealed that plasticity, the ability to adjust actions to cope with diverse opponents, allows for such robustness. This work introduces foundational concepts in evolutionary dynamical-systems games and elucidates the mechanisms underlying the self-organization of social institutions.