Interaction density drives cooperation in large evolutionary populations: Evidence from large-scale agent-based simulations

The emergence of cooperation among self-interested agents remains one of the central problems in economics, evolutionary biology, and complex systems science. This study investigates the structural conditions governing the emergence and stability of cooperative behavior in large evolutionary populations using large-scale agent-based simulations. We develop a high-performance computational framework in which populations of up to 100,000 agents repeatedly interact under Prisoner's Dilemma environments while behavioral tendencies evolve through stochastic mutation and evolutionary imitation dynamics. The model systematically explores a broad parameter space defined by mutation intensity and interaction density under multiple preference deformation (PD) regimes. The simulations reveal a highly structured and nonlinear cooperation landscape in which interaction density emerges as the dominant determinant of collective outcomes. The observed dynamics can be represented through an empirical relationship of the form: 𝐶 = 𝐹 ⁡ ( 𝐼 , 𝜇 ) where 𝐶 denotes equilibrium cooperation, 𝐼 represents interaction density, and 𝜇 captures mutation intensity. Cooperation remains relatively stable at low and intermediate interaction densities but progressively deteriorates once interaction density exceeds critical regions. In contrast, mutation intensity exerts comparatively weaker effects, functioning primarily as a mechanism of adaptive exploration and stochastic variability rather than as the principal driver of cooperation itself. Machine learning analysis using Random Forest models further confirms that interaction density overwhelmingly dominates all other explanatory variables in predicting equilibrium cooperation levels. The results additionally reveal differentiated behavioral regimes and metastable cooperation structures across the explored parameter space. Rather than increasing monotonically, cooperation exhibits saturation and eventual collapse under excessively dense interaction environments, suggesting that large populations may experience strategic overcrowding and systemic fragility effects that destabilize decentralized cooperative organization. These findings contribute to the literature on cooperation in complex adaptive systems by showing that cooperation can emerge endogenously from decentralized anonymous interactions without requiring reputation systems, repeated partner reciprocity, or centralized coordination mechanisms. More broadly, the study demonstrates how large-scale computational experiments combined with machine learning techniques can uncover empirical regularities governing collective behavior in evolutionary systems.