Evolution of cooperation in spatial public goods games with migration and interactive diversity

Evolutionary games on networks often assume that individuals do not move and adopt a uniform strategy toward all neighbors. In reality, however, individuals can migrate to seek more favorable conditions and may act differently depending on whom they interact with. Here, we fill this gap by extending the spatial public goods game on a two-dimensional lattice to include both migration and node-dynamics-based interactive diversity. Through systematic Monte-Carlo simulations, we demonstrate a clear division of labor: at low to moderate densities, mobility carves “escape corridors” that protect cooperators, whereas at high densities, interactive diversity spawns “imperfect” cooperative clusters able to endure strong social dilemmas. Most importantly, the combination of these two mechanisms substantially lowers the threshold for cooperation, enabling the system to sustain cooperation even under low-density and strong-dilemma conditions where previous models predict the collapse of cooperation. This complementary effect shows that migration seeds clusters while partner-specific reciprocity stabilizes them, creating a robust path to cooperation that neither mechanism can achieve alone. The result suggests a practical design rule: encourage limited mobility in sparse populations and foster interactive diversity in crowded ones to maximize prosocial behavior in complex adaptive systems.