The Impact of Neutral Subpopulations on Cooperation in Two-Layer Coupled Networks

Abstract

Sustaining cooperation under severe social dilemmas is a fundamental challenge in complex systems. This paper proposes a two-layer coupled network model integrating three neutral subpopulations, combining an upper human layer (Fermi rule) and a lower agent layer (Bush–Mosteller reinforcement learning). The core scientific contribution is revealing that the three-subpopulation structure induces closed invasion cycles. This cross-subpopulation reciprocal suppression effectively halts the global expansion of defectors. Monte Carlo simulations demonstrate that under a severe dilemma (b=1.8), optimizing the coupling strength boosts the cooperation persistence probability (PCC) by 91% and reduces defection persistence (PDD) by 55%, stabilizing the global cooperation rate at approximately 50%. Furthermore, for b>1.26, this model consistently outperforms the canonical BM model. Practically, these findings provide a theoretical foundation and a quantitative reference for designing cooperative mechanisms in human–machine collaboration and public governance.