Evolutionary game analysis and stability control scenarios of food safety supervision based on system dynamics

Introduction Food safety supervision involves dynamic strategic interactions between enterprises and government regulators. Traditional static models fail to capture the co-evolution of behaviors under varying policy incentives. This study develops a coupled evolutionary game-system dynamics (EG-SD) model to investigate how cost-benefit configurations and policy parameters shape long-term strategic outcomes in food safety governance, with the goal of identifying conditions that balance enterprise-government relationships and promote sustainable food systems. Methods An integrated EG-SD framework was constructed to model the two-player (enterprise and government) evolutionary game. Equilibrium stability conditions were derived analytically under different cost-benefit scenarios. Stability analysis was performed to identify evolutionary stable strategies (ESS). A numerical simulation was conducted to replicate four distinct case configurations, tracking strategy evolution over time under varying parameter sets. Results The stability analysis revealed that equilibrium outcomes depend critically on the relative magnitudes of supervision costs, penalty levels, and compliance benefits. Numerical simulations demonstrated the absence of any stable pure or mixed strategy in Case 1. In all simulated scenarios, enterprises consistently converged to a “not pay attention” strategy regardless of government actions. Government strategy was scenario-dependent: it fully adopted a “supervise” stance in some cases, but switched to a “not supervise” stance in Cases 3 and 4. No parameter configuration induced enterprise proactive compliance as a stable outcome. Discussion The government's scenario-dependent behavior indicates that supervision is effective only under specific cost-benefit thresholds. These findings underscore the necessity of redesigning regulatory dynamics to align economic incentives with long-term environmental and social health goals. Effective supervision requires not only enforcement but also mechanisms that make proactive compliance economically attractive for enterprises. The model provides a tool for testing policy interventions before implementation.