A stochastic and time-delay evolutionary game of food safety regulation under central government punishment mechanism.

Food safety is a pressing issue affecting public health, and strengthening food safety regulation has become a widespread consensus. This study addresses the three-party game involving food production enterprises, third-party testing agencies, and government regulatory authorities. Considering the influence of random disturbances and time delays on the strategy-choosing and behavioral evolution of game players, a three-party stochastic evolutionary game model for food safety regulation with time delays is established. The stability of the model is analyzed by using Lyapunov's method, and the strategy evolution of the game players is investigated while combining numerical simulations. The study shows that the net benefit of the players' expected strategies is key in determining whether the overall game system can reach the optimal equilibrium. The level of penalties imposed by the central government on local government regulators is key to food safety. The main factors influencing the strategy-choosing of game players are the level of penalties imposed by the local government regulators on third-party testing agencies, together with the supervision costs of the local government regulators. Random disturbances have a certain impact on strategy-choosing of the game players, with a greater impact on testing agencies, followed by food production enterprises, and a weaker impact on government regulatory authorities. The time delay factors exhibit a certain delay effect on the evolutionary path of strategy-choosing among the game players, which aligns with the actual situation. The findings of the study have implications for food safety regulation.