Four-party evolutionary game analysis of third-party recycling treatment of livestock and poultry breeding waste

In response to the problem of governmental failure to control livestock and poultry breeding pollution (LPBP) in countries or regions with a large number of small and medium-scale livestock and poultry farmers (SM-LPF), this paper proposes the theory of recycling treatment through the third-party companies (TPC). Firstly, based on the evolutionary game theory, this paper constructs an evolutionary game model with four parties, including SM-LPF, TPC, the consuming party (TCP) and the local government (TLG) into the same analysis framework. And then systematically derives the stability of strategies and possible different combinations of strategies of four parties based on expected utility theory and Lyapunov's first law. Finally, the theoretical derivation results are verified and sensitivity analysis of key parameters is carried out by combining the system dynamics method. The results show that: (1) There is a significant correlation between the four-party game players, and the strategy choice of each game player is influenced by other game players. TLG can promote the benign interaction of the four game players to achieve the desired evolutionary results of Scenario 3 (cooperation, investment, purchase, promotion) through the formulation of reasonable subsidy and reward and punishment mechanisms. (2) The main factors affecting the third-party recycling treatment include government regulation, internal factors, market demand for environmental protection services, and market demand for organic fertilizers. (3) TLG subsidies to SM-LPF have the greatest impact on the evolution of the system, and subsidies to other game players have less impact on the evolutionary results of the system, while it is found that there is an optimal interval for the proportion of local government subsidies to farmers, beyond which the system will be unstable. This study provides practical guidance and policy reference for promoting the participation of TPC in LPBP management and has theoretical and practical value for establishing mechanism of livestock and poultry breeding waste recycling. It also enriches and develops the theory of third-party governance.