The impact of environment on individuals is particularly critical. In evolutionary games, adopting the strategy of the neighbor who performs better is nontrivial for the survival and maintenance of cooperation, in that such an action may help the agents to obtain higher benefit and more obvious evolutionary advantages. Inspired by this idea, we investigate the effect of the environment-based preference selection on the evolution of cooperation in spatial prisoner’s dilemma. A simple rule, incorporating individual preference selection via an adjustable parameter α to explore how the selection of the potential strategy sources influences individual behavior traits, is considered. Because social interaction may not be the only way of generating payoffs, we assume that the individual’s income is also affected by the environment. Besides, taking into account individual differences, we introduce the heterogeneity of the environment. Through numerous computing simulations, we find that environment-based preference selection, which accelerates the microscopic organization of cooperator clusters to resist the aggression of defectors, can truly promote cooperation within a large range of parameters. Our study indicates that the combination of heterogeneity and preference selection may be key for the sustainability of cooperation in structured populations.

Establishing a green reputation reduces environmental impacts, gains recognition, and increases production efficiency. We develop a stochastic optimal control model for monopolies and stochastic differential game models for duopoly and two-tier supply chains. These models involve the sales of green products, the green reputation of products, and comprehensive capital stock. The model is transformed into the Hamilton–Jacobi–Bellman (HJB) equation (system). By solving the HJB equation (system), we obtain the analytical results and draw the following meaningful management conclusions: 1) Under a green reputation, the advertising and production investments of green products mutually promote each other when the firm’s emissions decrease and the sales margin increases. 2) Improving the green supply chain structure will increase the capital stock, green reputation, and sales of firms. However, as we modify our assumptions, the model becomes more complex, and analytical results cannot be obtained. We hence develop a machine learning algorithm based on the deep Galerkin method to help solve it. We find that high sales profit margins can offset the investment constraints imposed by competitors’ market presence and emission levels, thereby stimulating advertising investment. Finally, we use data from two electric vehicle firms to estimate our model and compare it with two econometric models. We show that our model performs better or equivalently in fitting. Our research aims to help engineering managers and firm executives use the green reputation to guide production planning and investment management.

Our study examines a supply chain system involving a manufacturer, a third-party logistics (3PL), and a retailer. In this system, the capital-constrained retailer could obtain a loan from the bank under the guarantee of the capital-abundant upstream company (i.e., manufacturer or 3PL). Previous research has focused on the manufacturer or the 3PL acting as the guarantor and the manufacturer acting as the after-sales service provider. However, there is no research on the 3PL acting as the after-sales service provider. In the real world, in order to create a one-stop solution, 3PLs also carry out after-sales service business. We conduct an in-depth study of the influence of the two game modes (i.e., Nash game and manufacturer leadership Stackelberg game) between the manufacturer and the 3PL on the optimal scheme choice of guarantee finance and after-sales service. Our findings show that: (1) Only if the conditions of flourishing market are satisfied, Nash equilibrium is consistent with the profit maximization goal of all members of the supply chain. (2) Manufacturer leadership Stackelberg game could enable all members of the supply chain to achieve the consistent goal of maximizing profit. (3) The manufacturer leader Stackelberg game will have an inhibitory effect on quality, after-sales service, and supply chain performance; the Nash game will have a promoting effect on quality, after-sales service, and supply chain performance. Our study provides valuable insights for engineering managers in industrial production to select the combined roles of guarantor and servicer in supply chain systems.