In the Internet era, consumers prefer products with the attributes of social responsibility. Supply chain enterprises strengthen corporate social responsibility management for their own development. To improve CSR throughout the supply chain, it requires coordination and cooperation among the members of the supply chain. In this paper, we consider a three-tier supply chain system consisting of a supplier, a manufacturer, and a retailer and use stochastic differential game to study the CSR coordination of the supply chain. The following indicators are (...) investigated under four decision situations, such as the optimal level of CSR effort for the supply chain members, the optimal value of profit for the supply chain members and the supply chain system, and the expectation and variance of CSR goodwill. Some important results are obtained. Compared with decentralized decision-making, the optimal level of CSR effort increases for the supplier and the manufacturer under local alliance decision-making without cost sharing, whereas the optimal level of CSR effort remains unchanged for the retailer. Compared with local alliance decision-making without cost sharing, the optimal level of CSR effort remains unchanged for the supplier and the manufacturer under local alliance decision-making with cost sharing. When the sum of the marginal profit for the supplier and the manufacturer is greater than half of the marginal profit for the retailer, the optimal level of CSR effort increases for the retailer. Compared with local alliance decision-making with cost sharing, the optimal level of CSR effort increases for the supply chain members under overall alliance decision-making. From decentralized decision-making to local alliance decision-making without cost sharing, to local alliance decision-making with cost sharing, and then to overall alliance decision-making, the optimal value of profit increases for the supply chain members and the supply chain system. Also, the expectation and variance of CSR goodwill increase. (shrink)