考虑企业社会责任(corporate social responsibility, CSR)商誉对市场需求的影响, 在Nash非合作博弈、以制造商为主导的Stackelberg博弈、以零售商为主导的Stackelberg博弈和合作博弈4种情形下, 分别构建微分博弈模型, 研究制造商和零售商的最优CSR努力水平、CSR商誉的最优轨迹和利润最优值, 并结合数值模拟, 验证理论推导的正确性. 研究结果表明: 最优CSR成本补贴率仅与边际利润有关, 与其他因素无关; 与Nash非合作博弈相比, 在Stackelberg博弈情形下, 当主导者的边际利润大于跟随者边际利润的一半时, 主导者对跟随者进行CSR成本补贴, 且主导者的最优CSR努力水平保持不变, 跟随者的最优CSR努力水平提高, 制造商和零售商的利润均提高; 与Stackelberg博弈相比, 在合作博弈情形下, 制造商和零售商的最优CSR努力水平均提高, 供应链系统的利润也随之提高.

In this paper, the impact of corporate social responsibility (CSR) goodwill on market demand was considered. For the cases of Nash non-cooperative game, manufacturer-led Stackelberg game, retailer-led Stackelberg game, and cooperative game, differential game models were constructed and the optimal level of CSR effort for the manufacturer and the retailer, the optimal trajectory of CSR goodwill, and the optimal value of profit was studied. Also, the correctness of the theoretical derivations was verified through numerical simulations, and some important results were obtained. First, the optimal subsidy rate of CSR cost is related to marginal profit and is unaffected by other factors. Second, compared with the Nash non-cooperative game, in the case of Stackelberg game, the leader subsidizes the CSR cost of the follower when the marginal profit of the leader is greater than half the marginal profit of the follower. Moreover, the optimal level of CSR effort for the leader remains unchanged, while the optimal level of CSR effort for the follower increases, so the profits improve for both the manufacturer and the retailer. Third, compared to the Stackelberg game, in the case of cooperative games, the optimal level of CSR effort improves for both the manufacturer and the retailer, and the profit also increases for the supply chain system.