关键词: 电商生态系统, 微分博弈, 商誉值, 均衡策略, HJB方程

Abstract: Under the backdrop of the digital economy, the rapid development of the e-commerce industry has played a significant driving role in societal progress. With the advancement of social intelligence, online shopping has become increasingly convenient, leading to a yearly increase in the volume of online transactions. Despite the COVID-19 pandemic, the overall transaction scale during “6.18” e-commerce festival in 2022 reached a new high, maintaining a positive growth trend. With the flourishing growth of the e-commerce sector, an increasing number of merchants actively seek opportunities to collaborate with e-commerce platforms. Therefore, how to appropriately manage the collaborative coordination between e-commerce platforms and the merchants joining these platforms to achieve the optimal allocation of social resources has become a focal point of concern for all stakeholders in society.
To study the optimal cooperation mode between e-commerce platforms and merchants while considering both of the commodity goodwill and the continuity of time, this article constructs a differential game model consisting of an e-commerce platform and n merchants selling similar goods. By employing the Hamilton-Jacobi-Bellman equation, we discuss the optimal decision-making regarding effort levels, reputation values, and optimal revenue values for both the e-commerce platform and merchants under the decentralized decision-making model, the Stackelberg leader-follower game model, and the centralized decision-making model. After conducting a theoretical analysis of the effort levels of participants, the commodity goodwill, and the overall system revenue under these three decision-making models, combining it with numerical experimental analysis by applying real data used by JD Open Platform, we have reached the following conclusions:
(1)Compared to the decentralized decision-making model, when the e-commerce platform adopts the Stackelberg leader-follower game decision-making model, the optimal effort level of the platform will remain unchanged. However, the platform can motivate merchants to invest more effort by sharing their costs. In the centralized decision-making model, both the e-commerce platform and merchants exert higher effort levels than those under the decentralized and Stackelberg leader-follower game models.
(2)In terms of commodity goodwill jointly established by e-commerce platform and merchants, the value of commodity goodwill is the highest under centralized decision model, followed by Stackelberg master-slave game model. In the centralized decision-making model, the e-commerce platform and merchants are aligned, leading to maximum effort exertion in selling commodities. This, in turn, results in the highest commodity goodwill. Enhanced goodwill increases consumer trust, which is a valuable asset for both the platform and merchants.
(3)In terms of the overall benefit to the e-commerce ecosystem, the centralized decision-making model generates the highest system-wide revenue. In the Stackelberg leader-follower game model, the e-commerce platform’s cost-sharing with merchants leads to increased overall revenue compared to the decentralized decision-making model.
Through the comparative analysis of theory and numerical experiments, it is evident that the Stackelberg leader-follower game model and the centralized decision-making model, compared to the decentralized model focused on individual gains, promote cooperation between e-commerce platforms and merchants, thus favoring the long-term development of the e-commerce ecosystem. Partial or deep cooperation between e-commerce platforms and merchants can yield higher returns for both parties and contribute to the sustainable development of the entire e-commerce ecosystem.

Key words: e-commerce ecosystem, differential game, reputation value, optimal decision-making, HJB equation