Differential game of product–service supply chain considering consumers’ reference effect and supply chain members’ reciprocity altruism in the online-to-offline mode

Supply chain members’ reciprocal altruism and consumers’ quality and service reference effects are important behavioral factors that affect the decision-making of supply chain members. This article incorporates these factors into a product–service supply chain consisting of a manufacturer and a retailer in the online-to-offline (O2O) environment. Based on the inherent dynamics of the model, we construct a differential game model between the manufacturer and the retailer. Based on the Bellman continuous dynamic programming theory, this study analyzes the quality strategy of the manufacturer, the service level strategy of the retailer, and the performance of the supply chain system under three decision-making patterns (decentralization, centralization, and reciprocal altruism) within the O2O framework. The results show that compared with the decentralized decision-making model, reciprocal altruism helps members develop higher quality and service levels, improve brand goodwill, and obtain greater utility. The results are verified by numerical examples, and sensitivity analysis of consumer quality and the service reference effect, channel preference, and members’ reciprocal altruism behavior on the supply chain performance is carried out. The results show: (1) Consumers’ reference effects cause an “anchoring mentality” among consumers, which leads the manufacturer to lower the quality level and the retailer to lower the service level. This hurts the performance of the product–service supply chain. Consumers’ channel preference has an important impact on supply chain members’ strategies and performance. (2) Retailers should encourage consumers to purchase products online and use offline channel services as sales assistance measures to satisfy consumers’ experience utility. (3) As a positive social preference, the supply chain performance under the members’ reciprocal altruism decision-making model is Pareto-improved and receives additional social benefits. (4) Only when the manufacturer and the retailer have pure altruistic preference, that is, minimum return and maximum altruism, the total profit of the supply chain can reach that of the centralized decision-making scenario.