Differential game model of cooperative advertising in a supply chain with deteriorating items, competing retailers and reference price effects

The phenomenon of cooperative advertising between manufacturers and retailers in the market has always been widespread. Considering a supply chain consisting of one manufacturer and multiple retailers with competitive relationships, we explore advertising strategies for deteriorating items when market demand is affected by reference price. By establishing a differential game model, the equilibrium advertising strategies and supply chain profits under different situations are analysed from a long-term and dynamic perspective under decentralized and centralized control, and trajectories of goodwill and reference prices over time are presented. The results show that: (1) The manufacturer can guide the retailers’ advertising efforts by adjusting its own marginal profit under certain conditions. (2) In the decentralized situation, the manufacturer does not always share advertising costs for the retailers. (3) The manufacturer is willing to invest more advertising efforts in centralized situation, but the retailers do not always invest more in centralized situation. (4) The total profits of the supply chain in the centralized situation are better than in the decentralized situation. These conclusions provide the theoretical basis for managers to design optimal strategies after considering profits and brand image comprehensively.