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

The phenomenon of cooperative advertising 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 decentralised and centralised control, and the trajectories of goodwill and reference prices over time are presented. The conclusions derived provide implications for managers to design optimal advertising strategies.