Research on the optimization of cooperative advertising strategy in the promotion of water-saving products based on differential game

The promotion of water-saving products is one of the vital ways to implement water conservation action, and advertising is a significant way to promote water-saving products. Taking the two-level Supply Chain consisting of a leading manufacturer and a retailer as an example and considering the advertising cost-sharing ratio of the two, as well as the government's R&D subsidies to manufacturers and product subsidies to consumers, this study establishes differential game models in three cases, that is, non-cooperative contract without cost sharing, cooperative contract with cost sharing, and collaborative cooperation contract. Also, numerical simulation is adopted to analyze the sensitivity of important parameters. The results show that the product goodwill and market demand for water-saving products can achieve Pareto optimality under the collaborative cooperation contract. In addition, the cooperative contract with cost sharing can realize Pareto improvement of the optimal benefit of the Supply Chain under certain conditions. Moreover, in the absence of the government's R&D subsidies, the overall benefits can achieve Pareto optimality under the collaborative cooperation contract. This study provides theoretical guidance and reference for the advertising cooperation strategy for the main bodies in the Supply Chain.