Abstract: With the increasingly fierce market competition and changing consumer demands, product innovation has become one of the key factors for enterprises to maintain their competitive advantage. By continuously launching new products or improving existing ones, enterprises can attract more customers, increase market share and sales revenue. Product innovation can also increase brand value, and enhance a company's image and position in the minds of consumers, thereby strengthening consumer loyalty and laying the foundation for the long-term development of the enterprise.
By conducting in-depth research on product innovation, we can reveal the important influencing factors of product innovation on the long-term development of enterprises, explore innovation management models and methods, and provide theoretical guidance for enterprise innovation management. Systematic research on product innovation can help enterprises better understand market demand and consumer preferences, guide them in formulating innovation strategies and product development strategies, and improve their innovation capabilities and competitiveness. Product innovation research can also provide policy recommendations for government departments, and promote the development of an innovative economy, industrial upgrading and economic transformation.
This article is based on a supply chain consisting of a manufacturer and a retailer. The manufacturer is responsible for researching and developing products to improve their innovation level, while the retailer is responsible for marketing innovative products to increase their visibility. We use dynamic differential game theory to conduct research. Firstly, the product innovation of the manufacturer and the product marketing strategies of the retailer in the supply chain are studied in the absence of cost sharing and government subsidy. Then, two incentive measures, cost sharing and government subsidy, are introduced into product innovation and product marketing in the supply chain. The impact of cost sharing and government subsidy on manufacturer product innovation and retailer product marketing is explored, and the conditions for the existence of cost sharing and government subsidy are further analyzed. Finally, the best product innovation and product marketing scenarios through comparative analysis are explored.
The research results indicate that cost sharing can improve the product marketing efforts of the retailer, but it does not change the manufacturer's innovation efforts. Government subsidy can increase the manufacturer's product innovation efforts but cannot change the retailer's product marketing efforts. Both the cost sharing and the government subsidy can increase product market demand and consumer utility, thereby improving the profits of various entities in the supply chain. Cost sharing mainly increases the profits of the retailer, while the government subsidy increases the profits of the manufacturer. Through comparison with the research results under four different scenarios, it can be found that in the absence of the cost sharing and the government subsidy, the innovation and marketing efforts of products are low, which leads to lower market demand and consumer utility, ultimately resulting in lower profits for supply chain members. When there is the cost sharing or the government subsidy, it will improve product innovation or marketing efforts, which will lead to an improvement in market demand and consumer utility, ultimately resulting in an improvement in the profits of supply chain members. However, we cannot determine which scenario is more beneficial for product innovation and marketing. When the cost sharing and government subsidy coexist, both the manufacturer's product innovation efforts and the retailer's product marketing efforts reach their maximum, which maximizes the market demand and consumer utility of the product, ultimately maximizing the total profits of supply chain members.
Through this study, we have some suggestions. Firstly, in the process of product innovation, supply chain members should cooperate with each other and actively promote the formation of cost sharing models to promote product innovation and marketing. Secondly, government management departments should actively subsidize enterprises engaged in product innovation, stimulate their enthusiasm for innovative research and development, and promote technological progress and economic development.

Key words: product innovation, product marketing, differential game, cost sharing, government subsidy

摘要： 研究供应链中产品创新的最优决策对于增强供应链韧性和破解技术难题具有重要意义。本文基于一个制造商和一个零售商组成的供应链,运用动态微分博弈方法,研究供应链中的产品创新和产品营销,探索成本分担机制和政府补贴机制对产品创新和产品营销的影响,并分析出各种机制存在的条件。研究结果表明:成本分担机制和政府补贴机制分别能够提升产品的营销力度和创新水平,且两者都能够带来市场需求和消费者效用的提高,进而改善供应链中各主体的收益,其中成本分担机制主要增加了零售商的收益,政府补贴机制主要增加了制造商的收益。当成本分担机制和政府补贴机制单独存在时,不能确定那种机制对供应链收益的改善效果较好,但当成本分担机制和政府补贴机制同时存在时,其对供应链收益的改善效果最佳。

关键词: 产品创新, 产品营销, 微分博弈, 成本分担, 政府补贴