管理评论

管理评论 ›› 2025, Vol. 37 ›› Issue (3): 238-249.

• 物流与供应链管理 • 上一篇    

CPA模式下供应链网络广告微分博弈模型

于浍1,2, 张浩男3, 陈东彦3,4, 武志辉1   

  1. 1. 哈尔滨理工大学自动化学院, 哈尔滨 150080;
    2. 哈尔滨理工大学黑龙江省复杂集成与控制实验室, 哈尔滨 150080;
    3. 哈尔滨理工大学经济与管理学院, 哈尔滨 150080;
    4. 哈尔滨理工大学理学院, 哈尔滨 150080
  • 收稿日期:2023-01-31 发布日期:2025-04-02
  • 作者简介:于浍（通讯作者），哈尔滨理工大学自动化学院副教授，博士生导师，博士；张浩男，哈尔滨理工大学经济与管理学院博士研究生；陈东彦，哈尔滨理工大学经济与管理学院、理学院教授，博士生导师，博士；武志辉，哈尔滨理工大学自动化学院副教授，硕士生导师，博士。
  • 基金资助:
    黑龙江省自然科学基金优秀青年项目(YQ2023G004)；国家自然科学基金项目(72001059)；黑龙江省复杂智能系统与集成重点实验室开放课题（HPKL-CISI-202203）。

Differential Game Model of Online Advertising in the Supply Chain System under the CPA Mode

Yu Hui1,2, Zhang Haonan3, Chen Dongyan3,4, Wu Zhihui1   

  1. 1. School of Automation, Harbin University of Science and Technology, Harbin 150080;
    2. Heilongjiang Province Key Laboratory of Complex Intelligent Systems and Integration, Harbin University of Science and Technology, Harbin 150080;
    3. College of Economics and Management, Harbin University of Science and Technology, Harbin 150080;
    4. School of Applied Science, Harbin University of Science and Technology, Harbin 150080
  • Received:2023-01-31 Published:2025-04-02

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摘要： 为了规避网络广告延时效应带来的不确定性风险，企业往往会采用效果付费（cost per action，CPA）方式进行网络推广。本文在CPA模式下研究考虑延时效应的供应链网络广告决策与协调问题。首先，建立含有时间延迟的品牌信誉动态模型和效果依赖的网络广告投入成本模型，并构建CPA模式下供应链网络广告微分博弈模型，再利用最优控制理论求解得到分散式决策与集中式决策下供应链系统的最优网络广告策略、定价策略、品牌信誉以及利润。其次，对决策结果进行综合比较分析，明确供应链系统的最佳决策机制，参照最佳决策供应链系统，设计一种动态批发价格契约，使供应链实现完美协调。最后，通过数值算例验证研究结果的有效性，对网络广告投入、品牌信誉、利润以及协调参数进行灵敏度分析。研究发现，与传统广告研究结论不同，CPA模式下制造商的最优网络广告投入高度依赖于时间，且遵循“逐降-早停”原则；CPA模式下短暂的网络广告延时效应和良好的销售效果可以增加双方合作的积极性，进而企业倾向于整体获利最大的集中式决策机制。本文研究成果为供应链企业网络推广实践提供了重要的理论指导。

关键词: 网络广告, 延时效应, CPA(cost per action)模式, 微分博弈

Abstract: To avoid the uncertainty risk brought by the delayed effect of online advertising, enterprises often adopt CPA (cost per action) advertising for network promotion. This paper explores the online advertising decision and coordination problem for a supply chain with the delayed effect under the CPA mode. By establishing goodwill as a delay differential equation and time-dependent online advertising cost function, the deferential game model is firstly constructed for online advertising in a supply chain under the CAP mode. Next, the optimal control theory is utilized to derive the optimal online advertising and pricing strategies, product goodwill, and supply chain profits under the decentralized and centralized decision scenarios. Then, the decision results are compared and analyzed, and the best decision-making mechanism of the supply chain system is proposed. A dynamic wholesale price contract is designed to coordinate the supply chain perfectly based on the best decision-making supply chain as a benchmark. Finally, numerical examples are given to show the effectiveness of the presented results and provide the sensitivity analysis of online advertising investment, goodwill, profit and coordination parameters. It is found that, unlike the traditional advertising situation, the optimal advertising investment of the manufacturer is time-dependent under the CPA mode and follows the principle of “gradual reduction-early termination.” Under the CPA mode, the shorter delayed effect of online advertising and the better sales results can enhance the cooperation enthusiasm of two sides. As a result, enterprises tend to adopt the centralized decision-making mechanism that can ensure the maximum profit of the whole supply chain. The research results provide some theoretical guidance for the marketing practice of supply chain enterprises.

Key words: online advertising, delayed effect, CPA(cost per action)mode, differential game