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

Abstract

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

Yu Hui, Zhang Haonan, Chen Dongyan, Wu Zhihui. Differential Game Model of Online Advertising in the Supply Chain System under the CPA Mode[J]. Management Review, 2025, 37(3): 238-249.

References

[1] 陈宏军,江若尘. 现代广告学[M]. 北京: 科学出版社, 2006 Chen H. J., Jiang R. C. Modern Advertisement[M]. Beijing: Science Press, 2006
[2] Manchanda P., Dube J. P., Goh K. Y., et al. The Effect of Banner Advertising on Internet Purchasing[J]. Journal of Marketing Research, 2006,43(1):98-108
[3] Hoffman D. L., Novak T. P. Advertising and Pricing Models for the Web[M] //Internet Publishing and Beyond: The Economics of Digital Information and Intellectual Property. MA: MIT Press, 2000
[4] Novak T. P., Hoffman D. L. New Metrics for New Media: Toward the Development of Web Measurement Standards[J]. World Wide Web, 1997,2(1):213-246
[5] 金雪涛. 网络广告定价标准的改进研究[J]. 江西财经大学学报, 2004,(2):119-120 Jin X. T. Research on Improvement of Pricing Standards for Online Advertising[J]. Journal of Jiangxi University of Science and Economics, 2004,(2):119-120
[6] 林宏伟,邵培基,余步雷. 基于风险规避的网络广告两阶段收益定价模型[J]. 系统工程学报, 2013,28(3):327-337 Lin H. W., Shao P. J., Yu B. L. Two-stage Revenue Pricing Model for Internet Advertising with the Risk-aversion[J]. Journal of Systems Engineering, 2013,28(3):327-337
[7] Hu Y. J., Shin J., Tang Z. Incentive Problems in Performance-based Online Advertising: Cost Per Click versus Cost Per Action[J]. Management Science, 2015,62(7):2022-2038
[8] 李莉,胡娇. 基于效果定价模式的网络直播广告定价决策研究[J]. 管理工程学报, 2024,38(1):193-204 Li L., Hu J. Pricing Strategies of Live Streaming Ads Based on Effect Pricing Model[J]. Journal of Industrial Engineering/Engineering Management, 2024,38(1):193-204
[9] Wang R. B., Gou Q. L., Choi T. M., et al. Advertising Strategies for Mobile Platforms with “Apps”[J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2018,48(5):767-778
[10] Li X., Li Y., Cao W. Cooperative Advertising Models in O2O Supply Chains[J]. International Journal of Production Economics, 2019,215:144-152
[11] 欧海鹰. 在线广告投放选择及商品网络定价的演化博弈[J]. 管理评论, 2015,27(6):179-185 Ou H. Y. Online Advertising and Pricing Strategy Based on Evolutionary Game[J]. Management Review, 2015,27(6):179-185
[12] 欧海鹰. 在线广告发布商与广告主的竞合策略研究[J]. 管理评论, 2015,27(10):108-117 Ou H. Y. Research on the Optimal Strategy of Online Publisher and the Advertiser within a Game Framework[J]. Management Review, 2015,27(10):108-117
[13] 周慧妮,吴鹏,王筱纶. 溢出效应和网络贴合度扰动下的二级供应链网络广告投放策略分析[J]. 计算机集成制造系统, 2020,26(1):223-239 Zhou H. N., Wu P., Wang X. L.Analysis of Online Advertising Strategy of Two-stage Supply Chain Disturbed by Spillover Effect and Product Web-fit[J]. Computer Integrated Manufacturing Systems, 2020,26(1):223-239
[14] 赖红珍,周艳菊,陈晓红,等. 考虑供应链上游社会责任履行的供应链协调机制研究[J]. 系统工程理论与实践, 2023,43(9):2502-2519 Lai H. Z., Zhou Y. J., Chen X. H., et al. Research on Supply Chain Coordination Mechanism Considering the Social Responsibility Practices of the Upstream Supply Chain[J]. System Engineering-Theory & Practice, 2023,43(9):2502-2519
[15] 侯艳辉,管敏,王家坤,等. 全媒体时代基于微分博弈的网络舆情引导激励机制研究[J]. 中国管理科学, 2023,31(8):239-252 Hou Y. H., Guan M., Wang J. K., et al. Research on the Incentive Mechanism of Network Public Opinion Guidance Based on Differential Game in the Omnimedia Era[J]. Chinese Journal of Management Science, 2023,31(8):239-252
[16] 贾晓霞,智路平,李巧艳. 基于滞后主成分回归的电商平台广告效果评价研究[J]. 技术与创新管理, 2020,41(3):308-318 Jia X. X., Zhi L. P., Li Q. Y. Research on the Advertising Effectiveness Evaluation of E-commerce Platform Based on the NBD-PCR[J]. Technology and Innovation Management, 2020,41(3):308-318
[17] 陈东彦,于浍,侯玲. 考虑延时效应的供应链动态合作广告策略研究[J]. 管理科学学报, 2017,20(9):25-35 Chen D. Y., Yu H., Hou L. Dynamic Cooperative Advertising Strategies in a Supply Chain with Lagged Effect[J]. Journal of Management Sciences in China, 2017,20(9):25-35
[18] Yu H., Yang W., Xu N., et al. Advertising Strategy and Contract Coordination for a Supply Chain System: Immediate and Delayed Effects[J]. Kybernetes, 2023,5(21):235-261
[19] Yu H., Chen D. Y. New Optimal Control Decisions for Channel System with Lagged Effect: Dynamic Advertising and Pricing Cases[J]. IEEE Access, 2019,7:75350-75359
[20] 郭大伟,戴更新,马德青,等. 考虑双延迟效应的供应链动态营销合作策略[J]. 系统工程, 2019,37(6):46-57 Guo D. W., Dai G. X., Ma D. Q., et al. Supply Chain Dynamic Marketing Cooperation Strategy Considering Double Delay Effect[J]. Systems Engineering, 2019,37(6):46-57
[21] 刘浪,陈思仪,陈烁. 制造商价格竞争的纵向延时合作广告与定价策略[J]. 中国管理科学, 2024,32(9):182-192 Liu L., Chen S. Y., Chen S. Vertical Delayed Cooperative Advertising and Pricing Strategy for Manufacturer Price Competition[J]. Chinese Journal of Management Science, 2024,32(9):182-192
[22] 卓四清,韩雪. 碳补贴和时滞效应下低碳供应链微分博弈研究[J]. 运筹与管理, 2022,31(8):7-14 Zhuo S. Q., Han X. Research on Differential Game of Low Carbon Supply Chain Considering Government Subsidy and Lag Effect[J]. Operations Research and Management Science, 2022,31(8):7-14
[23] 曹霞,李玮佳. 考虑延迟效应的标准联盟技术标准化[J]. 系统管理学报, 2024,33(4):1008-1024 Cao X., Li W. J. Technical Standardization of Standards Alliance Considering Delay Effect[J]. Journal of Systems & Management, 2024,33(4):1008-1024
[24] Nerlove M., Arrow K. J. Optimal Advertising Policy under Dynamic Conditions[J]. Economica, 1962,29(114):129-142
[25] Machowska D. Delayed Effects of Cooperative Advertising in Goodwill Dynamics[J]. Operations Research Letters, 2019,47(3):178-184
[26] 王玉燕,申亮. 基于第三方电商平台销售的E-供应链广告策略研究[J]. 管理评论, 2019,31(10):124-132 Wang Y. Y., Shen L. A Study of E-supply Chain Advertisement Strategy Based on the Third Party E-commerce Platform for Sales[J]. Management Review, 2019,31(10):124-132
[27] 兰建义,时启超,冯中伟,等. 生鲜电商供应链企业社会责任分担策略选择研究[J]. 中国管理科学, 2024,32(9):201-213 Lan J. Y., Shi Q. C., Feng Z. W., et al. Research on Corporate Social Responsibility Sharing Strategy Selection in Fresh E-commerce Supply Chain[J]. Chinese Journal of Management Science, 2024,32(9):201-213