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Dynamic Game Analysis on Cooperative Advertising Strategy in a Manufacturer-Led Supply Chain with Risk Aversion

Author

Listed:
  • Jia Liu

    (College of Economics and Management, Northeast Agricultural University, Harbin 150030, China
    School of Management, Heilongjiang University of Science and Technology, Harbin 150020, China)

  • Cuixia Li

    (College of Economics and Management, Northeast Agricultural University, Harbin 150030, China)

Abstract

This paper considers a dynamic Stackelberg game model for a manufacturer-led supply chain with risk aversion. Cooperative advertising strategy is applied to the marketing decisions of supply chain participants. Based on Stackelberg game and system dynamic theory, the game and complex dynamical behaviors are studied through the use of several methods, such as the stability region of the system, bifurcation diagram, attractor diagram, and the largest Lyapunov exponent diagram. The expected utilities of participants are given and compared by numerical simulation. The results illustrate that a series of variations in adjustment speed of advertising expenditure, participation rate of local advertising expenditure by manufacturer, risk tolerance levels, and the effect coefficient of advertising expenditure may cause a loss of stability to the system and evolve into chaos. Meanwhile, the Nash equilibrium point and the expected utility of the manufacturer and retailer will change greatly. The parameter control method is further applied to control the chaos phenomenon of the system effectively. By means of analyzing the impact of relevant factors on the game model, the manufacturer and retailer can make optimal strategy decisions in the supply chain competition. The findings of this study mainly include the following three aspects. Firstly, for market stability and maximizing revenue, the manufacturer adjusts the participation rate appropriately, avoiding too high or too low values. Secondly, the manufacturer will try to reduce their own risk tolerance level for the economic revenue, and the retailer appropriately adjust the risk tolerance level to adapt to their own development according to their own enterprise strategy. Finally, both the manufacturer and retailer reduce their own effect coefficients of advertising expenditure. Meanwhile, they will attempt to increase their opponent’s effect coefficient to gain the most revenue. The research results of this study can provide important reference for the advertising expenditure decision and revenue maximization of participants in the context of risk aversion.

Suggested Citation

  • Jia Liu & Cuixia Li, 2023. "Dynamic Game Analysis on Cooperative Advertising Strategy in a Manufacturer-Led Supply Chain with Risk Aversion," Mathematics, MDPI, vol. 11(3), pages 1-24, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:3:p:512-:d:1039523
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    References listed on IDEAS

    as
    1. Zhang, Juan & Gou, Qinglong & Liang, Liang & Huang, Zhimin, 2013. "Supply chain coordination through cooperative advertising with reference price effect," Omega, Elsevier, vol. 41(2), pages 345-353.
    2. Tian, Yi & Ma, Junhai & Xie, Lei & Koivumäki, Timo & Seppänen, Veikko, 2020. "Coordination and control of multi-channel supply chain driven by consumers’ channel preference and sales effort," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    3. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    4. Karray, Salma, 2013. "Periodicity of pricing and marketing efforts in a distribution channel," European Journal of Operational Research, Elsevier, vol. 228(3), pages 635-647.
    5. Xi, Xuan & Zhang, Yulin, 2021. "Complexity analysis of production, fertilizer-saving level, and emission reduction efforts decisions in a two-parallel agricultural product supply chain," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    6. Zhang, Linghong & Wang, Jingguo, 2017. "Coordination of the traditional and the online channels for a short-life-cycle product," European Journal of Operational Research, Elsevier, vol. 258(2), pages 639-651.
    7. Ravi Anupindi & Yehuda Bassok, 1999. "Centralization of Stocks: Retailers vs. Manufacturer," Management Science, INFORMS, vol. 45(2), pages 178-191, February.
    8. Choi, Tsan-Ming & Ma, Cheng & Shen, Bin & Sun, Qi, 2019. "Optimal pricing in mass customization supply chains with risk-averse agents and retail competition," Omega, Elsevier, vol. 88(C), pages 150-161.
    9. Avinadav, Tal & Chernonog, Tatyana & Perlman, Yael, 2017. "Mergers and acquisitions between risk-averse parties," European Journal of Operational Research, Elsevier, vol. 259(3), pages 926-934.
    10. Taiguang Gao & Kui Wang & Yali Mei & Shan He & Yanfang Wang, 2022. "Supply Chain Pricing Models Considering Risk Attitudes under Free-Riding Behavior," Mathematics, MDPI, vol. 10(10), pages 1-22, May.
    11. Xie, Gang & Yue, Wuyi & Wang, Shouyang & Lai, Kin Keung, 2011. "Quality investment and price decision in a risk-averse supply chain," European Journal of Operational Research, Elsevier, vol. 214(2), pages 403-410, October.
    12. Marshall Fisher & Ananth Raman, 1996. "Reducing the Cost of Demand Uncertainty Through Accurate Response to Early Sales," Operations Research, INFORMS, vol. 44(1), pages 87-99, February.
    13. Sameh S Askar & Abdulrahman Al-Khedhairi, 2020. "Local and Global Dynamics of a Constraint Profit Maximization for Bischi–Naimzada Competition Duopoly Game," Mathematics, MDPI, vol. 8(9), pages 1-16, August.
    14. Giri, B.C. & Sharma, S., 2014. "Manufacturer's pricing strategy in a two-level supply chain with competing retailers and advertising cost dependent demand," Economic Modelling, Elsevier, vol. 38(C), pages 102-111.
    15. Xiao, Tiaojun & Yang, Danqin, 2008. "Price and service competition of supply chains with risk-averse retailers under demand uncertainty," International Journal of Production Economics, Elsevier, vol. 114(1), pages 187-200, July.
    16. Han Zhao & Hui Wang & Wei Liu & Shiji Song & Yu Liao, 2021. "Supply Chain Coordination with a Risk-Averse Retailer and the Call Option Contract in the Presence of a Service Requirement," Mathematics, MDPI, vol. 9(7), pages 1-19, April.
    17. Sameh S. Askar, 2020. "The Influences of Asymmetric Market Information on the Dynamics of Duopoly Game," Mathematics, MDPI, vol. 8(7), pages 1-12, July.
    18. Mehrnoosh Khademi & Massimiliano Ferrara & Bruno Pansera & Mehdi Salimi, 2015. "A dynamic game on Green Supply Chain Management," Papers 1503.04772, arXiv.org.
    19. Zhou, Yong-Wu & Li, Jicai & Zhong, Yuanguang, 2018. "Cooperative advertising and ordering policies in a two-echelon supply chain with risk-averse agents," Omega, Elsevier, vol. 75(C), pages 97-117.
    20. Choi, Tsan-Ming & Li, Duan & Yan, Houmin, 2008. "Mean-variance analysis of a single supplier and retailer supply chain under a returns policy," European Journal of Operational Research, Elsevier, vol. 184(1), pages 356-376, January.
    21. Xie, Jinxing & Wei, Jerry C., 2009. "Coordinating advertising and pricing in a manufacturer-retailer channel," European Journal of Operational Research, Elsevier, vol. 197(2), pages 785-791, September.
    22. Junhai Ma & Hao Ren & Miao Yu & Meihong Zhu, 2018. "Research on the Complexity and Chaos Control about a Closed-Loop Supply Chain with Dual-Channel Recycling and Uncertain Consumer Perception," Complexity, Hindawi, vol. 2018, pages 1-13, January.
    23. Karray, Salma & Zaccour, Georges, 2006. "Could co-op advertising be a manufacturer's counterstrategy to store brands?," Journal of Business Research, Elsevier, vol. 59(9), pages 1008-1015, September.
    24. Jia Liu & Guoliang Liu & Na Li & Hongliang Xu, 2014. "Dynamics Analysis of Game and Chaotic Control in the Chinese Fixed Broadband Telecom Market," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-8, May.
    25. Chen, Xingli & Zhou, Jianheng, 2021. "The complexity analysis and chaos control in omni-channel supply chain with consumer migration and advertising cost sharing," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    26. Vipul Agrawal & Sridhar Seshadri, 2000. "Impact of Uncertainty and Risk Aversion on Price and Order Quantity in the Newsvendor Problem," Manufacturing & Service Operations Management, INFORMS, vol. 2(4), pages 410-423, July.
    27. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
    28. Junhai Ma & Qiuxiang Li & Binshuo Bao, 2016. "Study on Complex Advertising and Price Competition Dual-Channel Supply Chain Models Considering the Overconfidence Manufacturer," Mathematical Problems in Engineering, Hindawi, vol. 2016, pages 1-18, September.
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