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

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