A Game-theoretic Approach with Cooperative Advertisement and Quality Level in Two-level Supply Chain with Considering Complementary Products and Uncertainty in Demand

Vertical cooperative advertisement is one of the market strategies in which the manufacturer pays for a part of the supplier's local advertisements. Considering the quality level of products in the model and demand function is necessary and exciting. In this paper, a two-level supply chain with one manufacturer and one supplier, and one complementary manufacturer is developed, which advertisement costs share among manufacturer and retailer. It means that we have a cooperative advertisement in this model. The demand in this paper has uncertainty, and retailers order products from the manufacturer with uncertainty. This supply chain and distribution channel with uncertainty in retailers' demand, products quality level, and considering complementary price and qualities is one of the most practical models in this field. The main aim of these models is to give insights to managers and decision-makers by investigating the effect of the participation rate and some of the important parameters on other essential variables and profit functions and display the relationship between this rate and the trend of the variables. There are two non-cooperative games, including manufacturer Stackelberg and supplier Stackelberg. The results are obtained from these games, and the trends are demonstrated.