Cooperative advertising plays a pivotal role within supply chains, acting as a primary source of funding across multiple tiers. It is very important to know the relationships of supply chain members in order to maintain the interests and efficiency of the whole chain. Coordination in making supply chain decisions has been proven as a powerful tool to maintain benefits and increase the efficiency of the entire supply chain However, existing research has predominantly concentrated on cooperative advertising within two-tier supply chains, frequently disregarding its implications on market demand. This study seeks to bridge this gap by delving into the intricate coordination of cooperative advertising within a three-tier supply chain structure that encompasses the supplier, manufacturer, and retailer, all set within the context of a price-sensitive market. To achieve this, we tackle the coordination challenge employing the Stackelberg model, with a distinctive leadership dynamic wherein the supplier takes the lead, followed by the manufacturer, and subsequently, the retailer. Our analysis incorporates two foundational models: one rooted in non-cooperative game theory, and the other based on cooperative game theory. By juxtaposing and contrasting these models, we undertake a comprehensive examination of the supply chain's profitability, exploring various strategies and shedding light on the benefits inherent to cooperative advertising.