Effective optimization in multi-level supply chains is crucial for ensuring coordination among suppliers, manufacturers, and retailers. Strategic decisions on inventory and pricing significantly impact overall supply chain performance, and competitive interactions across levels under dynamic market conditions add further complexity. The Cournot (quantity-based) competition model is commonly employed to analyze such interactions. In a two-level structure featuring one vendor and several buyers, the vendor typically leads by setting wholesale prices, while buyers respond by adjusting their order quantities and retail prices. This hierarchical relationship forms a Stackelberg competition framework, where decisions at one level cascade through and influence the entire supply chain. To improve realism and adaptability in such models, this study simulates a two-tier negotiation game involving one vendor and two buyers, where agents compete under Cournot conditions within a Stackelberg structure. A distinctive aspect of this research is the integration of ChatGPT as an intelligent intermediary platform that dynamically adjusts wholesale prices, order quantities, and retail prices in real time, based on the profitability and demand responses of the vendor and buyers. Across ten simulation rounds, the study analyzes ordering behavior and pricing strategies while also evaluating the extent to which these decisions approximate Nash and Stackelberg equilibrium points. This research contributes a hybrid framework that bridges classical game theory with AI-enhanced decision-making, offering new insights into how adaptive technologies can reshape strategic interactions and negotiation outcomes in modern supply chains.