Purpose This paper aims to investigate the vertical cooperative relationship between the core enterprise and the manufacturer within the platform ecosystem, specifically analyzing the optimal decision-making processes of both parties under the original equipment manufacturer (OEM) and original brand manufacturer (OBM) modes. Design/methodology/approach This paper uses game theory to analyze the problem, considering factors such as brand value difference, cross-selling and platform empowerment. It constructs the game models for both OEM and OBM modes and discusses the selection strategies for the cooperation mode. Findings The results indicate that the choice of cooperation mode by the manufacturer and the core enterprise depends on the relative size of their brand values. In cases of inconsistent choices, cooperation can be improved by designing a transfer payment contract. When the brand value is constant, the product price is comprehensively affected by cross-selling revenue, price elasticity coefficient, cost coefficient of sales effort and cost coefficient of platform empowerment. The enterprise reduces the price only when the potential revenue brought by increasing product sales exceeds the marginal profit brought by increasing product pricing; otherwise, it raises the sales price. Originality/value The platform ecosystem is emerging as a future direction for business mode development. However, there is a paucity of research on the cooperation modes between manufacturers and core enterprises within the platform ecosystem.