Trade-in programs offer consumers efficient and convenient repurchase services, thus stimulating market demand. Additionally, these programs contribute to transforming "old goods" into valuable resources instead of "waste," significantly promoting the green and low-carbon development within the household appliances and consumer electronics sectors. With the emergence of the platform economy, the implementation of trade-in initiatives within platform supply chains has gained increasing popularity. However, platform enterprises encounter numerous challenges in executing trade-ins within the supply chain context. One major challenge is the difficulty associated with the valuation of old products, attributed to the wide variety of models, disparate quality levels, and varying maintenance conditions, making precise valuation exceedingly complex. Another challenge lies in the profitability of recycling old products. The trade-in process involves substantial cost investments in establishing recycling channels, creating temporary storage spaces, forming and managing recycling teams, as well as overseeing storage personnel and inventory management. The inherently low value of old products and the inefficiency of non-professional recycling enterprises in processing these products further complicate the maximization of value from recycling, rendering it challenging for enterprises to derive profits from the recycling segment of trade-in programs. In response to these challenges, e-commerce platforms, manufacturers, and recycling platforms are exploring diverse cooperative trade-in models. Such cooperation among e-commerce platforms, manufacturers, and recycling platforms within the supply chain can reduce the investment required for establishing reverse logistics by either the e-commerce platforms or manufacturers. Concurrently, it increases the recycling flow for recycling platforms. Through the recycling platforms' scale effect in processing old products, the maximization of the value of old items is achievable. Thus, establishing cooperative models within the platform supply chain emerges as a pivotal approach for platform enterprises to navigate the outlined challenges. Identifying the most effective cooperation model to address the dilemmas faced by platform enterprises in implementing trade-ins constitutes a primary motivator for this research. Accordingly, this study examines a platform supply chain composed of e-commerce platforms, recycling platforms, and manufacturers. It begins by segmenting consumers holding old products and first-time buyers based on consumer utility theory. It then explores four scenarios: manufacturers independently implementing trade-ins, e-commerce platforms independently implementing trade-ins, manufacturers collaborating with recycling platforms for trade-ins, and e-commerce platforms collaborating with recycling platforms for trade-ins. Utilizing the Stackelberg game theory, this paper constructs four models for these scenarios. Subsequently, it employs a reverse induction solution method to determine the pricing of new and old products, as well as the equilibrium solutions for trade-in discounts. Finally, by comparing the equilibrium solutions and analyzing the profits of supply chain members under different scenarios, the study delineates the optimal trade-in cooperation strategy. The findings reveal: 1) Manufacturers exhibit greater enthusiasm for implementing trade-ins compared to e-commerce platforms. 2) Internet + recycling platforms invariably show a willingness to engage in trade-in cooperation with manufacturers or e-commerce platforms. 3) Collaborative efforts between manufacturers or e-commerce platforms and recycling platforms can negatively impact the sales of new products and the recycling of old products, with a more pronounced negative effect observed when e-commerce platforms collaborate with recycling platforms. 4) When the investment costs for reverse logistics are substantial, manufacturers or e-commerce retailers are incentivized to partner with recycling platforms for trade-ins. Moreover, when manufacturers collaborate with recycling platforms for trade-ins, the performance of manufacturers, Internet recycling platforms, and the overall supply chain exhibits improvement. In summary, as trade-in cooperation among e-commerce platforms, manufacturers, and recycling platforms continue to proliferate in today's business landscape, it has become imperative for members of the platform supply chain to carefully select suitable trade-in cooperation models. The conclusions of this paper provide a reference guide for platform supply chain members to make the right decisions in the trade-in cooperation context.