Proof of Corollary 4 and Corollary 5.

<div><p>The organization of sports events, while generating economic benefits, inevitably imposes significant environmental pressures. Conducting green and low-carbon sports events have become a global consensus. In addressing the carbon emissions and benefit coordination issues on the production end of infrastructure construction for large-scale sports events, we considers the significant role of digital platforms in the industry’s low-carbon transformation and upgrade, and innovatively incorporates platforms as decision-making entities and investigates the equilibrium strategies for low-carbon cooperation under three different power structures: one led by the sports events materials supplier, one by the materials distributor, and one by the integrated service platform. Additionally, it designs related cost-sharing contracts. The findings suggest that: centralized decision-making is more conducive to aligning the interests of various entities within the sports events platform supply chain. Different power structures have distinct impacts on overall supply chain profits and carbon emissions. Specifically, the supply chain achieves the highest overall profit under the domination of the integrated service platform, while the lowest level of carbon reduction occurs under the domination of the materials distributor. These results provide strategic insights for the low-carbon development of sports events and the coordinated cooperation within platform supply chain.</p></div>