Although the boom of e-commerce markets has brought great benefits and convenience to relevant platforms and consumers, it has also incurred serious packaging waste and environmental pollution. In response, an increasing number of platforms are actively replacing their disposable packaging with reusable packaging to mitigate the concerns of government agencies and green consumers. This paper investigates e-commerce platforms' reusable packaging adoption strategies in a competitive market with green consumers. By combining the Cournot game and evolutionary game models, we first explore the optimal reusable packaging adoption strategies of two competing platforms considering the presence of green consumers, and then analyze the impacts of key parameters on the evolutionary equilibrium outcomes. To check the robustness of our models, we relax some model assumptions to explore a general scenario, namely, we consider the presence of government subsidies and differences in consumers' green preferences. We find that market competition is not always bad news for platforms, especially those adopting reusable packaging. Furthermore, the evolutionary equilibrium outcome of platform reusable packaging adoption hinges on the ratio of the added value of reusable packaging products to the added value of disposable packaging products and the fixed cost of reusable packaging adoption. In particular, when this ratio exceeds one and the fixed cost is sufficiently high and decreasing, the two platforms will go through three sequential stages, namely, from Stage I in which neither platform adopts reusable packaging, to Stage II in which one platform adopts reusable packaging while the other fails to do so, and then to Stage III in which both platforms adopt reusable packaging. Lastly, government subsidies can make both platforms easier to adopt reusable packaging, whereas a low proportion of green consumers will inevitably impede the large-scale application of reusable packaging.