By introducing the concept of sustainable development, managers and policymakers in many industries have been encouraged to consider environmental and social issues in addition to economic objectives in their planning. Following this concept, sustainable supply chain management has become the main concern of many studies. Among all the strategies to achieve sustainability targets in a supply chain, cooperating with third-party logistics companies has attracted lots of attention. By providing more sustainable and efficient transportation services, 3PLs can help all types of regular, closed-loop, and circular SCs achieve more profit, while they are still sustainable, at least in distribution and collection/recycling stages. This study investigates the sustainable multi-channel SC design problem in the presence of the government and 3PLs. To bring the present study closer to the real-world situation, the problem is modeled using an intuitionistic fuzzy uncertainty approach. Considering the government as the leader of the SC in two centralized and decentralized decision structures, game theory has been applied to model the game between players and obtain optimal decision values. For the first time in the literature, public awareness toward green activities of the players, emission reduction, uncertainty, and delivery time have been considered in this study. The results show the presence of a 3PL will reduce the delivery time and the amount of pollution. Also, the findings confirm that governments can control the players' activities and encourage them to apply green strategies using financial tools.