While previous studies overlook the collusive behavior of retailers under bidirectional competition, we study a closed-loop supply chain (CLSC) consisting of one manufacturer and two competing retailers whose competition exists in the forward and reverse channels. Considering the retailers' potential collusive behavior and the upstream manufacturer's interactive decisions, we build three two-tier game models: Stackelberg-collusion model, Stackelberg-Nash model, and Stackelberg-Stackelberg model. We first obtain the equilibrium decisions of the manufacturer and the retailers in the three models. Furthermore, we investigate whether collusion is beneficial to the two retailers. We find that the retailers' collusion always brings remarkable profit improvement to them as a whole, while the smaller retailers may suffer severe profit loss. A profit-sharing contract is, therefore, designed to guarantee that each retailer can gain more profit by collusion. We also compare the environmental benefit and social welfare among the three models and find that collusion may do harm to the environment or social welfare compared with other models. •This study investigates whether collusion always bring more profit to retailers.•We consider the retailers' potential collusive behavior.•We study retailers' competition in two directions with three behavior modes.•We find that collusion may do harm to the environment or social welfare.