Considering and analyzing various kinds of cooperation among supply chain members is an option for better managing each channel. It is noteworthy that in many real‐world cases, each of vertical and horizontal cooperation has an important role in the success of supply chains. Nevertheless, only vertical cooperation in most previous research is considered. This paper addresses both vertical and horizontal cooperation in two competitive reverse supply chains, each of which includes one collector, one remanufacturer, and one retailer. Our primary concern is to analyze quality improvement competition between the remanufacturers. Moreover, retail price competition between the retailers and the quality competition are simultaneously considered in the extended model. In this research, the investigated system has been analyzed under different structures including decentralized, centralized, horizontal cooperation, and coordinated decision‐making models. The results show that when the remanufacturers cooperate horizontally, the profit of each collector and that of the retailer will decrease compared with those in the decentralized structure. To overcome this problem, a new coordination contract named multiple‐link two‐part tariff is proposed to simultaneously coordinate the members of each chain. The proposed contract effectively convinces the remanufacturers to participate in the coordination model instead of the horizontal cooperation. Moreover, it provides a win–win–win condition for all chain members and improves the quality level of the remanufactured products. The results indicate the proper performance of the proposed contract in improving the benefits of the competing chains, especially when there exists no intense competition between the remanufacturers (i.e., when the market sensitivity to the quality of the remanufactured products is low and consequently less effort is needed to increase the quality of the remanufactured products). Moreover, the proposed contract not only is able to simultaneously increase both remanufactured products demand and of end‐of‐life products supply but also involves both economic and environmental benefits.