In order to provide uninterrupted services and fulfill the requirements of customers, Horizontal Cloud Federation Formation (HCFF) has been proposed as a new model enabling cloud providers to cooperate and enlarge their virtual machine infrastructure capacity. In this paper, we have established a synthesis on the main related works in the literature by classifying them into two classes: reactive protocols of HCFF and proactive protocols of HCFF, while doing a comparison between them according to a number of well chosen criteria. Furthermore, we have proposed three protocols of cloud federation formation based on the theory of cooperative games. The protocols are: Sequential Protocol of Horizontal Cloud Federation Formation (SPHCFF), Parallel PHCFF (PPHCFF), and Overlapping PHCFF (OPHCFF). More precisely, our main contribution in this research is the introduction of the notion “Overlapping Federations” with the OPHCFF protocol by referring to the class of Overlapping Coalition Formation Games. Moreover, we have developed a new system of three components based on Inter-Cloud architecture, and then we have implemented it in real time to evaluate the proposed protocols. The obtained experimental results have shown that the OPHCFF protocol improves the average response time, the rate of processed applications, and the profit compared with the introduced PPHCFF protocol. In addition, despite the dissimilarities of architectures, protocols, and mathematical models of existing works, we have arrived to manage a simulation comparison of our SPHCFF with a concurrent mechanism called Cloud Federation Formation Mechanism (CFFM). The obtained simulation results have shown that the proposed SPHCFF performs better than the CFFM mechanism, when the overload rate is large enough, in terms of profit, federation size, time execution, and failure rate.