Content delivery involves multiple entities, such as Content Providers (CPs) and Internet Service Providers (ISPs). To better serve its users, the CP may deploy resources (e.g.,caches) as close as possible to them. In this work, we consider the deployment of Virtual Servers (VSs) to stream live videos owned by the CP in the network of the ISP. An efficient deployment requires the knowledge of both the users' position and requests. However, the CP knows what users request but not their exact position, while the ISP has knowledge of users' locations but not of their requests (due to content encryption). To guarantee users' privacy, the ISP and the CP cannot exchange these information with each other. In this paper, we make the two parties cooperate by employing a secure multiparty computation protocol which does not require the two parties to reveal the aforementioned information. This protocol allows the ISP to obtain the number of requests for a specific live-video content issued from a given area at the cost of a negligible overhead. Knowing this information, the ISP efficiently deploys the VSs with the aim of minimizing the number of hops crossed by the live videos to reach their viewers. We assess the average number of hops saved when the geographic distribution of requests is known and we conclude that it is relevant. Then, we investigate scenarios in which the privacy of both the CP and the ISP can be violated, and we propose several countermeasures. In particular, the parties can distort their data when executing the protocol, which results in a trade-off between performance and privacy. We conclude that the fulfillment of stringent privacy requirements comes at significant performance loss.