Numerous real-time applications are currently deployed over mobile networks - ranging from multimedia streaming, to real-time online games, to video conferences/chat, to real-time stock exchanges, etc. Supporting such applications is challenging because they have very stringent Quality of Service (QoS) requirements in terms of both throughput and delay. To address this challenge, in this paper, we propose to assist such mobile applications by a cloud-based network environment, which consists of multiple servers and clients (users). In cloud networks, servers can create multiple replica of the popular content in order to provide the needed QoS for the various service requests of the users. However, in order to efficiently provide services to the potentially large amount of service requests, it is essential for servers to strategically respond to the requests from users. Since the strategic response involves the resource management of the servers, we design a strategy which explicitly considers the service requests (e.g., service types, data priorities, delay constraints) as well as the servers' resource usages (e.g., current loads of servers, contributions of servers). Since the servers are strategic, they will aim to maximize their own utilities. Simulation results verify that the proposed approach enables servers to manage their resources more efficiently compared to existing approaches, thereby providing prioritized data processing and operating in a desired range and leading also to an improved performance for the users.