The processing and storage of critical data in large-scale cloud networks necessitate the need for scalable security solutions. It has been shown that deploying all possible detection measures incur a cost on performance by using up valuable computing and networking resources, thereby resulting in Service Level Agreement (SLA) violations promised to the cloud-service users. Thus, there has been a recent interest in developing Moving Target Defense (MTD) mechanisms that helps to optimize the joint objective of maximizing security while ensuring that the impact on performance is minimized. Often, these techniques model the challenge of multi-stage attacks by stealthy adversaries as a single-step attack detection game and use graph connectivity measures as a heuristic to measure performance, thereby (1) losing out on valuable information that is inherently present in multi-stage models designed for large cloud networks, and (2) come up with strategies that have asymmetric impacts on performance, thereby heavily affecting the Quality of Service (QoS) for some cloud users. In this work, we use the attack graph of a cloud network to formulate a general-sum Markov Game and use the Common Vulnerability Scoring System (CVSS) to come up with meaningful utility values in each state of the game. We then show that, for the threat model in which an adversary has knowledge of a defender’s strategy, the use of Stackelberg equilibrium can provide an optimal strategy for placement of security resources. In cases where this assumption turns out to be too strong, we show that the Stackelberg equilibrium turns out to be a Nash equilibrium of the general-sum Markov Game. We compare the gains obtained using our method(s) to other baseline techniques used in cloud network security. Finally, we highlight how the method was used in a real-world small-scale cloud system.