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When multiple virtual machines (VMs) are co scheduled on the same physical machine, they may undergo a performance degradation. The performance degradation is due to the contention for shared resources like last level cache, hard disk, network bandwidth etc. This can lead to service-level agreement violations and thereby customer dissatisfaction. The classical approach to solve the co scheduling problem involves a central authority which decides a co schedule by solving a constrained optimization problem with an objective function such as average performance degradation. In this paper, we use the theory of stable matchings to provide an alternate game theoretic perspective to the co scheduling problem wherein each VM selfishly tries to minimize its performance degradation. We show that the co scheduling problem can be formulated as a Stable Roommates Problem (SRP). Since certain instances of the SRP do not have any stable matching, we reduce the problem to the Stable Marriages Problem (SMP) via an initial approximation. Gale and Shapley proved that any instance of the SMP has a stable matching and can be found in quadratic time. From a game theoretic perspective, the SMP can be thought of as a matching game which always has a Nash equilibrium. There are distributed algorithms for both the SRP and SMP problems. A VM agent in a distributed algorithm need not reveal its preference list to any other VM. This allows each VM to have a private cost function. A principal advantage of this problem formulation is that it opens up the possibility of applying the rich theory of matching markets from game theory to address various aspects of the VM co scheduling problem such as stability, coalitions and privacy both from a theoretical and practical standpoint. We also propose a new workload characterization technique for a combination of compute and memory intensive workloads. The proposed technique uses a sentinel program and it requires only two runs per workload for characterization. VMs can use this technique in deciding their partner preference ranks in the SRP and SMP problems. The characterization technique has also been used in proposing two new centralized VM co scheduling algorithms whose performance is close to the optimal Blossom algorithm.