With the rapid growth of servers and applications spurred by the Internet, the power consumption of servers has become critically important and must be efficiently managed. High energy consumption also translates into excessive heat dissipation which in turn, increases cooling costs and causes servers to become more prone to failure. This paper presents a theoretical and experimental framework and general methodology for hierarchical autonomic power & performance management in high performance distributed data centers. We optimize for power & performance (performance/watt) at each level of the hierarchy while maintaining scalability. We adopt mathematicallyrigorous optimization approach to provide the application with the required amount of memory at runtime. This enables us to transition the unused memory capacity to a low power state. Our experimental results show a maximum performance/watt improvement of 88.48% compared to traditional techniques. We also present preliminary results of using Game Theory to optimize performance/watt at the cluster level of a data center. Our cooperative technique reduces the power consumption by 65% when compared to traditional techniques (min-min heuristic).