Energy efficiency has become an important managerial variable of IT management. Whereas cloud computing promises significantly higher levels of energy efficiency, it is still not known, if and to what extent outsourcing of software applications to cloud service providers affects the overall energy efficiency. This research is concerned with the allocation of cloud services from providers to customers and addresses the problem of energy-aware service allocation. The distributed nature of the problem, i.e., the multiple loci of control, entails the failure of centralised solutions. Hence, we approach this problem from a multiagent system perspective, which preserves the distributed setting of multiple service providers and customers. The contribution of our research is a game-theoretic framework for analysing service provider and customer interactions and a novel distributed allocation mechanism based on this framework to approximate energy-efficient, optimal allocations. We demonstrate the usefulness and efficacy of the proposed artifact in several simulation experiments.