Nowadays many companies have available large amounts of raw, unstructured data. Among Big Data enabling technologies, a central place is held by the MapReduce framework and, in particular, by its open source implementation, Apache Hadoop. For cost effectiveness considerations, a common approach entails sharing server clusters among multiple users. The underlying infrastructure should provide every user with a fair share of computational resources, ensuring that Service Level Agreements (SLAs) are met and avoiding wastes. In this paper we consider two mathematical programming problems that model the optimal allocation of computational resources in a Hadoop 2.x cluster with the aim to develop new capacity allocation techniques that guarantee better performance in shared data centers. Our goal is to get a substantial reduction of power consumption while respecting the deadlines stated in the SLAs and avoiding penalties associated with job rejections. The core of this approach is a distributed algorithm for runtime capacity allocation, based on Game Theory models and techniques, that mimics the MapReduce dynamics by means of interacting players, namely the central Resource Manager and Class Managers.