CHAPTER Energy-Efficient Power Control Games 7.1 INTRODUCTION 7 Many wireless communications systems are optimized in terms of quality of service (QoS), which can include for example, performance criteria such as transmission rate, reliability, latency, or security. It turns out that applications where a trade- off between QoS and energy consumption has to be found have become more and more important, especially over the past decade. Wireless sensor networks (e.g., see Akyildiz et al. (2002)) and ad-hoc networks (e.g., see ElBatt and Ephremides (2004)) are two good examples that illustrate the importance of finding such a trade-off. As in other areas, like economics, finance, or physics, the way of measuring this trade-off, as considered in this chapter, corresponds to the benefit to cost ratio. In wireless com- munications, the transmission rate and transmit power are two common measures of the benefit and cost of a transmission, respectively. Therefore, the ratio of transmis-