Analysis of Relationship between Strategic and Aggregate Energy   Minimization in Delay-Constrained Wireless Networks
  We formulate two versions of the power control problem for wireless networks with latency constraints arising from duty cycle allocations In the first version, strategic power optimization, wireless nodes are modeled as rational agents in a power game, who strategically adjust their powers to minimize their own energy. In the other version, joint power optimization, wireless nodes jointly minimize the aggregate energy expenditure. Our analysis of these models yields insights into the different energy outcomes of strategic versus joint power optimization. We derive analytical solutions for power allocation under both models and study how they are affected by data loads and channel quality. We derive simple necessary conditions for the existence of Nash equilibria in the power game and also provide numerical examples of optimal power allocation under both models. Finally, we show that joint optimization can (sometimes) be Pareto-optimal and dominate strategic optimization, i.e the energy expenditure of all nodes is lower than if they were using strategic optimization. 
Rajgopal Kannan and Shuangqing Wei