  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.
