  This work characterizes an important solution concept of a relevant spectrum
game. Two energy-efficient sources communicating with their respective
destination compete for an extra channel brought by a relay charging the used
bandwidth through a pricing mechanism. This game is shown to possess a unique
Nash bargaining solution, exploiting a time-sharing argument. This
Pareto-efficient solution can be implemented by using a distributed
optimization algorithm for which each transmitter uses a simple gradient-type
algorithm and alternately updates its spectrum sharing policy. Typical
numerical results show to what extent spectral efficiency can be improved in a
system involving selfish energy-efficient sources.
