  In this paper, we address the problem of global transmit power minimization
in a self-congiguring network where radio devices are subject to operate at a
minimum signal to interference plus noise ratio (SINR) level. We model the
network as a parallel Gaussian interference channel and we introduce a fully
decentralized algorithm (based on trial and error) able to statistically
achieve a congiguration where the performance demands are met. Contrary to
existing solutions, our algorithm requires only local information and can learn
stable and efficient working points by using only one bit feedback. We model
the network under two different game theoretical frameworks: normal form and
satisfaction form. We show that the converging points correspond to equilibrium
points, namely Nash and satisfaction equilibrium. Similarly, we provide
sufficient conditions for the algorithm to converge in both formulations.
Moreover, we provide analytical results to estimate the algorithm's
performance, as a function of the network parameters. Finally, numerical
results are provided to validate our theoretical conclusions. Keywords:
Learning, power control, trial and error, Nash equilibrium, spectrum sharing.
