  This paper considers a non-cooperative game in which competing users sharing
a frequency-selective interference channel selfishly optimize their power
allocation in order to improve their achievable rates. Previously, it was shown
that a user having the knowledge of its opponents' channel state information
can make foresighted decisions and substantially improve its performance
compared with the case in which it deploys the conventional iterative
water-filling algorithm, which does not exploit such knowledge. This paper
discusses how a foresighted user can acquire this knowledge by modeling its
experienced interference as a function of its own power allocation. To
characterize the outcome of the multi-user interaction, the conjectural
equilibrium is introduced, and the existence of this equilibrium for the
investigated water-filling game is proved. Interestingly, both the Nash
equilibrium and the Stackelberg equilibrium are shown to be special cases of
the generalization of conjectural equilibrium. We develop practical algorithms
to form accurate beliefs and search desirable power allocation strategies.
Numerical simulations indicate that a foresighted user without any a priori
knowledge of its competitors' private information can effectively learn the
required information, and induce the entire system to an operating point that
improves both its own achievable rate as well as the rates of the other
participants in the water-filling game.
