  This paper considers the problem of how to allocate power among competing
users sharing a frequency-selective interference channel. We model the
interaction between selfish users as a non-cooperative game. As opposed to the
existing iterative water-filling algorithm that studies the myopic users, this
paper studies how a foresighted user, who knows the channel state information
and response strategies of its competing users, should optimize its
transmission strategy. To characterize this multi-user interaction, the
Stackelberg equilibrium is introduced, and the existence of this equilibrium
for the investigated non-cooperative game is shown. We analyze this interaction
in more detail using a simple two-user example, where the foresighted user
determines its transmission strategy by solving as a bi-level program which
allows him to account for the myopic user's response. It is analytically shown
that a foresighted user can improve its performance, if it has the necessary
information about its competitors. Since the optimal solution of Stackelberg
equilibrium is computationally prohibitive, we propose a practical
low-complexity approach based on Lagrangian duality theory. Numerical
simulations verify the performance improvements. Possible ways to acquire the
required information and to extend the formulation to more than two users are
also discussed.
