  Treating the interference as noise in the n-user interference channel, the
paper describes a novel approach to the rates region, composed by the
time-sharing convex hull of 2^n-1 corner points achieved through On/Off binary
power control. The resulting rates region is denoted crystallized rates region.
By treating the interference as noise, the n-user rates region frontiers has
been found in the literature to be the convex hull of n hyper-surfaces. The
rates region bounded by these hyper-surfaces is not necessarily convex, and
thereby a convex hull operation is imposed through the strategy of
time-sharing. This paper simplifies this rates region in the n-dimensional
space by having only an On/Off binary power control. This consequently leads to
2^n-1 corner points situated within the rates region. A time-sharing convex
hull is imposed onto those corner points, forming the crystallized rates
region. The paper focuses on game theoretic concepts to achieve that
crystallized convex hull via correlated equilibrium. In game theory, the
correlated equilibrium set is convex, and it consists of the time-sharing mixed
strategies of the Nash equilibriums. In addition, the paper considers a
mechanism design approach to carefully design a utility function, particularly
the Vickrey-Clarke-Groves auction utility, where the solution point is situated
on the correlated equilibrium set. Finally, the paper proposes a self learning
algorithm, namely the regret-matching algorithm, that converges to the solution
point on the correlated equilibrium set in a distributed fashion.
