  The behavior of rational and selfish players (receivers) over a
multiple-input multiple-output Gaussian broadcast channel is investigated using
the framework of noncooperative game theory. In contrast to the game-theoretic
model of the Gaussian multiple access channel where the set of feasible actions
for each player is independent of other players' actions, the strategies of the
players in the broadcast channel are mutually coupled, usually by a sum power
or joint covariance constraint, and hence cannot be treated using traditional
Nash equilibrium solution concepts. To characterize the strategic behavior of
receivers connected to a single transmitter, this paper models the broadcast
channel as a generalized Nash equilibrium problem with coupled constraints. The
concept of normalized equilibrium (NoE) is used to characterize the equilibrium
points and the existence and uniqueness of the NoE are proven for key
scenarios.
