  The emergence of heterogeneous decentralized networks without a central
controller, such as device-to-device communication systems, has created the
need for new problem frameworks to design and analyze the performance of such
networks. As a key step towards such an analysis for general networks, this
paper examines the strategic behavior of \emph{receivers} in a Gaussian
broadcast channel (BC) and \emph{transmitters} in a multiple access channel
(MAC) with sum power constraints (sum power MAC) using the framework of
non-cooperative game theory. These signaling scenarios are modeled as
generalized Nash equilibrium problems (GNEPs) with jointly convex and coupled
constraints and the existence and uniqueness of equilibrium achieving
strategies and equilibrium utilities are characterized for both the Gaussian BC
and the sum power MAC. The relationship between Pareto-optimal boundary points
of the capacity region and the generalized Nash equilibria (GNEs) are derived
for the several special cases and in all these cases it is shown that all the
GNEs are Pareto-optimal, demonstrating that there is no loss in efficiency when
players adopt strategic behavior in these scenarios. Several key equivalence
relations are derived and used to demonstrate a game-theoretic duality between
the Gaussian MAC and the Gaussian BC. This duality allows a parametrized
computation of the equilibria of the BC in terms of the equilibria of the MAC
and paves the way to translate several MAC results to the dual BC scenario.
