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The emergence of heterogeneous decentralized networks without a centralcontroller, such as device-to-device communication systems, has created theneed for new problem frameworks to design and analyze the performance of suchnetworks. As a key step towards such an analysis for general networks, thispaper examines the strategic behavior of \emph{receivers} in a Gaussianbroadcast channel (BC) and \emph{transmitters} in a multiple access channel(MAC) with sum power constraints (sum power MAC) using the framework ofnon-cooperative game theory. These signaling scenarios are modeled asgeneralized Nash equilibrium problems (GNEPs) with jointly convex and coupledconstraints and the existence and uniqueness of equilibrium achievingstrategies and equilibrium utilities are characterized for both the Gaussian BCand the sum power MAC. The relationship between Pareto-optimal boundary pointsof the capacity region and the generalized Nash equilibria (GNEs) are derivedfor the several special cases and in all these cases it is shown that all theGNEs are Pareto-optimal, demonstrating that there is no loss in efficiency whenplayers adopt strategic behavior in these scenarios. Several key equivalencerelations are derived and used to demonstrate a game-theoretic duality betweenthe Gaussian MAC and the Gaussian BC. This duality allows a parametrizedcomputation of the equilibria of the BC in terms of the equilibria of the MACand paves the way to translate several MAC results to the dual BC scenario.

Broadcast Channel Games: Equilibrium Characterization and a MIMO MAC-BC Game Duality