Characterization of equilibria for the degraded Gaussian broadcast and sum power MAC channels

The behavior of selfish players over a degraded Gaussian broadcast channel (BC) and a multiple access channel (MAC) with sum power constraints (sum power MAC) is investigated using non-cooperative game theory. By modeling the signaling scenarios as a generalized Nash equilibrium problem (GNEP) with jointly convex coupled constraints, this paper characterizes the existence and uniqueness of equilibrium points for both the degraded Gaussian BC and the sum power MAC. A relationship between Pareto-optimal boundary points and equilibrium rates is derived and it is shown that every point on the boundary is a equilibrium point for the degraded BC and sum power MAC, enabling the development of decentralized algorithms to enforce Pareto-optimal equilibria.