A Game Theoretic Model for the Gaussian Broadcast Channel

The strategic behavior of receivers (players) in a multiple-input multiple-output Gaussian broadcast channel is investigated using the framework of non-cooperative game theory. In contrast to the non-cooperative Gaussian multiple access channel game in which each player's feasible set of actions is independent of the actions of other players, the action space of receivers in the Gaussian broadcast channel is 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 in a broadcast channel game, this paper treats the broadcast channel power allocation (or covariance matrix selection) as a generalized Nash equilibrium problem with common constraints. The concept of normalized equilibrium (NoE) is used to characterize the equilibria and the existence and uniqueness of NoEs are proven for key scenarios.