A Game-theoretic Look at the Gaussian Multiaccess Channel

We study the issue of how to fairly allocate communication rate among the users of a Gaussian multiaccess channel. All users are assumed to value rate equally and each is assumed to have no limit on its desired rate. We adopt a cooperative game-theoretic viewpoint, i.e. it is assumed that the users can potentially form coalitions off line to threaten other users with jamming the channel, using this as an argument for deserving a larger share of the rate. To determine the characteristic function of the game, we first determine the capacity region of the Gaussian multiaccess arbitrarily varying channel, with an operational meaning of capacity somewhat modified from the usual one, which is more appropriate to our context and permits time sharing. We then propose a solution concept for the game through a set of natural fairness axioms and prove that there exists a unique fair allocation that satisfies the axioms. Moreover, we demonstrate that the unique allocation is always feasible and lies in the core of the game. It is also shown to possess some intuitively natural qualitative properties as the signal to noise ratio varies.