Rate allocation for strategic users in Gaussian multiple access wiretap channels

We consider a set of users communicating over a Gaussian multiple access channel in the presence of an eavesdropper. The information theoretic secrecy rates for such settings have been well studied under the assumptions that all users are cooperative. In more recent work, a game theoretic model was studied in which each user selected its own rate. This game was shown to have multiple possible equilibria. Here, we consider a related question in which a mechanism is used to solicit information from the users and then allocate secrecy rates among them. We study three simple mechanisms and analyze the performance of each for a small set of users (N = 2, 3) in terms of their worst-case efficiency. For N = 2, we give a closed form lower bound on the efficiency for each scheme and show one mechanism, which generalizes the well-known Kelly mechanism, has the best efficiency. We then consider N = 3 users and give numerical results for different user utility functions.