Secrecy games on the one-sided interference channel

In this paper, we study the two-user one-sided interference channel with confidential messages. In this interference channel, in addition to the usual selfishness of the users, the relationship between the two pairs of users is further adversarial in the sense of both receivers' desires to eavesdrop on the communication of the other pair. We develop a game-theoretic model to study the information-theoretic secure communications in this setting. We first start with a game-theoretic model where each pair's payoff is their own secrecy rate. The analysis of the binary deterministic interference channel with this payoff function shows that self-jamming of a transmitter, which injures the eavesdropping ability of its own receiver, is not excluded by the Nash equilibria. We propose a refinement for the payoff function by explicitly accounting for the desire of the receiver to eavesdrop on the other party's communication. This payoff function captures the adversarial relationship between the two pairs of users better. We determine the Nash equilibria for the binary deterministic channel for both payoff functions.