Power Allocation in Gaussian Interference Relay Channels via Game Theory

We address the power allocation problem for interference relay channels. Due to the competitive nature of the multi-user environment, we model the problem as a strategic non- cooperative game and show that this game always has a unique Nash equilibrium (NE), for any system profile. Two iterative algorithms, based on sequential and simultaneous updating, are proposed to achieve the unique NE in a distributed manner. We shall also prove that both algorithms always converge to the unique NE, from an arbitrary starting point. More importantly, the global optimality in terms of the sum information rate is achieved by the NE, when the interference is relatively low.