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We consider a network composed of two interfering point-to-point links wherethe two transmitters can exploit one common relay node to improve theirindividual transmission rate. Communications are assumed to be multi-band andtransmitters are assumed to selfishly allocate their resources to optimizetheir individual transmission rate. The main objective of this paper is to showthat this conflicting situation (modeled by a non-cooperative game) has somestable outcomes, namely Nash equilibria. This result is proved for threedifferent types of relaying protocols: decode-and-forward,estimate-and-forward, and amplify-and-forward. We provide additional results onthe problems of uniqueness, efficiency of the equilibrium, and convergence of abest-response based dynamics to the equilibrium. These issues are analyzed in aspecial case of the amplify-and-forward protocol and illustrated by simulationsin general.

Power Allocation Games in Interference Relay Channels: Existence Analysis of Nash Equilibria