Abstract — In this paper we study a distributed network comprising an interference channel in parallel with an interference relay channel. Therefore each source node can use two frequency bands and has to implement a certain power allocation policy. An example of application of such a model is the case where the performance of terminals operating in unlicensed bands would be enhanced by being allowed to exploit an additional frequency band in which a relay is available. In this network model, each user is selfish and wants to maximize its Shannon transmission rate. We analyze two cases. In the first case, the relaying node is assumed to implement an amplify-andforward (AF) protocol while in the second case it implements the decode-and-forward (DF) protocol introduced by Cover and El Gamal. For both cases we analyze the existence and uniqueness issues of the equilibrium of the aforementioned power allocation games. Several interesting and new results are provided. In particular: 1. The existence of a Nash equilibrium is shown to be always guaranteed in the case of the AF protocol; 2. The performance of a user or the network does not necessarily increase with the transmit power available at the relay; 3. We show that there is naturally a game in interference relay channels (even if the power allocation policy is fixed) when the DF protocol is used; this game is induced by the decentralized choice of the cooperation degree between each source node and the relay node. Index Terms — Game theory, information theory, cognitive radio, interference channel, open spectrum access, power allocatio
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