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We introduce a new channel, which consists of an interference channel (IC) in parallel with an interference relay channel (IRC), to analyze the interaction between two selfish and cognitive transmitters who compete for a relay implementing the amplify-and-forward protocol. It is shown that whatever the relay location there is always an equilibrium in the resource allocation game where the users selfishly share their power between the IC and IRC. The uniqueness and determination of this equilibrium is analyzed for two cases: the relay amplification gain is fixed; the IRC direct links are negligible. We show how to exploit this analysis to optimally locate the relay either in terms of individual rate or system sum-rate. Simulations are provided and show, in particular, how the users' selfish behavior leads to sharing the space in regions where the relay is used by only one user or not used at all.Index Terms-Cognitive radio, interference channel, open spectrum access, power allocation game, relay channel.

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.