The concept of cognitive radio (CR) has recently received great attention from the research community as a promising paradigm to achieve ef?cient use of the frequency resource by allowing the coexistence of licensed (primary) and unlicensed (secondary) users in the same bandwidth. We propose a novel Nash equilibrium (NE) problem to model concurrent communications of cognitive secondary users who compete against each other to maximize their information rate. The formulation contains constraints on the transmit power (and possibly spectral masks) as well as aggregate interference tolerable at the primary users’ receivers. The coupling among the strategies of the players due to the interference constraints presents a new challenge for the analysis of this class of Nash games that cannot be addressed using the game theoretical models proposed in the literature. For this purpose, we need the framework given by the more advanced theory of ?nite-dimensional Variational Inequalities (VI). This provides us with all the mathematical tools necessary to analyze the proposed NE problem (e.g., existence and uniqueness of the solution) and to devise alternative distributed algorithms along with their convergence properties.
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