In a cognitive radio network wherein primary and secondary users coexist, an efficient power allocation method represents one of the most important key aspects. This paper provides a novel approach based on a game theory framework to solve this problem in a distributed and fair way. Formulated as an optimization problem, the resource allocation problem between secondary users and primary users can be modeled and investigated with the Game Theory, and in particular S-Modular Games, since they provide useful tools for the definition of multi objective distributed algorithms in the context of radio communications. This paper provides also a performance comparison among the proposed game and two other algorithms, frequently used in this context: Simulated Annealing and Water Filling.