In cognitive radio (CR) networks, proper power controlling is of importance to ensure efficient operation of both primary and secondary networks. The previous work on power control in cognitive radios has mainly focused on the interactions among a set of secondary users while ignoring the influence of primary users. In , we introduced a new game model for power control in cognitive radios by incorporating the primary users into the player set of the game. In this new framework, the primary users are rewarded (for example, monetarily) for sharing their licensed spectrum with secondary users. In our proposed game formulation, they achieve this by setting a reasonable interference cap (IC) for the secondary users. However, the primary users are to be severely penalized if they do not meet their transmission quality. To ensure this, an exponential pricing term is incorporated into their utility function. Simultaneously, the secondary users aim to achieve energy efficient transmissions while not introducing too much interference to the primary as well as other secondary users. In this paper, we investigate the CR system design aspects based on our proposed new game theoretic spectrum sharing framework. In particular, the performance of the system is compared under different linear detector schemes at the secondary receiver, namely, the matched filter (MF) and the linear MMSE (LMMSE) receivers.