We first address the problem of power allocation at cognitive users (CUs) to maximize the throughput of a nonselfish symbiotic cognitive radio scheme, in which the CUs may assist the data transmission of primary users (PUs) via nonorthogonal amplifyand-forward (AF) cognitive relaying and obtain an incentive time for their own data transmission in a nonselfish manner. Then, an optimal power allocation algorithm is proposed based on the full channel state information (CSI) among PUs, CUs, and base station (BS). In order to reduce the feedback overhead, another power allocation algorithm is devised based only on the partial CSI, that is, the CSI of BS-PU and the CSI of BS-CUs. Simulation results demonstrate that, compared with the optimal power allocation algorithm, the power allocation algorithm with only the partial CSI can achieve a similar performance with a smaller channel feedback overhead.