Spectrum sharing effectively improves the spectrum usage by allowing secondary users (SUs) to dynamically and opportunistically share the licensed bands with primary users (PUs). The concept of cooperative spectrum sharing allows SUs to use portions of the PUs' radio resource for their own data transmission, under the condition that SUs help the PUs' transmission. The key issue with designing such a scheme is how to deal with the resource splitting of the network. In this paper we propose a relay-based cooperative spectrum sharing scheme in which the network consists of one PU and multiple SUs. The PU asks the SUs to relay its data in order to improve its energy efficiency, in return it rewards the SUs with a portion of its authorized spectrum. However each SU is only allowed to transmit its data via the rewarded channel at a power level proportional to the contribution it makes to the PU. Since energy cost is considered, the SUs must carefully determine their power level. This scheme forms a non-cooperative Stackelberg resource allocation game where the strategy of PU is the bandwidth it rewards and the strategy of each SU is power level of relay transmission. We first investigate the second stage of the sub-game which is addressed as power allocation game. We prove there exists an equilibrium in the power allocation game and provide a sufficient condition for the uniqueness of the equilibrium. We further prove a unique Stackelberg equilibrium exists in the resource allocation game. Distributed algorithms are proposed to help the users with incomplete information achieve the equilibrium point. Simulation results validate our analysis and show that our proposed scheme introduces significant utility improvement for both PU and SUs.