Existing spectrum-sharing schemes either allow the secondary-network users (SUs) to utilize the spectrum when primary-network users (PUs) remain idle, or require the SUs to coordinate with the PUs, causing signaling overhead. In this paper, we propose a game-theoretic spectrum-sharing scheme, which enables the SUs and PUs to utilize the spectrum simultaneously, without compromising the quality of service (QoS) of the PUs and ensuring reduced signaling overhead. We formulate a multi-priority non-cooperative power-control game by considering a scenario where multiple small cell base stations belonging to either the primary network or secondary network utilize the available spectrum resources at the same time. The base stations are empowered to adjust their transmit powers in an automated manner based on measured interference, until their transmit powers are stabilized. As a key idea, a game parameter, dynamic price coefficient, is designed to give the primary network priority over the secondary network for accessing the spectrum. We determine appropriate bounds for the game parameters to ensure the existence and uniqueness of the Nash equilibrium of the proposed game. Furthermore, we propose a novel dual-mode solution to reduce the real-time signaling overhead between the networks, by minimizing the information exchange during the game required to reach an equilibrium point. Extensive simulation results are presented to prove the convergence of the game to a Nash equilibrium, along with a throughput performance analysis.