In this paper, an incentive proactive cache mechanism in cache-enabled small cell networks (SCNs) is proposed, in order to motivate the content providers (CPs) to participate in the caching procedure. A network composed of a single mobile network operator (MNO) and multiple CPs is considered. The MNO aims to define the price it charges the CPs to maximize its revenue while the CPs compete to determine the number of files they cache at the MNO's small base stations (SBSs) to improve the quality of service (QoS) of their users. This problem is formulated as a Stackelberg game where a single MNO is considered as the leader and the multiple CPs willing to cache files are the followers. The followers game is modeled as a non-cooperative game and both the existence and uniqueness of a Nash equilibrium (NE) are proved. The closed-form expression of the NE which corresponds to the amount of storage each CP requests from the MNO is derived. An optimization problem is formulated at the MNO side to determine the optimal price that the MNO should charge the CPs. Simulation results show that at the equilibrium, the MNO and CPs can all achieve a utility that is up to $50$% higher than the cases in which the prices and storage quantities are requested arbitrarily.