In this paper, a new backhaul management approach is proposed for cache-enabled small cell networks (SCNs). Such networks are composed of a set of small base stations (SBSs) that are equipped with storage units and have to serve predicted and current requests. The predicted requests are served from the cache of the SBSs and each SBS has to download the related files ahead of time, while the current requests are served by the SBSs instantaneously from the backhaul. Due to the capacity-limited backhaul links, the SBSs cannot serve all the files with a given required rate. Indeed, the higher is the number of requested files in the network, the lower is the assigned backhaul capacity to each SBS. Since the predicted files are not urgent, the number of related files that are requested by the SBSs must be limited by the total capacity of the backhaul links and the number of current requests. Moreover, the backhaul links of SCNs can be heterogeneous and thus they can encompass a number of technologies such as fiber optical, millimeter Wave and sub-6 GHz bands. This problem is formulated as a minority game in which each SBS has to define the number of predicted files to download at a given time period, without affecting the required transmission rate of the current requests. For the formulated game, it is shown that there exists a unique fair proper mixed Nash equilibrium. Simulation results show that users can experience a transmission rate that is up to 4 times higher than the allocated rate in the conventional model in which the SBSs request all their predicted files.