The surge of mobile data traffic forces network operators to cope with capacity shortage. The deployment of small cells in 5G networks is meant to reduce latency, backhaul traffic and increase radio access capacity. In this context, mobile edge computing technology will be used to manage dedicated cache space in the radio access network. Thus, mobile network operators will be able to provision OTT content providers with new caching services to enhance the quality of experience of their customers on the move. In turn, the cache memory in the mobile edge network will become a shared resource. Hence, we study a competitive caching scheme where contents are stored at given price set by the mobile network operator. We first formulate a resource allocation problem for a tagged content provider seeking to minimize the expected missed cache rate. The optimal caching policy is derived accounting for popularity and availability of contents, the spatial distribution of small cells, and the caching strategies of competing content providers. It is showed to induce a specific order on contents to be cached based on their popularity and availability. Next, we study a game among content providers in the form of a generalized Kelly mechanism with bounded strategy sets and heterogeneous players. Existence and uniqueness of the Nash equilibrium are proved. Finally, extensive numerical results validate and characterize the performance of the model.