Mobile edge caching is a promising approach for enhancing content delivery efficiency and alleviating backbone network burden, via caching popular contents at network edge devices (e.g., base stations or WiFi access points). The successful commercial deployment relies on a comprehensive understanding of the economic interactions among different stakeholders involved. In this paper, we study an edge caching system consisting of a Content Provider (CP), an Internet Service Provider (ISP) who provides the backbone network service, a wireless Access Provider (AP) who provides the wireless access service, and a set of mobile End-Users (EUs), where the CP provides contents for EUs either via the remote server (on the Internet) or via the edge cache (purchased from the AP). We formulate their interactions as a three-stage Stackelberg game. In Stage I, the CP decides the edge cache space to purchase from the AP and cache access fee to charge EUs. In Stage II, the ISP and AP determine the backbone and wireless access service prices, respectively. In Stage III, EUs decide whether to subscribe to the CP' s edge cache service, taking the cache hit probability, cache access fee, backbone and wireless access prices into consideration. We analyze the subgame perfect equilibrium of the dynamic game systematically under two different network pricing scenarios: cooperative pricing and competitive pricing, depending on whether ISP and AP cooperate or compete with each other to make their pricing decisions. Our analysis and simulation results show that all profits of the CP, ISP, AP, and utilities of EUs can be increased by adopting edge cache, compared with the case without edge cache.