In this paper, the incentives in edge caching systems is addressed using tools from game theory. Provided the limited caching capacity and backhaul resources, the interactions of multiple stakeholders involved in the caching system are analyzed, with competition and cooperation. Due to the selfish nature of all entities in the wireless caching network, they are modeled as rational players with different interests. From the business point of view, the roles of these players in various caching scenarios are thoroughly discussed, including their strategies and utilities. The appropriate game models to study the interactions among multiple players are proposed with the solution concepts and algorithms. Given the existing literature, we investigate the potential research challenges and game models to solve them. A case study is examined showing the effectiveness of applying game theory into wireless caching-enabled networks. The numerical simulations illustrate that our proposed game models result in the win-win solution in both cases.