With the unprecedented reliance on cloud computing as the backbone for storing today's big data, we argue in this paper that the role of the cloud should be reshaped from being a passive virtual market to become an active platform for monetizing the big data through Artificial Intelligence (AI) services. The objective is to enable the cloud to be an active platform that can help big data service providers reach a wider set of customers and cloud users (i.e., data consumers) to be exposed to a larger and richer variety of data to run their data analytic tasks. To achieve this vision, we propose a novel game theoretical model, which consists of a mix of cooperative and competitive strategies. The players of the game are the big data service providers, cloud computing platform, and cloud users. The strategies of the players are modeled using the two-sided market theory that takes into consideration the network effects among involved parties, while integrating the externalities between the cloud resources and consumer demands into the design of the game. Simulations conducted using Amazon and google clustered data show that the proposed model improves the total surplus of all the involved parties in terms of cloud resources provision and monetary profits compared to the current merchant model.