Data sharing issues pervade online social and economic environments. To foster social progress, it is important to develop models of the interaction between data producers and consumers that can promote the rise of cooperation between the involved parties. We formalize this interaction as a game, the data sharing game, based on the Iterated Prisoner's Dilemma and deal with it through multi-agent reinforcement learning techniques. We consider several strategies for how the citizens may behave, depending on the degree of centralization sought. Simulations suggest mechanisms for cooperation to take place and, thus, achieve maximum social utility: data consumers should perform some kind of opponent modeling, or a regulator should transfer utility between both players and incentivise them.