We develop a spatial resource model in continuous time in which two agents/players strategically exploit a mobile resource in a two-region setup. To counteract the overexploitation of the resource (the tragedy of commons) that occurs when players are free to choose where to fish/hunt/extract/harvest, the regulator can establish a series of spatially structured policies. We compare the equilibria in the case of a common resource with those that emerge when the regulator either creates a natural reserve, or assigns Territorial User Rights to the players. We show that, when the discount rate is close to its "critical value", i.e. when technological and preference parameters dictate a low harvesting intensity/effort, the policies are ineffective in promoting the conservation of the resource and, in addition, they lead to a lower payoff for at least one of the players. Conversely, in a context of harsher harvesting intensity, the intervention can help to safeguard the resource, preventing extinction while also improving the welfare of both players.