We conduct a laboratory experiment to test a continuous-time model that represents a dynamic groundwater extraction problem in an infinite horizon. We compare the observations to the equilibrium path of the usual behaviors, for the case where the player is alone in extracting the resource (optimal control) and when two players extract the same resource simultaneously (differential game). We use a within-subjects design. This allows us to identify individual profiles of players playing alone and then characterize groups based on their composition with respect to these individual behaviors. We find that approximately a quarter of the players and groups succeed in playing (significantly) optimally, and none behave myopically. Moreover having an agent that behaved optimally in the control in the pair increases the likelihood that the group cooperates. We also identify other categories of players and groups that allows us to classify an additional 50% of the observations..