We study the impact of discrete versus continuous time on the behavior of agents in the context of a dynamic common pool resource game. To this purpose, we consider a linear quadratic model in which agents exploit a renewable resource with an infinite horizon and conduct a lab experiment. We use a differential game for continuous time and derive its discrete time approximation. When the agent is the sole owner of the resource, we fail to detect on a battery of indicators any difference between discrete and continuous time. Conversely, in the two-player setting, significantly more agents can be classified as myopic and end up with a low resource level in discrete time. Continuous time seems to allow for better cooperation and thus greater sustainability of the resource than does discrete time. Also, payoffs are more equally distributed in the continuous time setting.