Agents interacting on a body of water choose between technologies to catch fish. One is harmless to the resource, as it allows full recovery; the other yields high immediate catches, but low(er) future catches. Strategic interaction in one "objective" resource game may induce "subjective" games in the class of social dilemmas. Which unique "subjective" game is actually played depends crucially on how the agents discount their future payoffs. We examine equilibrium behavior and its consequences on sustainability of the common-pool resource system under exponential and hyperbolic discounting. A suffcient degree of patience on behalf of the agents may lead to equilibrium behavior averting exhaustion of the resource, though full restraint (both agents choosing the ecologically or environmentally sound technology) is not necessarily achieved. Furthermore, if the degree of patience between agents is suffciently dissimilar, the more patient is exploited by the less patient one in equilibrium. We demonstrate the generalizability of our approach developed throughout the paper. We provide recommendations to reduce the enormous complexity surrounding the general cases.