A standard model of the exploitation of a renewable resource by non-cooperating agents is considered. Under the assumption that the resource is sufficiently productive we prove that there exist infinitely many Markov-perfect Nash equilibria (MPNE). Although these equilibria lead to overexploitation of the resource (tragedy of the commons) it is shown that for any T > 0 there exist MPNE with the property that the resource stock stays in an arbitrary small neighborhood of the efficient steady state for at least T time periods. Furthermore, we derive a necessary and sufficient condition for maximal exploitation of the resource to qualify as a MPNE and show that this condition is satisfied if there are sufficiently many players, or if the players are sufficiently impatient, or if the capacity of each player is sufficiently high.