A general model for noncooperative extraction of common-property resource is considered. The main result is that this sequential game has a Nash equilibrium in stationary strategies. The proof is based on an inﬁnite dimensional ﬁxed-point theorem, and relies crucially on the topology of epi-convergence. A byproduct of the analysis is that Nash equilibrium strategies may be selected such that marginal propensities of consumption are bounded above by one.
Sequential games, Dynamic programming, Fixed point theorem, Nash equilibrium, Common property, Natural resources, Common property