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.
Amir, Rabah, "Sequential Games of Resource Extraction: Existence of Nash Equilibria" (1987). Cowles Foundation Discussion Papers. 1068.