Equilibria in a competitive model arising from linear production situations with a common-pool resource

In this paper we deal with linear production situations in which there is a limited common‐pool resource, managed by an external agent. The profit that a producer can attain depends on the amount of common‐pool resource obtained through a certain procedure. We contemplate a competitive process among the producers and study the corresponding non‐cooperative games, describing their (strict) Nash equilibria in pure strategies. It is shown that strict Nash equilibria form a subset of strong Nash equilibria, which in turn form a proper subset of Nash equilibria.