  The tragedy of the commons (TOC) is an unfortunate situation where a shared
resource is exhausted due to uncontrolled exploitation by the selfish
individuals of a population. Recently, the paradigmatic replicator equation has
been used in conjunction with a phenomenological equation for the state of the
shared resource to gain insight into the influence of the games on the TOC. The
replicator equation, by construction, models a fixed infinite population
undergoing microevolution. Thus, it is unable to capture any effect of the
population growth and the carrying capacity of the population although the TOC
is expected to be dependent on the size of the population. Therefore, in this
paper, we present a mathematical framework that incorporates the density
dependent payoffs and the logistic growth of the population in the
eco-evolutionary dynamics modelling the game-resource feedback. We discover a
bistability in the dynamics: a finite carrying capacity can either avert or
cause the TOC depending on the initial states of the resource and the initial
fraction of cooperators. In fact, depending on the type of strategic
game-theoretic interaction, a finite carrying capacity can either avert or
cause the TOC when it is exactly the opposite for the corresponding case with
infinite carrying capacity.
