Eco-evolutionary games for harvesting self-renewing common resource: Effect of growing harvester population

TL;DR

This paper models the interplay between growing harvesting populations and self-renewing resources using eco-evolutionary game theory, analyzing conditions to prevent the tragedy of the commons through analytical and numerical methods.

Contribution

It introduces a novel eco-evolutionary game model with resource feedback, providing analytical insights into avoiding the tragedy of the commons with a growing population.

Findings

Conditions under which TOC can be avoided are identified.

The model demonstrates how resource self-renewal influences population exploitation.

Analytical and numerical results support strategies for sustainable harvesting.

Abstract

The tragedy of the commons (TOC) is a ubiquitous social dilemma witnessed in interactions between a population of living entities and shared resources available to them: The individuals in the population tend to selfishly overexploit a common resource as it is arguably the rational choice, or in case of non-human beings, it may be an evolutionarily uninvadable action. How to avert the TOC is a significant problem related to the conservation of resources. It is not hard to envisage situations where the resource could be self-renewing and the size of the population may be dependent on the state of the resource through the fractions of the population employing different exploitation rates. If the self-renewal rate of the resource lies between the maximum and the minimum exploitation rates, it is not a priori obvious under what conditions the TOC can be averted. In this paper, we address this question analytically and numerically using the setup of an evolutionary game theoretical replicator equation that models the Darwinian tenet of natural selection. Through the replicator equation, while we investigate how a population of replicators exploit the shared resource, the latter's dynamical feedback on the former is also not ignored. We also present a transparent bottom-up derivation of the game-resource feedback model to facilitate future studies on the stochastic effects on the findings presented herein.