Cooperator driven oscillation in a time-delayed feedback-evolving game

TL;DR

This paper models how delays in cooperative actions' environmental impact influence the dynamics of cooperation and resource sustainability, revealing that proportional feedback delays can cause oscillations in cooperation and environment levels.

Contribution

It introduces a feedback-evolving game model incorporating time delays in environmental contributions, highlighting their role in inducing oscillatory dynamics.

Findings

Time delay can induce oscillations in cooperation and environment levels.

Fixed contribution amounts are unaffected by delays.

Proportional feedback delays lead to periodic oscillations.

Abstract

Considering feedback of collective actions of cooperation on common resources has vital importance to reach sustainability. But such efforts may have not immediate consequence on the state of environment and it is unclear how they influence the strategic and environmental dynamics with feedbacks. To address this issue, we construct a feedback-evolving game model in which we consider the growth capacity of resources and the punishment efficiency on defectors who do not provide returns to the environment. Importantly, we further assume a delay in adopting the contribution of cooperative individuals to environmental change in our model. We find that when this contribution amount from cooperators' endowment is fixed, the time delay has no particular consequence on the coevolutionary dynamics. However, when the return is proportional to their endowment, then the time delay can induce periodic oscillatory dynamics of cooperation level and environment. Our work reveals the potential effects of time delay of cooperative actions on the coevolutionary dynamics in strategic interactions with environmental feedback.