An oscillating tragedy of the commons in replicator dynamics with game-environment feedback

Classical game theory addresses how individuals make decisions given suitable incentives, for example, whether to use a commons rapaciously or with restraint. However, classical game theory does not typically address the consequences of individual actions that reshape the environment over the long term. Here, we propose a unified approach to analyze and understand the coupled evolution of strategies and the environment. We revisit the originating tragedy of the commons example and evaluate how overuse of a commons resource changes incentives for future action. In doing so, we identify an oscillatory tragedy of the commons in which the system cycles between deplete and replete environments and cooperation and defection behavior, highlighting new challenges for control and influence of feedback-evolving games.