Reward versus punishment: averting the tragedy of the commons in eco-evolutionary dynamics

Abstract

We consider an unstructured population of individuals who are randomly matched in an underlying population game in which the payoffs depend on the evolving state of the common resource exploited by the population. There are many known mechanisms for averting the overexploitation (tragedy) of the (common) resource. Probably one of the most common mechanism is reinforcing cooperation through rewards and punishments. Additionally, the depleting resource can also provide feedback that reinforces cooperation. Thus, it is an interesting question that how reward and punishment comparatively fare in averting the tragedy of the common (TOC) in the game-resource feedback evolutionary dynamics. Our main finding is that, while averting the TOC completely, rewarding cooperators cannot get rid of all the defectors, unlike what happens when defectors are punished; and as a consequence, in the completely replete resource state, the outcome of the population game can be socially optimal in the presence of the punishment but not so in the presence of the reward.