Punishment Cannot Sustain Cooperation in a Public Good Game with Free-Rider Anonymity

Individuals often have legitimate but publicly unobservable reasons for not partaking in cooperative social endeavours. This means others who lack legitimate reasons may then have the opportunity to behave uncooperatively, i.e. free-ride, and be indistinguishable from those with legitimate reasons. Free-riders have a degree of anonymity. In the context of a public good game we consider the effect of free-rider anonymity on the ability of voluntary punishment to sustain cooperative social norms. Despite only inducing a weak form of free-rider anonymity, punishment falls and cannot sustain cooperation.