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Structured populations facilitate cooperation in policed Public Goods Games

Societies consisting of cooperative individuals seem to require for their continuing success that defectors be policed. The precise connection between punishers and benefits, population structure, and division of labour, however, remains ill-understood. Many models assume costly "peer punishment" to enforce cooperation, but results in the economics literature suggest that this assumption may not be generally valid. In many human and animal societies, there is a division of labour between a purely supportive majority and a dedicated minority of police-like enforcers. Here we present several extensions to the Public Goods Game with punishment which allow for this possibility, and evaluate their influence on the level of cooperative behaviour. We find that a structure of separate subpopulations, which only interact through migration of individuals, can have a strong effect on the evolutionary dynamics of a system and significantly facilitate cooperation. Forcing defectors to contribute and enabling fitness transfers to punishers both have a weak positive effect on cooperation levels. In the presence of group competition, however, evolutionary effects can paradoxically hinder cooperation.