Review: Game theory of public goods in one-shot social dilemmas without assortment

We review the theory of public goods in biology. In the N-person prisoner's dilemma, where the public good is a linear function of the individual contributions, cooperation requires some form of assortment, for example due to kin discrimination, population viscosity or repeated interactions. In most social species ranging from bacteria to humans, however, public goods are usually a non-linear function of the contributions, which makes cooperation possible without assortment. More specifically, a polymorphic state can be stable in which cooperators and non-cooperators coexist. The existence of mixed equilibria in public goods games is a fundamental result in the study of cooperation that has been overlooked so far, because of the disproportionate attention given to the two- and N-person prisoner's dilemma. Methods and results from games with pairwise interactions or linear benefits cannot, in general, be extended to the analysis of public goods. Game theory helps explain the production of public goods in one-shot, N-person interactions without assortment, it leads to predictions that can be easily tested and allows a prescriptive approach to cooperation.