  Biological and social systems are structured at multiple scales, and the
incentives of individuals who interact in a group may diverge from the
collective incentive of the group as a whole. Mechanisms to resolve this
tension are responsible for profound transitions in evolutionary history,
including the origin of cellular life, multi-cellular life, and even societies.
Here we synthesize a growing literature that extends evolutionary game theory
to describe multilevel evolutionary dynamics, using nested birth-death
processes and partial differential equations to model natural selection acting
on competition within and among groups of individuals. We apply this theory to
analyze how mechanisms known to promote cooperation within a single group --
including assortment, reciprocity, and population structure -- alter
evolutionary outcomes in the presence of competition among groups. We find that
population structures most conducive to cooperation in multi-scale systems may
differ from those most conducive within a single group. Likewise, for
competitive interactions with a continuous range of strategies we find that
among-group selection may fail to produce socially optimal outcomes, but it can
nonetheless produce second-best solutions that balance individual incentives to
defect with the collective incentives for cooperation. We conclude by
describing the broad applicability of multi-scale evolutionary models to
problems ranging from the production of diffusible metabolites in microbes to
the management of common-pool resources in human societies.
