  Evolutionary game dynamics are often studied in the context of different
population structures. Here we propose a new population structure that is
inspired by simple multicellular life forms. In our model, cells reproduce but
can stay together after reproduction. They reach complexes of a certain size,
n, before producing single cells again. The cells within a complex derive
payoff from an evolutionary game by interacting with each other. The
reproductive rate of cells is proportional to their payoff. We consider all
two-strategy games. We study deterministic evolutionary dynamics with
mutations, and derive exact conditions for selection to favor one strategy over
another. Our main result has the same symmetry as the well-known sigma
condition, which has been proven for stochastic game dynamics and weak
selection. For a maximum complex size of n=2 our result holds for any intensity
of selection. For n > 2 it holds for weak selection. As specific examples we
study the prisoner's dilemma and hawk-dove games. Our model advances
theoretical work on multicellularity by allowing for frequency-dependent
interactions within groups.
