We study the role of unbiased migration in cooperation in the framework of the spatial evolutionary game on a variety of spatial structures, namely a regular lattice, continuous plane and complex networks. A striking finding is that migration plays a universal role in cooperation, regardless of the spatial structure. For a high degree of migration, cooperators cannot survive owing to their failure to form cooperator clusters that resist attacks by defectors. Meanwhile, for a low degree of migration, cooperation is considerably enhanced relative to that in the static spatial game, which is due to the strengthening of the boundaries of cooperator clusters by the occasional accumulation of cooperators along the boundaries. The cooperator cluster thus becomes more robust than that in the static game and defectors near the boundary can be assimilated by cooperators. The cooperator cluster thus expands, which facilitates cooperation. The general role of migration will be substantiated by sufficient simulations relating to heuristic explanations.
