We study the coevolution of networks and action choices in a Prisoners' Dilemma. Agents in our model learn about both action choices and choices of interaction partners (links) by imitating successful behavior of others. The resulting dynamics yields outcomes where both cooperators and defectors coexist under a wide range of parameters. Two scenarios can arise. Either there is "full separation" of defectors and cooperators, i.e. they are found in two different, disconnected components. Or there is "marginalization" of defectors, i.e. connected networks emerge with a center of cooperators and a periphery of defectors. (C) 2010 Elsevier B.V. All rights reserved.