We study an Iterated Prisoner's Dilemma game in which players are posi
tioned on a lattice and interact with their near neighbours. Periodica
lly the strategy at every site is replaced by the most successful one
of its neighbours and itself. We search for collective behaviour acid
find dynamically stable ''communities'' with three or even four distin
ct strategies coexisting. Multi-strategy ''communities'' are more immu
ne to invasion by other strategies than are homogeneous states of the
individual members. An explanation of this phenomenon is provided.