  We analyze a cooperative game, where the cooperative act is not based on the
previous behaviour of the co-player, but on the similarity between the players.
This system has been studied in a mean-field description recently [A. Traulsen
and H. G. Schuster, Phys. Rev. E 68, 046129 (2003)]. Here, the spatial
extension to a two-dimensional lattice is studied, where each player interacts
with eight players in a Moore neighborhood. The system shows a strong
segregation independent on parameters. The introduction of a local conversion
mechanism towards tolerance allows for four-state cycles and the emergence of
spiral waves in the spatial game. In the case of asymmetric costs of
cooperation a rich variety of complex behavior is observed depending on both
cooperation costs. Finally, we study the stabilization of a cooperative fixed
point of a forecast rule in the symmetric game, which corresponds to
cooperation across segregation borders. This fixed point becomes unstable for
high cooperation costs, but can be stabilized by a linear feedback mechanism.
