title: Similarity-based cooperation and spatial segregation.
abstract: We analyze a cooperative game, where the cooperative act is not based on the previous behavior of the coplayer, but on the similarity between the players. This system has been studied in a mean-field description recently [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 of 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.
authors.affiliation: Institut für Theoretische Physik und Astrophysik, Christian-Albrechts Universität, Olshausenstrasse 40, 24098 Kiel, Germany. traulsen@theo-physik.uni-kiel.de
authors.forename: Arne
authors.initials: A
authors.lastname: Traulsen
authors.forename: Jens Christian
authors.initials: JC
authors.lastname: Claussen