Pattern formation in spatial games

Pattern formation is crucial for maintaining biodiversity and cooperation in nature and human society. We review recent works on the formation of spatial patterns in the framework of evolutionary games, involving rock-paper-scissors game and social dilemmas. The rock-paper-scissors game, as a basic paradigm for characterizing nonhierarchical cyclical competition in ecosystems, has been widely used for studying biodiversity sustained by species coexistence. Spiral waves and target waves have been observed in spatially dispersed population with mobility, which has been deemed play significant roles in species coexistence. For social dilemmas, the formation of cooperator clusters is a key factor for the survival of cooperators who can resist the invasion of defectors in the pattern of clusters. Several underlying mechanisms contributing to the formation of various spatial patterns will be reviewed in spatial games.