Abstract
The progression of game theory from classical to evolutionary and spatial games provided a powerful means to study cooperation, and enabled a better understanding of general cooperation-promoting mechanisms. However, current standard models assume that at any given point players must choose either cooperation or defection, meaning that regardless of the spatial structure in which they exist, they cannot differentiate between their neighbours and adjust their behaviour accordingly. This is at odds with interactions among organisms in nature who are well capable of behaving differently towards different members of their communities. We account for this natural fact by introducing a new type of player-dubbed link players-who can adjust their behaviour to each individual neighbour. This is in contrast to more common node players whose behaviour affects all neighbours in the same way. We proceed to study cooperation in pure and mixed populations, showing that cooperation peaks at moderately low densities of link players. In such conditions, players naturally specialize in different roles. Node players tend to be either cooperators or defectors, while link players form social insulation between cooperative and defecting clusters by acting both as cooperators and defectors. Such fairly complex processes emerging from a simple model reflect some of the complexities observed in experimental studies on social behaviour in microbes and pave a way for the development of richer game models.