Effects of Empathy on the Evolutionary Dynamics of Fairness in Group-Structured Systems

Figure 1

Model schematic. (a) Evolutionary dynamics with global migration. Ten individuals (represented by nodes, ), eight of whom (nodes with ) play independent strategies and the remainder (nodes with ) play empathetic strategies (), are distributed to four groups (shaded by blue, ). At a given generation, an individual with an independent strategy is chosen to reproduce one offspring (empty square) and an individual (node under cross) is chosen to die. The newborn offspring adopts independent strategies with probability and empathetic strategies with . The offspring stays in his parent’s group with probability , and he migrates to another group with . (b) Illustration of the migration range r. Each node (white circle) and each edge represent a group and a potential migration path, respectively. For example, when , an individual equally migrates to two groups that are the direct neighbors of his parent’s group.

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