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A vast body of experiments share the view that social norms are major factorsfor the emergence of fairness in a population of individuals playing thedictator game (DG). Recently, to explore which social norms are conducive tosustaining cooperation has obtained considerable concern. However, thus far fewstudies have investigated how social norms influence the evolution of fairnessby means of indirect reciprocity. In this study, we propose an indirectreciprocal model of the DG and consider that an individual can be assigned asthe dictator due to its good reputation. We investigate the `leading eight'norms and all second-order social norms by a two-timescale theoreticalanalysis. We show that when role assignment is based on reputation, four of the`leading eight' norms, including stern judging and simple standing, lead to ahigh level of fairness, which increases with the selection intensity. Our workalso reveals that not only the correct treatment of making a fair split withgood recipients but also distinguishing unjustified unfair split from justifiedunfair split matters in elevating the level of fairness.

Social norms of fairness with reputation-based role assignment in the dictator game