Evolution of fairness subjected to circle interaction on directed networks

This study aims to investigate how symmetry breaking of roles affects the evolution of fairness. Apart from bidirectional interaction, we study the evolution of fairness by using directed networks. In this sense, one player suggests how to split a resource with the other one with the connection of outgoing edge, meanwhile receives a offer proposed by a third player. We construct three kinds of circle interactions to explore the origin of evolutionary fairness, including bidirectional interaction, triangle circle interaction and long circle interaction. Our work demonstrates that role symmetry induced by indirect interaction suppresses the evolution of fairness. It is found that increasing circle distance will inhibit the evolution of fairness. Our investigation may shield light on the origin of fairness in human evolution.