Heterogeneous cooperative leadership structure emerging from random regular graphs

Abstract

This paper investigates the evolution of cooperation and the emergence of hierarchical leadership structure in random regular graphs. It is found that there exist different learning patterns between cooperators and defectors, and cooperators are able to attract more followers and hence more likely to become leaders. Hence, the heterogeneous distributions of reputation and leadership can emerge from homogeneous random graphs. The important directed game-learning skeleton is then studied, revealing some important structural properties, such as the heavy-tailed degree distribution and the positive in-in degree correlation.