Stable leaders pave the way for cooperation under time-dependent exploration rates

The exploration of different behaviors is part of the adaptation repertoire of individuals to new environments. Here, we explore how the evolution of cooperative behavior is affected by the interplay between exploration dynamics and social learning, in particular when individuals engage on the Prisoner's Dilemma along the edges of a social network. We show that when the population undergoes a transition from strong to weak exploration rates a decline in the overall levels of cooperation is observed. However, both constant and variable exploration rates are shown to be beneficial for cooperation as long as leaders (highly connected individuals) adopt lower exploration rates than followers (less connected individuals). This result suggests that noisy decision-making at the periphery of social networks may, in some cases, translate into major benefits at the population level.Â