Evolution of cooperation under indirect reciprocity and arbitrary exploration rates

Cooperation has been recognized as an evolutionary puzzle since Darwin, and remains identified as one of the biggest challenges of the XXIst century. Indirect Reciprocity (IR), a key mechanism that humans employ to cooperate with each other, establishes that individual behaviour depends on reputations, which in turn evolve depending on social norms that classify behaviours as good or bad. While it is well known that different social norms give rise to distinct cooperation levels, it remains unclear how the performance of each norm is influenced by the random exploration of new behaviours, often a key component of social dynamics where a plethora of stimuli may compel individuals to deviate from pre-defined behaviours. Here we study, for the first time, the impact of varying degrees of exploration rates - the likelihood of spontaneously adopting another strategy, akin to a mutation probability in evolutionary dynamics - in the emergence of cooperation under IR. We show that high exploration rates may either improve or harm cooperation, depending on the underlying social norm at work. Regarding some of the most popular social norms studied to date, we find that cooperation under Simple-standing and Image-score is enhanced by high exploration rates, whereas the opposite occurs for Stern-judging and Shunning.