  Image scoring sustains cooperation in the repeated two-player prisoner's
dilemma through indirect reciprocity, even though defection is the uniquely
dominant selfish behaviour in the one-shot game. Many real-world dilemma
situations, however, firstly, take place in groups and, secondly, lack the
necessary transparency to inform subjects reliably of others' individual past
actions. Instead, there is revelation of information regarding groups, which
allows for `group scoring' but not for image scoring. Here, we study how
sensitive the positive results related to image scoring are to information
based on group scoring. We combine analytic results and computer simulations to
specify the conditions for the emergence of cooperation. We show that under
pure group scoring, that is, under the complete absence of image-scoring
information, cooperation is unsustainable. Away from this extreme case,
however, the necessary degree of image scoring relative to group scoring
depends on the population size and is generally very small. We thus conclude
that the positive results based on image scoring apply to a much broader range
of informational settings that are relevant in the real world than previously
assumed.
