  Explaining the emergence and maintenance of cooperation among selfish
individuals from an evolutionary perspective remains a grand challenge in
biology, economy, and social sciences. Social exclusion is believed to be an
answer to this conundrum. However, previously related studies often assume
one-shot interactions and ignore how free-riding is identified, which seem to
be too idealistic. In this work, we consider repeated interactions where
excluders need to pay a monitoring cost to identify free-riders for exclusion
and free-riders cannot participate in the following possible game interactions
once they are identified and excluded by excluders in the repeated interaction
process. We reveal that the introduction of such exclusion can prevent the
breakdown of cooperation in repeated group interactions. In particular, we
demonstrate that an evolutionary oscillation among cooperators, defectors, and
excluders can appear in infinitely large populations when early exclusion is
implemented. In addition, we find that the population spends most of the time
in states where cooperators dominate for early exclusion when stochastic
mutation-selection is considered in finite populations. Our results highlight
that early exclusion is successful in solving the mentioned enigma of
cooperation in repeated group interactions.
