  Despite recent advances in reputation technologies, it is not clear how
reputation systems can affect human cooperation in social networks. Although it
is known that two of the major mechanisms in the evolution of cooperation are
spatial selection and reputation-based reciprocity, theoretical study of the
interplay between both mechanisms remains almost uncharted. Here, we present a
new individual-based model for the evolution of reciprocal cooperation between
reputation and networks. We comparatively analyze four of the leading moral
assessment rules---shunning, image scoring, stern judging, and simple
standing---and base the model on the giving game in regular networks for
Cooperators, Defectors, and Discriminators. Discriminators rely on a proper
moral assessment rule. By using individual-based models, we show that the four
assessment rules are differently characterized in terms of how cooperation
evolves, depending on the benefit-to-cost ratio, the network-node degree, and
the observation and error conditions. Our findings show that the most tolerant
rule---simple standing---is the most robust among the four assessment rules in
promoting cooperation in regular networks.
