  Indirect reciprocity in which players cooperate with unacquainted other
players having good reputations is a mechanism for cooperation in relatively
large populations subjected to social dilemma situations. When the population
has group structure, as is often found in social networks, players in
experiments are considered to show behavior that deviates from existing
theoretical models of indirect reciprocity. First, players often show ingroup
favoritism (i.e., cooperation only within the group) rather than full
cooperation (i.e., cooperation within and across groups), even though the
latter is Pareto efficient. Second, in general, humans approximate outgroup
members' personal characteristics, presumably including the reputation used for
indirect reciprocity, by a single value attached to the group. Humans use such
a stereotypic approximation, a phenomenon known as outgroup homogeneity in
social psychology. I propose a model of indirect reciprocity in populations
with group structure to examine the possibility of ingroup favoritism and full
cooperation. In accordance with outgroup homogeneity, I assume that players
approximate outgroup members' personal reputations by a single reputation value
attached to the group. I show that ingroup favoritism and full cooperation are
stable under different social norms (i.e., rules for assigning reputations)
such that they do not coexist in a single model. If players are forced to
consistently use the same social norm for assessing different types of
interactions (i.e., ingroup versus outgroup interactions), only full
cooperation survives. The discovered mechanism is distinct from any form of
group selection. The results also suggest potential methods for reducing
ingroup bias to shift the equilibrium from ingroup favoritism to full
cooperation.

Physics and Society;Social and Information Networks;Populations and Evolution