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.
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