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Bounded generalized reciprocity (BGR) predicts that people cooperate to maintain a positive reputation with ingroup, but not outgroup, members—and this explains ingroup favoritism in cooperation. We propose that the benefits of maintaining a positive reputation are not limited by group boundaries and so people may cooperate to maintain a good reputation among outgroup members when they will meet and interact with members of that group again. According to this unbounded indirect reciprocity perspective, reputation can promote cooperation with both ingroup and outgroup members. Alternatively, social identity theory (SIT) favors social identity versus reputation as an explanation for cooperation among ingroup members. We test these hypotheses across five studies (Ns = 619, 607, 613, 360, and 615) that manipulate reputation, social identification, and partner's group membership in a cooperative decision …