In reality, it is often groups rather than individuals that make decisions. In previous experiments, groups have frequently been shown to act differently from individuals in several ways. It has been claimed that inter-group interactions may be (1) more competitive, (2) more rational, or (3) more prosocial than inter-individual interactions. While some of these observed differences may be due to differences in the experimental designs, it is still not clear which of the three motivations is prevailing as they have often been behaviorally confounded in previous experiments. We use Rubinstein's alternating offers bargaining game to compare inter-individual with inter-group behavior since it allows separating the predictions of competitive, rational and prosocial behavior. We find that groups are, on average, more rational bargainers than individuals.