Often, it is rather groups 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 selfish-rational, or (3) more prosocial than inter-individual interactions. While some of these observed differences may be due to differences in the experimental setups, it is still not clear which of the three kinds of behavior is prevailing as they have hardly been distinguishable 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, selfish-rational, and prosocial behavior. We find that groups are, on average, more selfish-rational bargainers than individuals, in particular when being in a weak as opposed to a strong position.