In a laboratory ultimatum bargaining experiment, responder behavior is more consistent with game-theoretic predictions when responders indicate a binding minimum acceptable offer (MAO) or when rejection penalizes a “hostage” third player. In general, female subjects indicated higher MAOs but had a much greater reaction than males to the presence of a third player. Offers increase in the presence of a binding MAO but are not affected by a third player. Behavior in our experiment is also generally consistent with hypotheses based on a popular personality test instrument.