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In previous studies of the Ultimatum Game (UG), it has been found that proposers do not maximize self-interest by making extremely unfair offers, but instead make relatively fair offers. The main issue is whether or not the proposer's fair behavior is motivated by fear of rejection or by a concern for fairness. We, therefore, conducted this study to examine the impact on the proposer's decision in the UG when information was obtained about the responder's minimum acceptable offer (MAO). The results show that a high percentage of the proposer's offers were close to the MAO, indicating that fear of rejection, rather than concern for fairness, accounted for the proposer's positive offer. We also found that Machiavellian personality traits played an important role in the proposer's offering behavior. This indicated that fear of rejection may be more prominently displayed by people scoring highly in Machiavellianism.