This paper analyses the following propositions: (i) Are people generally self-interested; (ii) If people tend to be generous, what is their motive, i.e., whether they fear rejection or do they prefer fairness; and (iii) Is there any behavioural difference in bargaining between males and females? We conduct an ultimatum bargaining experiment in a “same gender pairings” setting and observe the overall offers made by the proposers and the rejection rates of the responders. In order to test the second hypothesis we compare the offers that proposers anticipate will be accepted by the responders and the offers they actually make. If actual offer exceeds the minimum acceptable offer, anticipated by the proposer, we conclude that he is fair minded, otherwise, he is considered generous due to fear of rejection. In order to test the third hypothesis, we compare the offers and responses made by males and females in this game. Our results indicate that people on average, are not self-interested and tend to exhibit generosity. This behaviour is dictated by a fear of rejection rather than a concern for fairness. Further, this fear of rejection is very realistic, particularly, in the case of males, where the rejection rates for unfair offers are very high. Regarding gender differences, we find females to be more generous than males. However, reason for this generosity could not be found, since there is no significant difference in the degree of fairness or fear of rejection across the two genders. We also do not find any conclusive evidence that females are more reciprocal than males.