In the two-person ultimatum game, an allocator is required to split a given sum of money with a recipient. Subsequently the recipient can either accept or reject the offer. If it is accepted, both players receive their respective splits, while if it is rejected neither of them get anything. Using evolutionary psychology as the theoretical framework, we predicted and found that males made more generous offers when pitted against a female as opposed to a male. While females made equal offers independently of the sex of the recipient. That male allocators are altruistic towards female recipients and competitive with male recipients is construed as a manifestation of social rules, which evolve from the male pre-disposition to use resources for attracting mates. In contrast, females have not evolved such a pre-disposition, and thus, female allocators are more concerned about fairness when making offers to recipients. Several alternate explanations of the above findings are discussed and the evolutionary explanation is concluded as the most parsimonious one. Other potential moderators that are amenable to evolutionary explanations, namely, physical attractiveness, age and ethnicity of participants, are also discussed in this context.