Experimental results on the ultimatum game show clearly that (1) large frac
tions of players offer a "fair" allocation and (2) that unfair (but positiv
e) offers are systematically rejected. We offer an explanation of this beha
vior using the "indirect evolutionary approach" which is based on the assum
ption that players behave rationally for given preferences but that their p
references change through an evolutionary process. We prove that despite an
onymous interaction a preference for punishing unfair offers is an evolutio
narily successful strategy if players interact in small groups. This leads
players to split the: resource equally almost always. However, the equal sp
lit is not due to "true fairness" (or "altruism") but is entirely caused by
the (justified) fear that unfair offers might be rejected. (C) 1999 Academ
ic Press.