It's to your individual benefit to be more (unconsciously) selfish and calculating in these situations, whether the other people in your group have a fairness drive or not.

Not if you are punished for selfishness. I'm not sure how reasonable the following analysis it (since I didn't study this kind of thing at all); it suggests that fairness is a stable strategy, and given some constraints a more feasible one than selfishness:

M. A. Nowak, et al. (2000). `Fairness versus reason in the ultimatum game.'. Science 289(5485):1773-1775. (PDF)