Speculative, as Tyler Cowen would say.
When people play the Dictator Game Ultimatum Game [thanks Alex] they don't play the way economists would predict. The Nash Equilibrium is for the first player to propose a 99:1 division of the pie take-it-or-leave-it offer, and the second player to accept. Because 1% is better than nothing, so the second player will accept, and the first player knows this.
But proposals like that tend to get rejected. And 50:50 splits tend to be common. (But IIRC non-WEIRD people do play Nash, but I can't find a link.)
50% is a magic number, if there are two players. (I wonder what would happen if the Dictator Game were played with three apples, or one bottle of scotch and one bottle of beer?)