FOr a while the learning literature in behavioral/experimental economics was very active (though I always thought learning was a misnomer, I think of it more as adaptation). REcently I've come across a new paper that puts some of these ideas to a more direct test:
Heinrich H. Nax, Maxwell N. Burton-Chellew, Stuart A. West and H. Peyton Young have a paper on "Learning in a Black Box" where they look at subjects that play a public good game either with information, or in the "black box" treatment, where they basically just press buttons and get to see what happens to their own payoff. The results are qualitatively quite similar, when they compare behavior across a couple of public good games with different parameters.
It might be nice to use this technique to in general test how much of "fairness" results could be achieved via a "black box" technique.
I am aware that psychologists, foremost Ido Erev has done lots of "black box" choices over lotteries, I am not aware that this technique has been used much when testing behavior in games...