Today Nick Rowe mentions the dictator/ultimatum game (I choose to divide a pot and if you refuse the division, we both get nothing ... or the dictator version where you get no input). It's another case where the maximum entropy guess is better than game theory. Game theory says the solution is 99.9% (or more) for the dictator and x = 0.1% (or less) for the other person if people were truly rational. Maximum entropy guesses x ≈ 50%, but allows x ≤ 50% if information transfer is non-ideal. It also would guess x = 33% for three players, x = 25% for four, etc.