In a two-level ultimatum game one player offers an amount to two other
players who then, in the case of acceptance, divide this amount by pl
aying an ultimatum game. The first offer has to be accepted by the sec
ond proposer. Only the first proposer knew the true cake size whose a
priori-probabilities were commonly known. The fact that most proposers
with the large cake offered two thirds of the small cake has importan
t implications for the theory of distributive justice better informed
parties do not question that others want a fair share and, thus, prete
nd fairness by 'hiding behind some small cake'.