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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 playing an ultimatum game. The first offer has to be accepted by the second 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 important implications for the theory of distributive justice: better informed parties do not question that others want a fair share and, thus, pretend fairness by ‘hiding behind some small cake'
Güth et al. (Wed,) studied this question.