power and responsibility
\citet{Rustichini/Villeval:2014} examine how power affects perceptions of fairness. As a side result, they find that advantageous and disadvantageous players accept that allocations are biased in favor of the more powerful. Power may affect moral judgments, where power is varied by the type of game (powerful: dictator and trust game responder, not powerful: ultimatum game proposer) and hence not really systematically.
\citet{Bosco/Marcheselli:2006} introduce a hierarchy between control and treatment group, where this means that (i) people receive unequal initial shares and (ii) those with largest shares become dictators.
In none of these experiments, power is carefully controlled (in the first the nature of and the role in the game and in the second endowments change at the same time).