Inequality in Hierarchies

The paper examines allocation of a resource in "hierarchies", where individuals are exogenously ordered and those ranked higher in the ordering make claim on the resource earlier. Individuals get strictly increasing and strictly concave payoff from resource extracted, giving rise to endogenous resource distribution. A "donor" supplies costly resource after the agents sequentially commit to resource shares. I characterize equilibrium resource distributions for a large class of donor's objectives (including utilitarian and egalitarian cases). When hierarchies are large, equilibrium resource shares follow a Geometric distribution over the ranks, irrespective of donor objective. With utilitarian (or egalitarian) donor, efficiency arises when payoffs are approximately linear