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Equivalence results in the allocation of indivisible objects : A unified view

This paper studies probabilistic mechanisms that allocate indivisible objects to agents by hierarchical exchange using the top-trading cycles algorithm. The main result of this paper is a general technique for proving that seemingly different probabilistic mechanisms are in fact equivalent. This approach simplifies and unifies several equivalence results in the literature. The same technique is used to generalize these results to mechanisms in which the priority structure for each object is given by a tree (instead of a linear ordering of the agents).