Pareto-optimal assignments by hierarchical exchange

Papai’s <CitationRef CitationID="CR9">2000</CitationRef> hierarchical exchange mechanisms for house allocation problems determine matchings as the outcome of multiple rounds of trading cycles. Any hierarchical exchange mechanism can be defined through a structure of ownership, which determines the ownership of houses after any round of trading cycles. Given a permutation of agents, a “permuted” hierarchical exchange mechanism can be constructed by consistently permuting agents over the entire structure of ownership. The paper shows that for any Pareto-efficient matching and any hierarchical exchange mechanism, there is a permutation of agents in the ownership structure such that the induced permuted hierarchical exchange mechanism leads to this matching. Copyright Springer-Verlag Berlin Heidelberg 2014