Consistent strategy-proof assignment by hierarchical exchange

We characterize the family of efficient, consistent, and strategy-proof rules in house allocation problems. These rules follow an endowment inheritance and trade procedure as in Pápai’s hierarchical exchange rules (Pápai in Econometrica <Emphasis Type="Bold">68, 1403–1433, <CitationRef CitationID="CR13">2000</CitationRef>) and closely resemble Ergin’s priority rules (Ergin in Econometrica <Emphasis Type="Bold">70, 2489–2497, <CitationRef CitationID="CR7">2002</CitationRef>). We prove that if there are at least four objects, these are the only rules that are efficient in two-agent problems, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$2$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mn>2</mn> </mrow> </math> </EquationSource> </InlineEquation>-consistent, and strategy-proof. A corollary is that these three basic properties together imply the full requirements of efficiency, consistency, group strategy-proofness, and reallocation-proofness. Copyright Springer-Verlag Berlin Heidelberg 2014