Consistent strategy-proof assignment by hierarchical exchange
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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 Ppai's hierarchical exchange rules (Ppai in Econometrica 68, 1403- 1433, 2000) and closely resemble Ergin's priority rules (Ergin in Econometrica 70, 2489-2497, 2002). We prove that if there are at least four objects, these are the only rules that are efficient in two-agent problems, 2-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. 2013 Springer-Verlag Berlin Heidelberg.