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 Papai's hierarchical exchange rules (Papai 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, -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.