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, S., 2000. Strategy-proof assignment by hierarchical exchange, Econometrica 68, 1403-1433] and closely resemble Ergin’s Priority Rules [Ergin, H., 2002. Efficient resource allocation on the basis of priorities, Econometrica, 70, 2489-2497]. We prove that if there are at least four objects, these are the only rules that are efficient in two-agent problems, 2consistent, and strategy-proof. A corollary is that these three basic properties together imply the full requirements of efficiency, consistency, group strategy-proofness, and reallocation-profness. JEL classification: D61, D63, C70.