Essays on House Allocation Problems

Abstract

We study discrete resource allocation problems in which agents have unit demand and strict preferences over a set of indivisible objects. Such problems are known as house allocation problems. We define a new property that we call “balancedness." We characterize the top trading cycles from individual endowments by Pareto efficiency, group strategy-proofness, reallocation-proofness and balancedness. When there are at least four agents or just two agents, we characterize the top trading cycles from individual endowments by Pareto efficiency, group strategy-proofness and balancedness. When there are three agents, an allocation rule is Pareto efficient, group strategy-proof and balanced if and only if it is a top trading cycles rule from individual endowments or a trading cycles rule with three brokers.

We also study house allocation problems with weak preferences. We show that the serial dictatorship with fixed tie-breaking satisfies weak Pareto efficiency, strategy-proofness, non-bossiness, and consistency. Furthermore, the serial dictatorship with fixed tie-breaking is not Pareto dominated by any Pareto efficient and strategy-proof rule. We also show that the random serial dictatorship with fixed (or random) tiebreaking is equivalent to the top trading cycles from random endowments with fixed (or random) tie-breaking.