Reallocation Mechanisms Under Distributional Constraints in the Full Preference Domain

We study the problem of reallocating indivisible goods among a set of agents in one-sided matching market, where the feasible set for each good is subject to an associated distributional matroid or M-convex constraint. Agents’ preferences are allowed to have ties and not all the agents have initial endowments. We present feasible, Pareto optimal, strategy-proof mechanisms for the problems with matroid or M-convex constraints. Strategy-proofness is proved based on new structural properties over first choice graphs, which should be of independent interest. These mechanisms strictly generalize the best-known mechanism for non-strict preferences [21] with all desired properties carried over.