We study problems of allocating objects among people. Some objects may be initially owned and the rest are unowned. Each person needs exactly one object and initially owns at most one object. We drop the common assumption of strict preferences. Without this assumption, it suffices to study...

We revisit the classical object reallocation problem under strict preferences. When attention is constrained to the set of Pareto-efficient rules, it is known that TTC is the only rule that is strategyproof and individually-rational. We hence relax this constraint and consider pair-efficiency. A...

This paper studies the problem of assigning a set of indivisible objects to a set of agents when monetary transfers are not allowed and agents reveal only ordinal preferences, but random assignments are possible. We offer two characterizations of the probabilistic serial mechanism, which assigns...

We search for impartiality in the allocation of objects when monetary transfers are not possible. Our main focus is anonymity. The standard definition requires that if agents' names are permuted, their assignments should be permuted in the same way. Since no rule satisfies this definition in...

We consider house (re)allocation problems (Shapley and Scarf, 1974) with strict preferences. We are concerned with the possibility that a pair of agents may gain by swapping their endowments before the operation of the chosen rule. A rule is called endowments-swapping-proof if it is immune to...

Strategy‐proofness (SP) is a sought‐after property in social choice functions because it ensures that agents have no incentive to misrepresent their private information at both the interim and ex post stages. Group strategy‐proofness (GSP), however, is a notion that is applied to the ex...

We consider house allocation problems (Shapley and Scarf, 1974) with strict preferences. We introduce a new axiom called pre-exchange-proofness, which states that no pair of agents gain by exchanging their endowments with each other prior to the operation of the chosen rule. We establish that a...

We present a survey of the emerging literature on the design of matching markets. We survey the articles on discrete resource allocation problems, their solutions, and their applications in three related domains. The first domain gives the theoretical background regarding the basic models,...

We study the allocation of indivisible objects under the general endowment structures proposed by Pápai (2000) – the consistent inheritance structures – which specify the initial endowment of objects and also the inheritance of remaining objects after subsets of agents are matched and...