House allocation with fractional endowments

This paper studies a generalization of the well known house allocation problem in which agents may own fractions of different houses summing to an arbitrary quantity, but have use for only the equivalent of one unit of a house. It departs from the classical model by assuming that arbitrary quantities of each house may be available to the market. Justified envy considerations arise when two agents have the same initial endowment, or when an agent is in some sense disproportionately rewarded in comparison to her peers. For this general model, an algorithm is designed to find a fractional allocation of houses to agents that satisfies ordinal efficiency, individual rationality, and no justified envy. The analysis extend to the full preference domain. Individual rationality, ordinal efficiency, and no justified envy conflict with weak strategyproofness. Moreover, individual rationality, ordinal efficiency and strategyproofness are shown to be incompatible. Finally, two reasonable notions of envy-freeness, no justified envy and equal-endowment no envy, conflict in the presence of ordinal efficiency and individual rationality. All of the impossibility results hold in the strict preference domain.house allocation, fractional endowments, fairness, individual rationality

House allocation with fractional endowments

This paper studies a generalization of the well known house allocation problem in which agents may own fractions of different houses summing to an arbitrary quantity, but have use for only the equivalent of one unit of a house. It departs from the classical model by assuming that arbitrary quantities of each house may be available to the market. Justified envy considerations arise when two agents have the same initial endowment, or when an agent is in some sense disproportionately rewarded in comparison to her peers. For this general model, an algorithm is designed to find a fractional allocation of houses to agents that satisfies ordinal efficiency, individual rationality, and no justified envy. The analysis extend to the full preference domain. Individual rationality, ordinal efficiency, and no justified envy conflict with weak strategyproofness. Moreover, individual rationality, ordinal efficiency and strategyproofness are shown to be incompatible. Finally, two reasonable notions of envy-freeness, no justified envy and equal-endowment no envy, conflict in the presence of ordinal efficiency and individual rationality. All of the impossibility results hold in the strict preference domain

Random assignment with multi-unit demands

We consider the multi-unit random assignment problem in which agents express preferences over objects and objects are allocated to agents randomly based on the preferences. The most well-established preference relation to compare random allocations of objects is stochastic dominance (SD) which also leads to corresponding notions of envy-freeness, efficiency, and weak strategyproofness. We show that there exists no rule that is anonymous, neutral, efficient and weak strategyproof. For single-unit random assignment, we show that there exists no rule that is anonymous, neutral, efficient and weak group-strategyproof. We then study a generalization of the PS (probabilistic serial) rule called multi-unit-eating PS and prove that multi-unit-eating PS satisfies envy-freeness, weak strategyproofness, and unanimity.Comment: 17 page

Allocation of an indivisible object on the full preference domain: Axiomatic characterizations

We study the problem of allocating an indivisible object to one of several agents on the full preference domain when monetary transfers are not allowed. Our main requirement is strategy-proofness. The other properties we seek are Pareto optimality, non-dictatorship, and non-bossiness. We provide characterizations of strategy-proof rules that satisfy Pareto optimality and non-bossiness, non-dictatorship and non-bossiness, and Pareto optimality and non-dictatorship. As a consequence of these characterizations, we show that a strategy-proof rule cannot satisfy Pareto optimality, non-dictatorship, and non-bossiness simultaneously

Organizing time banks: Lessons from matching markets

A time bank is a group of people that set up a common platform to trade services among themselves. There are several well-known problems associated with this type of time banking, e.g., high overhead costs and difficulties to identify feasible trades. This paper constructs a non-manipulable mechanism that selects an individually rational and time-balanced allocation which maximizes exchanges among the members of the time bank (and those allocations are efficient). The mechanism works on a domain of preferences where agents classify services as unacceptable and acceptable (and for those services agents have specific upper quotas representing their maximum needs)

Competitive Equilibrium in the Random Assignment Problem

This paper studies the problem of random assignment with fractional endowments. In the random assignment problem, a number of objects has to be assigned to a number of agents. Though the objects are indivisible, an assignment can be probabilistic: it can give an agent some probability of getting an object. Fractional endowments complicate the matter because the assignment has to make an agent weakly better off than his endowment. I first formulate an exchange economy that resembles the random assignment problem and prove the existence of competitive equilibrium in this economy. I then propose a pseudo-market mechanism for the random assignment problem that is based on the competitive equilibrium. This mechanism is individually rational, Pareto Optimal and justified envy-free but not incentive compatible

Organizing Time Exchanges: Lessons from Matching Markets

This paper considers time exchanges via a common platform (e.g., markets for exchanging time units, positions at education institutions, and tuition waivers). There are several problems associated with such markets, e.g., imbalanced outcomes, coordination problems, and inefficiencies. We model time exchanges as matching markets and construct a non-manipulable mechanism that selects an individually rational and balanced allocation which maximizes exchanges among the participating agents (and those allocations are efficient). This mechanism works on a preference domain whereby agents classify the goods provided by other participating agents as either unacceptable or acceptable, and for goods classified as acceptable agents have specific upper quotas representing their maximum needs