94 research outputs found
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
The size of the core in assignment markets
Assignment markets involve matching with transfers, as in labor markets and
housing markets. We consider a two-sided assignment market with agent types and
stochastic structure similar to models used in empirical studies, and
characterize the size of the core in such markets. Each agent has a randomly
drawn productivity with respect to each type of agent on the other side. The
value generated from a match between a pair of agents is the sum of the two
productivity terms, each of which depends only on the type but not the identity
of one of the agents, and a third deterministic term driven by the pair of
types. We allow the number of agents to grow, keeping the number of agent types
fixed. Let be the number of agents and be the number of types on the
side of the market with more types. We find, under reasonable assumptions, that
the relative variation in utility per agent over core outcomes is bounded as
, where polylogarithmic factors have been suppressed. Further,
we show that this bound is tight in worst case. We also provide a tighter bound
under more restrictive assumptions. Our results provide partial justification
for the typical assumption of a unique core outcome in empirical studies
Lotteries in student assignment: An equivalence result
This paper formally examines two competing methods of conducting a lottery in assigning students to schools, motivated by the design of the centralized high school student assignment system in New York City. The main result of the paper is that a single and multiple lottery mechanism are equivalent for the problem of allocating students to schools in which students have strict preferences and the schools are indifferent. In proving this result, a new approach is introduced, that simplifies and unifies all the known equivalence results in the house allocation literature. Along the way, two new mechanisms---Partitioned Random Priority and Partitioned Random Endowment---are introduced for the house allocation problem. These mechanisms generalize widely studied mechanisms for the house allocation problem and may be appropriate for the many-to-one setting such as the school choice problem.Matching, random assignment
Minimizing regret when dissolving a partnership
We study the problem of dissolving an equal-entitlement partnership when the objective is to minimize maximum regret. We initially focus on the family of linear-pricing mechanisms and derive regret-optimizing strategies. We also demonstrate that there exist linear-pricing mechanisms satisfying ex-post efficiency. Next, we analyze a binary-search mechanism which is ex-post individually rational. We discuss connections with the standard Bayesian-Nash framework for both linear and binary-search mechanisms. On a more general level, we show that if entitlements are unequal, ex-post efficiency and ex-post individual rationality impose significant restrictions on permissible mechanisms. In particular, they rule out both linear and binary-search mechanisms.Partnership dissolution; minimax regret; fair division; allocative efficiency
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