58,534 research outputs found
The Pareto Frontier for Random Mechanisms
We study the trade-offs between strategyproofness and other desiderata, such
as efficiency or fairness, that often arise in the design of random ordinal
mechanisms. We use approximate strategyproofness to define manipulability, a
measure to quantify the incentive properties of non-strategyproof mechanisms,
and we introduce the deficit, a measure to quantify the performance of
mechanisms with respect to another desideratum. When this desideratum is
incompatible with strategyproofness, mechanisms that trade off manipulability
and deficit optimally form the Pareto frontier. Our main contribution is a
structural characterization of this Pareto frontier, and we present algorithms
that exploit this structure to compute it. To illustrate its shape, we apply
our results for two different desiderata, namely Plurality and Veto scoring, in
settings with 3 alternatives and up to 18 agents.Comment: Working Pape
Alternative characterizations of Boston mechanism
Kojima and Ünver (2011) are the first to characterize the class of mechanisms coinciding with the Boston mechanism for some priority order. By mildly strengthening their central axiom, we are able to pin down the Boston mechanism outcome for every priority order. Our main result shows that a mechanism is outcome equivalent to the Boston mechanism at every priority if and only if it respects both preference rankings and priorities and satisfies individual rationality for schools. In environments where each student is acceptable to every school, respecting both preference rankings and priorities is enough to characterize the Boston mechanism
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
Cake Cutting Algorithms for Piecewise Constant and Piecewise Uniform Valuations
Cake cutting is one of the most fundamental settings in fair division and
mechanism design without money. In this paper, we consider different levels of
three fundamental goals in cake cutting: fairness, Pareto optimality, and
strategyproofness. In particular, we present robust versions of envy-freeness
and proportionality that are not only stronger than their standard
counter-parts but also have less information requirements. We then focus on
cake cutting with piecewise constant valuations and present three desirable
algorithms: CCEA (Controlled Cake Eating Algorithm), MEA (Market Equilibrium
Algorithm) and CSD (Constrained Serial Dictatorship). CCEA is polynomial-time,
robust envy-free, and non-wasteful. It relies on parametric network flows and
recent generalizations of the probabilistic serial algorithm. For the subdomain
of piecewise uniform valuations, we show that it is also group-strategyproof.
Then, we show that there exists an algorithm (MEA) that is polynomial-time,
envy-free, proportional, and Pareto optimal. MEA is based on computing a
market-based equilibrium via a convex program and relies on the results of
Reijnierse and Potters [24] and Devanur et al. [15]. Moreover, we show that MEA
and CCEA are equivalent to mechanism 1 of Chen et. al. [12] for piecewise
uniform valuations. We then present an algorithm CSD and a way to implement it
via randomization that satisfies strategyproofness in expectation, robust
proportionality, and unanimity for piecewise constant valuations. For the case
of two agents, it is robust envy-free, robust proportional, strategyproof, and
polynomial-time. Many of our results extend to more general settings in cake
cutting that allow for variable claims and initial endowments. We also show a
few impossibility results to complement our algorithms.Comment: 39 page
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