53 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
Partial Strategyproofness: Relaxing Strategyproofness for the Random Assignment Problem
We present partial strategyproofness, a new, relaxed notion of
strategyproofness for studying the incentive properties of non-strategyproof
assignment mechanisms. Informally, a mechanism is partially strategyproof if it
makes truthful reporting a dominant strategy for those agents whose preference
intensities differ sufficiently between any two objects. We demonstrate that
partial strategyproofness is axiomatically motivated and yields a parametric
measure for "how strategyproof" an assignment mechanism is. We apply this new
concept to derive novel insights about the incentive properties of the
probabilistic serial mechanism and different variants of the Boston mechanism.Comment: Working Pape
Aggregate efficiency in random assignment problems
We introduce aggregate efficiency (AE) for random assignments (RA) by requiring higher expected numbers of agents be assigned to their more preferred choices. It is shown that the realizations of any aggregate efficient random assignment (AERA) must be an AE permutation matrix. While AE implies ordinally efficiency, the reverse does not hold. And there is no mechanism treating equals equally while satisfying weak strategyproofness and AE. But, a new mechanism, the reservation-1 (R1), is identified and shown to provide an improvement on grounds of AE over the probabilistic serial mechanism of Bogomolnaia and Moulin (2001). We prove that R1 is weakly strategyproof, ordinally efficient, and weak envy--free. Moreover, the characterization of R1 displays that it is the probabilistic serial mechanism updated by a principle decreed by the Turkish parliament concerning the random assignment of new doctors: Modifying the axioms of Hasimoto, et. al. (2012) characterizing the probabilistic serial mechanism to satisfy this principle, fully characterizes R1
Deep Learning for Two-Sided Matching
We initiate the use of a multi-layer neural network to model two-sided
matching and to explore the design space between strategy-proofness and
stability. It is well known that both properties cannot be achieved
simultaneously but the efficient frontier in this design space is not
understood. We show empirically that it is possible to achieve a good
compromise between stability and strategy-proofness-substantially better than
that achievable through a convex combination of deferred acceptance (stable and
strategy-proof for only one side of the market) and randomized serial
dictatorship (strategy-proof but not stable)
Strategyproofness-Exposing Mechanism Descriptions
A menu description presents a mechanism to player in two steps. Step (1)
uses the reports of other players to describe 's menu: the set of 's
potential outcomes. Step (2) uses 's report to select 's favorite outcome
from her menu. Can menu descriptions better expose strategyproofness, without
sacrificing simplicity? We propose a new, simple menu description of Deferred
Acceptance. We prove that -- in contrast with other common matching mechanisms
-- this menu description must differ substantially from the corresponding
traditional description. We demonstrate, with a lab experiment on two
elementary mechanisms, the promise and challenges of menu descriptions
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