239 research outputs found
Envy Freedom and Prior-free Mechanism Design
We consider the provision of an abstract service to single-dimensional
agents. Our model includes position auctions, single-minded combinatorial
auctions, and constrained matching markets. When the agents' values are drawn
from a distribution, the Bayesian optimal mechanism is given by Myerson (1981)
as a virtual-surplus optimizer. We develop a framework for prior-free mechanism
design and analysis. A good mechanism in our framework approximates the optimal
mechanism for the distribution if there is a distribution; moreover, when there
is no distribution this mechanism still performs well.
We define and characterize optimal envy-free outcomes in symmetric
single-dimensional environments. Our characterization mirrors Myerson's theory.
Furthermore, unlike in mechanism design where there is no point-wise optimal
mechanism, there is always a point-wise optimal envy-free outcome.
Envy-free outcomes and incentive-compatible mechanisms are similar in
structure and performance. We therefore use the optimal envy-free revenue as a
benchmark for measuring the performance of a prior-free mechanism. A good
mechanism is one that approximates the envy free benchmark on any profile of
agent values. We show that good mechanisms exist, and in particular, a natural
generalization of the random sampling auction of Goldberg et al. (2001) is a
constant approximation
Guaranteeing Envy-Freeness under Generalized Assignment Constraints
We study fair division of goods under the broad class of generalized
assignment constraints. In this constraint framework, the sizes and values of
the goods are agent-specific, and one needs to allocate the goods among the
agents fairly while further ensuring that each agent receives a bundle of total
size at most the corresponding budget of the agent. Since, in such a constraint
setting, it may not always be feasible to partition all the goods among the
agents, we conform -- as in recent works -- to the construct of charity to
designate the set of unassigned goods. For this allocation framework, we obtain
existential and computational guarantees for envy-free (appropriately defined)
allocation of divisible and indivisible goods, respectively, among agents with
individual, additive valuations for the goods.
We deem allocations to be fair by evaluating envy only with respect to
feasible subsets. In particular, an allocation is said to be feasibly envy-free
(FEF) iff each agent prefers its bundle over every (budget) feasible subset
within any other agent's bundle (and within the charity). The current work
establishes that, for divisible goods, FEF allocations are guaranteed to exist
and can be computed efficiently under generalized assignment constraints.
In the context of indivisible goods, FEF allocations do not necessarily
exist, and hence, we consider the fairness notion of feasible envy-freeness up
to any good (FEFx). We show that, under generalized assignment constraints, an
FEFx allocation of indivisible goods always exists. In fact, our FEFx result
resolves open problems posed in prior works. Further, for indivisible goods and
under generalized assignment constraints, we provide a pseudo-polynomial time
algorithm for computing FEFx allocations, and a fully polynomial-time
approximation scheme (FPTAS) for computing approximate FEFx allocations.Comment: 29 page
Designated school choice
Turkish government changed the high-school placement system for several concerns in 2018. The government as a designer designates and orders schools to each student in terms of location. Then students reveal their preference list over these designated schools. The government desires students to be assigned to as possible as the closest schools. However, students’ preference list is independent from the designation order. In this context, there is an incompatibility between the students’ preferences and the concern of the designer. The thesis will solve this sort of incompatibility. Two-Stage-Generalized-Priority-Mechanism proposed in the thesis finds the set of all possible designer-optimal matchings. At the second-stage, TSGPM yields the best designer-optimal matching in terms of the students’ preference list. At the last part of the thesis, strategic properties of the mechanism will be discusse
Who Should Get Vaccinated? Individualized Allocation of Vaccines Over SIR Network
How to allocate vaccines over heterogeneous individuals is one of the
important policy decisions in pandemic times. This paper develops a procedure
to estimate an individualized vaccine allocation policy under limited supply,
exploiting social network data containing individual demographic
characteristics and health status. We model spillover effects of the vaccines
based on a Heterogeneous-Interacted-SIR network model and estimate an
individualized vaccine allocation policy by maximizing an estimated social
welfare (public health) criterion incorporating the spillovers. While this
optimization problem is generally an NP-hard integer optimization problem, we
show that the SIR structure leads to a submodular objective function, and
provide a computationally attractive greedy algorithm for approximating a
solution that has theoretical performance guarantee. Moreover, we characterise
a finite sample welfare regret bound and examine how its uniform convergence
rate depends on the complexity and riskiness of social network. In the
simulation, we illustrate the importance of considering spillovers by comparing
our method with targeting without network information
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