Hossein Esfandiari University of M aryland Guy Kortsarz Rutgers University 1 Presented by Hedyeh Beyhaghi Cornell University Pairwise Kidney Exchange Kidney transplant is the only treatment for several types of ID: 581048
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Slide1
New Mechanisms for Pairwise Kidney Exchange
Hossein Esfandiari University of Maryland
Guy KortsarzRutgers University
1
*Presented by
Hedyeh
Beyhaghi
Cornell UniversitySlide2
Pairwise Kidney Exchange
Kidney transplant is the only treatment for several types of kidney diseases.Some times, the patient and the donor are not compatible.2
PatientDonorSlide3
Graph Model
3
PatientDonorSlide4
Graph Model
4
Hospital 1
Hospital 2Slide5
Graph Model - Hospitals
5
Hospital 1
Hospital 2Slide6
Mix and Match
6
0
1
1
Ashlagi
, Fischer,
Kash
,
Procaccia
, EC’10
2-approximation truthful mechanismSlide7
Large Utility
Variance7
0
0
1Slide8
Low-Risk Mechanisms
In a real application, agents may not accept a large variance on their utility. 8
Definition: A mechanism is low-risk if the variance of the utility of all agents are . Theorem: There exist a low-risk 2-approximation truthful mechanism for the kidney exchange game, in which the variance of the utility of each agent it at most Slide9
A Low-Risk Mechanism
9
M&MM&MR-MergeR-MergeM&M
M&M
R-Merge
Our main technical contribution:
We can merge the outcome of two independent run of a mechanism
s.t.
for each agent
The expected
utility remains
the same.
The variance of the
utility
decreasesSlide10
Deterministic Algorithms
We modify Mix-and-Match to use at most random bits.For each agent
(Average utility in layer ) = (Average utility in layer ) 10M&MM&MD-Merge
M&M
M&M
D-Merge
D-Merge
leaves
Layer 1
Layer 2
Layer 3Slide11
Deterministic AlgorithmsAlmost truthfulness
11
Theorem: There exist a deterministic 2-approximation mechanism for the kidney exchange game, in which no agent gains more than by hiding her vertices. Slide12
12