1. New Mechanisms for Pairwise Kidney Exchange
Hossein Esfandiari
University of Maryland
Guy Kortsarz
Rutgers University
*Presented by Hedyeh Beyhaghi Cornell University

2. 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.
Patient
Donor

3. Graph Model
Patient
Donor

4. Graph Model
Hospital 1
Hospital 2

5. Graph Model - Hospitals

6. Mix and Match 1 1 Ashlagi, Fischer, Kash, Procaccia, EC’10
2-approximation truthful mechanism 1 1

7. Large Utility Variance1

8. Low-Risk Mechanisms
In a real application, agents may not accept a large variance on their utility.
Definition: A mechanism is low-risk if the variance of the utility of all agents are 𝑂(1).
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 2+𝜖

9. A Low-Risk Mechanism
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 decreases
R-Merge
R-Merge
R-Merge
M&M
M&M
M&M
M&M

10. Deterministic Algorithms
We modify Mix-and-Match to use at most log 𝑛 random bits.
For each agent
(Average utility in layer 𝑖) = (Average utility in layer 𝑖+1 ) ±2
D-Merge
Layer 3
Layer 2
D-Merge
D-Merge
2 log⁡(𝑛) =𝑛 leaves
M&M
M&M
M&M
M&M
Layer 1

11. Deterministic Algorithms Almost truthfulness
Theorem: There exist a deterministic 2-approximation mechanism for the kidney exchange game, in which no agent gains more than 2log⁡(𝑛) by hiding her vertices.