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

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

Graph Model Patient Donor

Graph Model Hospital 1 Hospital 2

Graph Model - Hospitals

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

Large Utility Variance 1

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

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

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

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.