- Friday 7 December 2018
- Dr Jorgen Kratz; University of York
The focus of this paper is a kidney exchange problem in which a planner sorts patients into "priority groups" based on, for example, the urgency of their conditions. The planner may choose to allow cyclical exchanges, chains, altruistically unbalanced exchanges and transplants across the blood group barrier. I introduce a class of matchings called "priority group matchings", which give priority to patients in higher priority groups. Priority group matchings are always Pareto efficient no matter how patients are sorted into priority groups or how the kidney exchange program is designed by the planner. I also present a computational method for finding priority group matchings. Threshold matchings are a subclass of priority group matchings that prioritise patients above some threshold (in terms of, for example, urgency). I show that a higher threshold leads to a (weakly) higher number of transplants. Threshold matchings generalise several well-known classes of matchings, including maximum matchings and priority matchings.