CS364A: Algorithmic Game Theory Lecture #10: Kidney Exchange and Stable Matching∗

Many people suffer from kidney failure and need a kidney transplant. Currently, the US waiting list for kidneys has about 100,000 people on it. An old idea, used also for other organs, is deceased donors — when someone dies and is a registered organ donor, their organs can be transplanted into others. One special feature of kidneys is that a healthy person has two of them and can survive just fine with only one of them. This creates the possibility of living organ donors, such as a family member of the patient in need. Unfortunately, having a living kidney donor is not always enough — sometimes a patientdonor pair is incompatible, meaning that the donor’s kidney is unlikely to function well in the patient. Blood and tissue types are the primary culprits for incompatibilities. For example, a patient with O blood type can only receive a kidney from a donor with the same blood type, and similarly an AB donor can only donate to an AB patient. Suppose patient P1 is incompatible with its donor D1 because they have blood types A and B, respectively. Suppose P2 and D2 are in the opposite boat, with blood types B and A, respectively (Figure 1). Even though (P1,D1) may never have met (P2,D2), exchanging donors seems like a pretty good idea — P1 can get its kidney from D2 and P2 from D1. This is called a kidney exchange. A few kidney exchanges were done, on an ad hoc basis, around the beginning of this century. These isolated successes make clear the need for a nationwide kidney exchange, where incompatible patient-donor pairs can register and be matched with others. How should such an exchange be designed? The goal of such an exchange is to thicken the kidney exchange market to enable as many matches as possible. National kidney exchanges sprang up around the middle of last decade. We’ll cover some of the early design ideas for these exchanges, as well as current challenges. These exchanges