Transplants of donated stem cells save the lives of many patients with blood diseases. Donation is somewhat painful, but rarely has lasting adverse effects. Patients can accept transplants only from donors with compatible immune systems. Those lacking a sibling match must seek donations from the population at large. The probability that two persons of the same race are compatible is less than 1/10,000. Health authorities maintain a registry of several million genetically-tested potential donors who have agreed to donate if asked. We study the peculiar structure of voluntary public good provision represented by the registry, and compare the marginal benefits and marginal costs of expanding the registry.

The plight of multiracial leukemia patients who are unable to find matching stem cell donors has received much media attention. These news stories, while dramatic, are short on statistical information and long on misconceptions. We apply simple probability theory, the genetics of sexual diploid reproduction, and the theory of public goods to produce estimates of the probabilities that multiracial patients will find matching donors in the existing registry. We then compute the benefits and costs of registering more potential donors of single and mixed races. c