  Kidney exchange programs have been developed to overcome the compatibility
challenges for the patient with incompatible donors in kidney transplantation.
A registry of such incompatible donor-recipient pairs is created, and
compatibility is achieved through the exchange of donors. Single-center kidney
exchange registries do not have a significant pool size for achieving the full
benefits of the kidney exchange program. Thus multi-registry exchange
transplants seem to be a natural way forward. There are various challenges in
multi-registry exchange programs, such as different constraints for each
registry, varying bound on cycle lengths, and data sharing among registries.
Researchers have proposed different merging mechanisms with a sequential
merger, full merger with fair allocations, and full merger without any
restrictions. To form a stable multi-registry sharing mechanism, registries
should be individually rational both in the long run as well as in the short
run. In this paper, an Integer Programming model for a multi-registry exchange
program has been proposed with individual rationality constraints for each
registry. A simulation study is conducted to compare the benefits of
multi-registry programs with individual registry allocations on Indian data,
and multiple analyses have been done. It was concluded that registries with
lower arrival rates could benefit 7-9\% in terms of the number of transplants
and 4-6\% in terms of quality of matches in a typical kidney exchange registry.
Registry with more hard to match patients will benefit significantly larger
than registries with more easy to match patients.
