A game-theoretic approach to donor kidney sharing.

Graft survival in renal transplantation is a function, amongst other things, of the degree of histocompatibility lymphocyte-A (HLA) tissue matching achieved between donor and recipient. Yet a donor procured at centre A might match a transplant candidate at centre B and vice versa. This raises the question of whether, and under what circumstances, surgeons will offer and exchange donor kidneys and gain from such trade in terms of graft survival. We analyse the problem in a game-theoretic framework where the choice of strategy 'to offer or not?' is evaluated in the context of the uncertainty of reciprocation by the other player(s) in the game. The equilibrium solution to a number of variations of the game is predicted to be non-cooperation resulting in collectively sub-optimal graft survival rates. Some policy options for improving cooperation are considered including exchange incentives and coercive measures.