A theoretical and computational equilibria analysis of a multi-player kidney exchange program

A main aim of kidney exchange programs (KEPs) is to maximize the number of transplants within a pool of incompatible patient-donor pairs by exchanging donors. A KEP involving pairs from pools of several hospitals, regions, or countries has the potential to increase the number of transplants. These entities may behave strategically and strive to maximize the transplant benefit for their patients. Recently, a decentralized non-cooperative game was formulated to model this situation, and the game solutions (equilibria) for the 2-player case were characterized when each player's utility is the number of her patients receiving a kidney and exchanges are restricted to pairwise. In this paper, we generalize the result on the existence of social welfare equilibra for N-players and discuss the impact in the game solutions when transplant information quality is introduced, changing the players’ utilities. Furthermore, the game theory model is analyzed through computational experiments on instances generated by leveraging data of the Canadian Kidney Paired Donation Program. These experiments highlight the importance of using the concept of Nash equilibrium, as well as, the need of further research to assist policy makers once measures on transplant quality are available.