  The goal of a kidney exchange program (KEP) is to maximize number of
transplants within a pool of incompatible patient-donor pairs by exchanging
donors. A KEP can be modelled as a maximum matching problem in a graph. A KEP
between incompatible patient-donor from pools of several hospitals, regions or
countries has the potential to increase the number of transplants. These
entities aim is to maximize the transplant benefit for their patients, which
can lead to strategic behaviours. Recently, this was formulated as a
non-cooperative two-player game and the game solutions (equilibria) were
characterized when the entities objective function is the number of their
patients receiving a kidney. In this paper, we generalize these results for
$N$-players and discuss the impact in the game solutions when transplant
information quality is introduced. Furthermore, the game theory model is
analyzed through computational experiments on instances generated through the
Canada Kidney Paired Donation Program. These experiments highlighting the
importance of using the concept of Nash equilibrium, as well as, the
anticipation of the necessity to further research for supporting police makers
once measures on transplant quality are available.

Computer Science and Game Theory