Collaborative Research: The Optimal Timing of Kidney Exchanges: A Markov Game Approach

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The objective of this collaborative research project is to provide much more accurate valuations of potential paired kidney exchanges (PKEs). Given an arbitrary-sized PKE, consider the question of when (in terms of patient health) an exchange should occur. An exchange is only possible if every patient in the exchange desires it. This problem is naturally formulated as an infinite-horizon stochastic game. Analyzing this stochastic game reveals several unique features (e.g. the exchange probabilities completely characterize the equilibria, and one can restrict attention to equilibria in which only one patient randomizes). One can then demonstrate a one-to-one correspondence between the equilibria of this game and the feasible points of a certain mixed-integer program. Extensions include iterative approaches to this game, as well as modeling extensions, such as cadaveric kidney arrivals and altruistic donors. This goal will be accomplished in three ways: 1) By comparing quality-adjusted life expectancies, it will value exchanges where the patients and donors are well matched more than others; 2) It will consider dynamic patient health; and 3) It allows patients to determine when the transplantations should occur.Given the severe shortage of kidneys and the potential of paired kidney exchanges, this research can lead to much better matching between patients and donors. Medical researchers, graduate students and undergraduate students will benefit from this research as it blends important aspects of operations research, medicine, and economics.