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Valuing Prearranged Paired Kidney Exchanges: A Stochastic Game Approach

Author

Listed:
  • Murat Kurt

    () (University of Pittsburgh)

  • Mark S. Roberts

    () (University of Pittsburgh)

  • Andrew J. Schaefer

    () (University of Pittsburgh)

  • M. Utku Ünver

    (Boston College)

Abstract

End-stage renal disease (ESRD) is the ninth-leading cause of death in the U.S. Transplantation is the most viable renal replacement therapy for ESRD patients, but there is a severe disparity between the demand for kidneys for transplantation and the supply. This shortage is further complicated by incompatibilities in blood-type and antigen matching between patient-donor pairs. Paired kidney exchange (PKE), a cross-exchange of kidneys among incompatible patient-donor pairs, overcomes many difficulties in matching patients with incompatible donors. In a typical PKE, transplantation surgeries take place simultaneously so that no donor may renege after her intended recipient receives the kidney. Therefore, in a PKE, the occurrence of a transplantation requires compatibility among the pairs' willingnesses to exchange. We consider an arbitrary number of autonomous patients with probabilistically evolving health statuses in a prearranged PKE, and model their transplant timing decisions as a discrete-time non-zero-sum noncooperative stochastic game. We explore necessary and sufficient conditions for patients' decisions to be a stationary-perfect equilibrium, and formulate a mixed-integer linear programming representation of equilibrium constraints, which provides a characterization of the socially optimal stationary-perfect equilibria. We carefully calibrate our model using a large scale nationally representative clinical data, and empirically confirm that randomized strategies, which are less consistent with clinical practice and rationality of the patients, do not yield a significant social welfare gain over pure strategies. We also quantify the social welfare loss due to patient autonomy and demonstrate that maximizing the number of transplants may be undesirable. Our results highlight the importance of the timing of an exchange and the disease severity on matching patient-donor pairs.

Suggested Citation

  • Murat Kurt & Mark S. Roberts & Andrew J. Schaefer & M. Utku Ünver, 2011. "Valuing Prearranged Paired Kidney Exchanges: A Stochastic Game Approach," Boston College Working Papers in Economics 785, Boston College Department of Economics, revised 14 Oct 2011.
  • Handle: RePEc:boc:bocoec:785
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    References listed on IDEAS

    as
    1. Tayfun Sönmez & Alvin E. Roth & M. Utku Ünver, 2007. "Efficient Kidney Exchange: Coincidence of Wants in Markets with Compatibility-Based Preferences," American Economic Review, American Economic Association, pages 828-851.
    2. Roth, Alvin E. & Sonmez, Tayfun & Utku Unver, M., 2005. "Pairwise kidney exchange," Journal of Economic Theory, Elsevier, vol. 125(2), pages 151-188, December.
    3. P. Jean-Jacques Herings & Ronald J. A. P. Peeters, 2003. "Equilibrium Selection In Stochastic Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 5(04), pages 307-326.
    4. Saidman, Susan L. & Roth, Alvin E. & Sonmez, Tayfun & Unver, M. Utku & Delmonico, Francis L., 2014. "Increasing the Opportunity of Live Kidney Donation by Matching for Two and Three Way Exchanges," MPRA Paper 58247, University Library of Munich, Germany.
    5. Alvin E. Roth & Tayfun Sönmez, 2005. "A Kidney Exchange Clearinghouse in New England," American Economic Review, American Economic Association, pages 376-380.
    6. Alvin E. Roth & Tayfun Sönmez & M. Utku Ünver, 2004. "Kidney Exchange," The Quarterly Journal of Economics, Oxford University Press, vol. 119(2), pages 457-488.
    7. Oguzhan Alagoz & Lisa M. Maillart & Andrew J. Schaefer & Mark S. Roberts, 2007. "Choosing Among Living-Donor and Cadaveric Livers," Management Science, INFORMS, pages 1702-1715.
    8. Herings, P. Jean-Jacques & Peeters, Ronald J. A. P., 2004. "Stationary equilibria in stochastic games: structure, selection, and computation," Journal of Economic Theory, Elsevier, pages 32-60.
    9. Tayfun Sönmez & Alvin E. Roth & M. Utku Ünver, 2007. "Efficient Kidney Exchange: Coincidence of Wants in Markets with Compatibility-Based Preferences," American Economic Review, American Economic Association, pages 828-851.
    10. Pakes, Ariel & McGuire, Paul, 2001. "Stochastic Algorithms, Symmetric Markov Perfect Equilibrium, and the 'Curse' of Dimensionality," Econometrica, Econometric Society, vol. 69(5), pages 1261-1281, September.
    11. Jae-Hyeon Ahn & John C. Hornberger, 1996. "Involving Patients in the Cadaveric Kidney Transplant Allocation Process: A Decision-Theoretic Perspective," Management Science, INFORMS, pages 629-641.
    12. Roth, Alvin E. & Sonmez, Tayfun & Unver, Utku & Delmonico, Francis & Saidman, Susan L., 2014. "Utilizing List Exchange and Non-directed Donation through “Chain” Paired Kidney Donations," MPRA Paper 58246, University Library of Munich, Germany.
    13. M. Utku Ünver, 2010. "Dynamic Kidney Exchange," Review of Economic Studies, Oxford University Press, vol. 77(1), pages 372-414.
    14. Stefanos A. Zenios, 2002. "Optimal Control of a Paired-Kidney Exchange Program," Management Science, INFORMS, pages 328-342.
    15. Xuanming Su & Stefanos Zenios, 2004. "Patient Choice in Kidney Allocation: The Role of the Queueing Discipline," Manufacturing & Service Operations Management, INFORMS, pages 280-301.
    16. Howard, David H., 2002. "Why do transplant surgeons turn down organs?: A model of the accept/reject decision," Journal of Health Economics, Elsevier, vol. 21(6), pages 957-969, November.
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    More about this item

    Keywords

    medical decision making; paired kidney exchange; game theory; Markov decision processes; integer programming;

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • I11 - Health, Education, and Welfare - - Health - - - Analysis of Health Care Markets

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