Mathematical Programming

, Volume 161, Issue 1–2, pp 389–417 | Cite as

Nash equilibria in the two-player kidney exchange game

  • Margarida Carvalho
  • Andrea Lodi
  • João Pedro Pedroso
  • Ana Viana
Full Length Paper Series A


Kidney exchange programs have been set in several countries within national, regional or hospital frameworks, to increase the possibility of kidney patients being transplanted. For the case of hospital programs, it has been claimed that hospitals would benefit if they collaborated with each other, sharing their internal pools and allowing transplants involving patients of different hospitals. This claim led to the study of multi-hospital exchange markets. We propose a novel direction in this setting by modeling the exchange market as an integer programming game. The analysis of the strategic behavior of the entities participating in the kidney exchange game allowed us to prove that the most rational game outcome maximizes the social welfare and that it can be computed in polynomial time.


Kidney exchange Nash equilibrium Social welfare  Matching 

Mathematics Subject Classification

91A80 05C85 90C27 



We are indebted with Nicolás Stier-Moses for reading a preliminary version of the paper and providing useful feedbacks. This work was partially supported by national funds through Fundação para a Ciência e a Tecnologia (FCT) within projects PTDC/IIMGES/2830/ 2014 (mKEP - Models and optimisation algorithms for multi-country kidney exchange programs). The first author acknowledges the support of Fundação para a Ciência e a Tecnologia (FCT) through a PhD grant number SFRH/BD/79201/2011 (POPH/FSE program). The second author acknowledges the support of MIUR under the PRIN2012 grant. We would like to thank the anonymous referees for their valuable comments that significantly contributed to the improvement of this work.


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Copyright information

© Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society 2016

Authors and Affiliations

  • Margarida Carvalho
    • 1
  • Andrea Lodi
    • 2
    • 3
  • João Pedro Pedroso
    • 1
  • Ana Viana
    • 4
  1. 1.INESC TEC and Faculdade de Ciências daUniversidade do PortoPortoPortugal
  2. 2.University of BolognaBolognaItaly
  3. 3.École Polytechnique de MontréalMontrealCanada
  4. 4.INESC TEC and Instituto Superior de Engenharia do PortoPortoPortugal

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