Nash equilibria in the two-player kidney exchange game
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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.
KeywordsKidney exchange Nash equilibrium Social welfare Matching
Mathematics Subject Classification91A80 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.
- 1.Abraham, D.J., Blum, A., Sandholm, T.: Clearing algorithms for barter exchange markets: enabling nationwide kidney exchanges. In: Proceedings of the 8th ACM Conference on Electronic Commerce EC ’07, pp. 295–304, ACM, New York, NY (2007)Google Scholar
- 3.Ashlagi, I., Roth, A.: Individual rationality and participation in large scale, multi-hospital kidney exchange. In: Proceedings of the 12th ACM Conference on Electronic Commerce, EC ’11, pp. 321–322, ACM, New York, NY (2011)Google Scholar
- 4.Ashlagi, I., Roth, A.: Individual rationality and participation in large scale, multi-hospital kidney exchange. Working Paper, http://web.mit.edu/iashlagi/www/papers/LargeScaleKidneyExchange_1_13 (2011)
- 7.Caragiannis, I., Filos-Ratsikas, A., Procaccia, A.D.: An improved 2-agent kidney exchange mechanism. In: Chen, N., Elkind, E., Koutsoupias, E. (eds.) Internet and Network Economics, Vol. 7090 of Lecture Notes in Computer Science. Springer, Berlin, pp. 37–48 (2011)Google Scholar
- 8.Cechlárová, K., Fleiner, T., Manlove, D.: The kidney exchange game. In: Proceedings of the 8th International Symposium on Operational Research SOR, 5, pp. 77–83 (2005)Google Scholar
- 11.Dickerson, J.P., Procaccia, A.D., Sandholm, T.: Price of Fairness in Kidney Exchange. In: Proceedings of the 2014 International Conference on Autonomous Agents and Multi-agent Systems AAMAS ’14, pp. 1013–1020 (2014)Google Scholar
- 14.Hajaj, C., Dickerson, J.P., Hassidim, A., Sandholm, T., Sarne, D.: Strategy-proof and efficient kidney exchange using a credit mechanism. In: Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence, January 25–30, pp. 921–928, Austin, TX (2015)Google Scholar
- 16.Manlove, D.F., O’Malley, G.: Paired and altruistic kidney donation in the UK: algorithms and experimentation. In: Klasing, R., (ed.), Experimental Algorithms, Vol. 7276 of Lecture Notes in Computer Science. Springer, Berlin pp. 271–282 (2012)Google Scholar