An Improved 2-Agent Kidney Exchange Mechanism

  • Ioannis Caragiannis
  • Aris Filos-Ratsikas
  • Ariel D. Procaccia
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7090)

Abstract

We study a mechanism design version of matching computation in graphs that models the game played by hospitals participating in pairwise kidney exchange programs. We present a new randomized matching mechanism for two agents which is truthful in expectation and has an approximation ratio of 3/2 to the maximum cardinality matching. This is an improvement over a recent upper bound of 2 [Ashlagi et al., EC 2010] and, furthermore, our mechanism beats for the first time the lower bound on the approximation ratio of deterministic truthful mechanisms. We complement our positive result with new lower bounds. Among other statements, we prove that the weaker incentive compatibility property of truthfulness in expectation in our mechanism is necessary; universally truthful mechanisms that have an inclusion-maximality property have an approximation ratio of at least 2.

Keywords

Approximation Ratio Electronic Commerce Input Graph Maximum Cardinality White Node 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Abraham, D., Blum, A., Sandholm, T.: Clearing algorithms for barter exchange markets: enabling nationwide kidney exchanges. In: Proc. of the 8th ACM Conference on Electronic Commerce (EC), pp. 295–304 (2007)Google Scholar
  2. 2.
    Ashlagi, I., Fischer, F., Kash, I.A., Procaccia, A.D.: Mix and match. In: Proc. of the 11th ACM Conference on Electronic Commerce (EC), pp. 305–314 (2010)Google Scholar
  3. 3.
    Ashlagi, I., Roth, A.E.: Individual rationality and participation in large scale, multi-hospital kidney exchange. In: Proc. of the 12th ACM Conference on Electronic Commerce (EC), p. 321 (2011), http://web.mit.edu/iashlagi/www/papers/LargeScaleKidneyExchange_1_13.pdf
  4. 4.
    Biró, P., Manlove, D.F., Rizzi, R.: Maximum weight cycle packing in directed graphs, with application to kidney exchange programs. Discrete Mathematics, Algorithms, and Applications 1(4), 499–517 (2009)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Nisan, N.: Introduction to mechanism design for computer scientists. In: Algorithmic Game Theory, ch. 9, pp. 209–241. Cambridge University Press (2007)Google Scholar
  6. 6.
    Procaccia, A.D., Tennenholtz, M.: Approximate mechanism design without money. In: Proc. of the 10th ACM Conference on Electronic Commerce (EC), pp. 177–186 (2009)Google Scholar
  7. 7.
    Rees, M., Pelletier, R., Mulgaonkar, S., Laskow, D., Nibhanupudy, B., Kopke, J., Roth, A.E., Ünver, M.U., Sandholm, T., Rogers, J.: Report from a 60 transplant center multiregional kidney paired donation program. Transplantation 86(2S), 1 (2008)CrossRefGoogle Scholar
  8. 8.
    Roth, A.E., Sönmez, T., Ünver, M.U.: Kidney exchange. Quarterly Journal of Economics 119, 457–488 (2004)CrossRefMATHGoogle Scholar
  9. 9.
    Roth, A.E., Sönmez, T., Ünver, M.U.: Pairwise kidney exchange. Journal of Economic Theory 125, 151–188 (2005)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Roth, A.E., Sönmez, T., Ünver, M.U.: Efficient kidney exchange: coincidence of wants in markets with compatibility-based preferences. American Economic Review 97, 828–851 (2007)CrossRefGoogle Scholar
  11. 11.
    Saidman, S., Roth, A.E., Sönmez, T., Ünver, M.U., Delmonico, F.: Increasing the opportunity of live kidney donation by matching for two- and three-way exchanges. Transplantation 81(5), 773 (2006)CrossRefGoogle Scholar
  12. 12.
    Sönmez, T., Ünver, M.U.: Market design for kidney exchange. In: Neeman, Z., Niederle, N., Vulkan, M. (eds.) Oxford Handbook of Market Design, Oxford University Press (to appear)Google Scholar
  13. 13.
    Toulis, P., Parkes, D.: A random graph model of kidney exchanges: efficiency, individual-rationality and incentives. In: Proc. of the 12th ACM Conference on Electronic Commerce (EC), pp. 323–332 (2011)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Ioannis Caragiannis
    • 1
  • Aris Filos-Ratsikas
    • 1
  • Ariel D. Procaccia
    • 2
  1. 1.Department of Computer Engineering and InformaticsUniversity of PatrasRioGreece
  2. 2.Computer Science DepartmentCarnegie Mellon UniversityPittsburghUSA

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