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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
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)
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)
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
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)
Nisan, N.: Introduction to mechanism design for computer scientists. In: Algorithmic Game Theory, ch. 9, pp. 209–241. Cambridge University Press (2007)
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)
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)
Roth, A.E., Sönmez, T., Ünver, M.U.: Kidney exchange. Quarterly Journal of Economics 119, 457–488 (2004)
Roth, A.E., Sönmez, T., Ünver, M.U.: Pairwise kidney exchange. Journal of Economic Theory 125, 151–188 (2005)
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)
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)
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)
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Caragiannis, I., Filos-Ratsikas, A., Procaccia, A.D. (2011). An Improved 2-Agent Kidney Exchange Mechanism. In: Chen, N., Elkind, E., Koutsoupias, E. (eds) Internet and Network Economics. WINE 2011. Lecture Notes in Computer Science, vol 7090. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25510-6_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-25510-6_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-25509-0
Online ISBN: 978-3-642-25510-6
eBook Packages: Computer ScienceComputer Science (R0)