An Improved 2-Agent Kidney Exchange Mechanism
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.
KeywordsApproximation Ratio Electronic Commerce Input Graph Maximum Cardinality White Node
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- 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.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.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
- 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.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
- 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.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