A Bounded-Risk Mechanism for the Kidney Exchange Game
In this paper we consider the pairwise kidney exchange game. This game naturally appears in situations that some service providers benefit from pairwise allocations on a network, such as the kidney exchanges between hospitals.
Ashlagi et al.  present a 2-approximation randomized truthful mechanism for this problem. This is the best known result in this setting with multiple players. However, we note that the variance of the utility of an agent in this mechanism may be as large as \(\varOmega (n^2)\), which is not desirable in a real application. In this paper we resolve this issue by providing a 2-approximation randomized truthful mechanism in which the variance of the utility of each agent is at most \(2+\epsilon \).
As a side result, we apply our technique to design a deterministic mechanism such that, if an agent deviates from the mechanism, she does not gain more than \(2\lceil \log _2 m\rceil \).
- 1.Ashlagi, I., et al.: Mix and match: a strategyproof mechanism for multi-hospital kidney exchange. Games Econ. Behav. (2013)Google Scholar
- 2.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, pp. 321–322. ACM (2011)Google Scholar
- 5.Dughmi, S., Roughgarden, T., Vondrák, J., Yan, Q.:An approximately truthful-in-expectation mechanism for combinatorial auctions using value queries. arXiv preprint arXiv:1109.1053 (2011)
- 7.Lesca, J., Perny, P.: Almost-truthful mechanisms for fair social choice functions. In: ECAI, pp. 522–527 (2012)Google Scholar
- 9.Sonmez, T., Unver, M.U.: Market design for kidney exchange. In: The Handbook of Market Design, p. 93 (2013)Google Scholar