Low-Risk Mechanisms for the Kidney Exchange Game

TL;DR

This paper introduces a low-variance, approximately truthful mechanism for the kidney exchange game, reducing risk for participants while maintaining a good approximation ratio, and proposes a framework for similar mechanisms in other problems.

Contribution

It presents a novel low-variance, approximately truthful mechanism for the kidney exchange game, improving practical applicability over previous methods.

Findings

Achieves a 2-approximation with variance at most 2+ε.

Develops a deterministic almost truthful mechanism with bounded gain from deviation.

Potential applicability of the approach to other problems.

Abstract

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 $\Omega(n^2)$, 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 $2+\epsilon$. Interestingly, we could apply our technique to design a deterministic mechanism such that, if an agent deviates from the mechanism, she does not gain more than $2\lceil \log_2 m\rceil$. We call such a mechanism an almost truthful mechanism. Indeed, in a practical scenario, an almost truthful mechanism is likely to imply a truthful mechanism. We believe that our approach can be used to design low risk or almost truthful mechanisms for other problems.