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. present a @math -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 @math , which is not desirable in a real application. In this paper we resolve this issue by providing a @math -approximation randomized truthful mechanism in which the variance of the utility of each agent is at most @math . 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 @math . 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.
As kidney exchange programs are growing, manipulation by hospitals becomes more of an issue. Assuming that hospitals wish to maximize the number of their own patients who receive a kidney, they may have an incentive to withhold some of their incompatible donor–patient pairs and match them internally, thus harming social welfare. We study mechanisms for two-way exchanges that are strategyproof, i.e., make it a dominant strategy for hospitals to report all their incompatible pairs. We establish lower bounds on the welfare loss of strategyproof mechanisms, both deterministic and randomized, and propose a randomized mechanism that guarantees at least half of the maximum social welfare in the worst case. Simulations using realistic distributions for blood types and other parameters suggest that in practice our mechanism performs much closer to optimal. 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 (, 2010 2]) 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.