  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.
