  We study the problem of allocating divisible resources among $n$ agents,
hopefully in a fair and efficient manner. With the presence of strategic
agents, additional incentive guarantees are also necessary, and the problem of
designing fair and efficient mechanisms becomes much less tractable. While
there are flourishing positive results against strategic agents for homogeneous
divisible items, very few of them are known to hold in cake cutting.
  We show that the Maximum Nash Welfare (MNW) mechanism, which provides
desirable fairness and efficiency guarantees and achieves an \emph{incentive
ratio} of $2$ for homogeneous divisible items, also has an incentive ratio of
$2$ in cake cutting. Remarkably, this result holds even without the free
disposal assumption, which is hard to get rid of in the design of truthful cake
cutting mechanisms.
  Moreover, we show that, for cake cutting, the Partial Allocation (PA)
mechanism proposed by Cole et al. \cite{DBLP:conf/sigecom/ColeGG13}, which is
truthful and $1/e$-MNW for homogeneous divisible items, has an incentive ratio
between $[e^{1 / e}, e]$ and when randomization is allowed, can be turned to be
truthful in expectation. Given two alternatives for a trade-off between
incentive ratio and Nash welfare provided by the MNW and PA mechanisms, we
establish an interpolation between them for both cake cutting and homogeneous
divisible items.
  Finally, we study the existence of fair mechanisms with a low incentive ratio
in the connected pieces setting. We show that any envy-free cake cutting
mechanism with the connected pieces constraint has an incentive ratio of
$\Theta(n)$.
