  The stellar initial mass function (IMF) is believed to be non-universal among
early-type galaxies (ETGs). Parameterizing the IMF with the so-called IMF
mismatch parameter $\alpha_{\rm IMF}$, which is a measure of the stellar
mass-to-light ratio of an ensemble of stars and thus of the 'heaviness' of its
IMF, one finds that for ETGs $\alpha_{\rm e}$ (i.e. $\alpha_{\rm IMF}$
integrated within the effective radius $R_{\rm e}$) increases with $\sigma_{\rm
e}$ (the line-of-sight velocity dispersion $\sigma_{\rm los}$ integrated within
$R_{\rm e}$) and that, within the same ETG, $\alpha_{\rm IMF}$ tends to
decrease outwards. We study the effect of dissipationless (dry) mergers on the
distribution of the IMF mismatch parameter $\alpha_{\rm IMF}$ in ETGs using the
results of binary major and minor merging simulations. We find that dry mergers
tend to make the $\alpha_{\rm IMF}$ profiles of ETGs shallower, but do not
alter significantly the shape of the distributions in the spatially resolved
$\sigma_{\rm los}\alpha_{\rm IMF}$ space. Individual galaxies undergoing dry
mergers tend to decrease their $\alpha_{\rm e}$, due to erosion of $\alpha_{\rm
IMF}$ gradients and mixing with stellar populations with lighter IMF. Their
$\sigma_{\rm e}$ can either decrease or increase, depending on the merging
orbital parameters and mass ratio, but tends to decrease for cosmologically
motivated merging histories. The $\alpha_{\rm e}$-$\sigma_{\rm e}$ relation can
vary with redshift as a consequence of the evolution of individual ETGs: based
on a simple dry-merging model, ETGs of given $\sigma_{\rm e}$ are expected to
have higher $\alpha_{\rm e}$ at higher redshift, unless the accreted satellites
are so diffuse that they contribute negligibly to the inner stellar
distribution of the merger remnant.
