  We present for the first time a suite of cosmological simulations for a
particular class of interacting Dark Energy cosmologies characterised by a
background expansion history constrained to be indistinguishable from $\Lambda
$CDM. Such Constrained Interacting Dark Energy scenario -- or CIDER -- has been
recently proposed by Barros et al. 2019 and has the appealing feature of
suppressing structure formation at late times, thereby possibly alleviating the
persisting $\sigma _{8}$ tension while leaving background observables
unaffected. A crucial step to assess the viability of such scenarios is then
represented by quantifying their impact on structure formation at non-linear
scales, which is what we start investigating with the simulations discussed in
the present work. We show that -- for reasonable parameter choices -- the
reconstructed scalar potential is close to an exponential for most of the
matter dominated epoch, and that the nonlinear evolution of structures in these
models imprints specific footprints on matter and halo statistics that may
allow to break degeneracies with standard cosmological parameters.
