  Merging haloes with similar masses (i.e., major mergers) pose significant
challenges for halo finders. We compare five halo finding algorithms' (AHF,
HBT, Rockstar, SubFind, and VELOCIraptor) recovery of halo properties for both
isolated and cosmological major mergers. We find that halo positions and
velocities are often robust, but mass biases exist for every technique. The
algorithms also show strong disagreement in the prevalence and duration of
major mergers, especially at high redshifts (z>1). This raises significant
uncertainties for theoretical models that require major mergers for, e.g.,
galaxy morphology changes, size changes, or black hole growth, as well as for
finding Bullet Cluster analogues. All finders not using temporal information
also show host halo and subhalo relationship swaps over successive timesteps,
requiring careful merger tree construction to avoid problematic mass accretion
histories. We suggest that future algorithms should combine phase-space and
temporal information to avoid the issues presented.
