  We introduce a simple but powerful technique to study processes driven by two
or more reinforcement mechanisms in competition. We apply our method to two
types of models: to non conservative zero range processes on finite graphs, and
to multi-particle random walks with positive and negative reinforcement on the
edges. The results hold for a broad class of reinforcement functions, including
those with superlinear growth. Our technique consists in a comparison of the
original processes with suitable reference models. To implement the comparison
we estimate a Radon-Nikodym derivative on a carefully chosen set of
trajectories. Our results describe the almost surely long time behaviour of the
processes. We also prove a phase transition depending on the strength of the
reinforcement functions.
