  We consider quasi-variational inequalities (QVIs) with general non-local
drivers and related systems of reflected backward stochastic differential
equations (BSDEs) in a Brownian filtration. We show existence and uniqueness of
viscosity solutions to the QVIs by first considering the standard (local)
setting and then applying a contraction argument. In addition, the contraction
argument yields existence and uniqueness of solutions to the related systems of
reflected BSDEs and extends the theory of probabilistic representations of PDEs
in terms of BSDEs to our specific setting.
