  In this paper, we deal with the solutions of systems of PDEs with bilateral
inter-connected obstacles of min-max and max-min types. These systems arise
naturally in stochastic switching zero-sum game problems. We show that when the
switching costs of one side are regular, the solutions of the min-max and
max-min systems coincide. Then, this common viscosity solution is related to a
multi-dimensional doubly reflected BSDE with bilateral interconnected
obstacles. Finally, its relationship with the the values of a zero-sum
switching game is studied.
