  This paper is concerned with the switching game of a one-dimensional backward
stochastic differential equation (BSDE). The associated Bellman-Isaacs equation
is a system of matrix-valued BSDEs living in a special unbounded convex domain
with reflection on the boundary along an oblique direction. In this paper, we
show the existence of an adapted solution to this system of BSDEs with oblique
reflection by the penalization method, the monotone convergence, and the a
priori estimates.
