  Let G be a compact Lie group acting on a smooth manifold M. In this paper, we
consider Meinrenken's G-equivariant bundle gerbe connections on M as objects in
a 2-groupoid. We prove this 2-category is equivalent to the 2-groupoid of gerbe
connections on the differential quotient stack associated to M, and isomorphism
classes of G-equivariant gerbe connections are classified by degree three
differential equivariant cohomology. Finally, we consider the existence and
uniqueness of conjugation-equivariant gerbe connections on compact semisimple
Lie groups.
