  In this paper, we establish propagation of chaos (POC) for doubly mean
reflected backward stochastic differential equations (MRBSDEs). MRBSDEs
differentiate the typical RBSDEs in that the constraint is not on the paths of
the solution but on its law. This unique property has garnered significant
attention since the inception of MRBSDEs. Rather than directly investigating
these equations, we focus on approximating them by interacting particle systems
(IPS). We propose two sets of IPS having mean-field Skorokhod problems,
capturing the dynamics of IPS reflected in a mean-field way. As the dimension
of the IPS tends to infinity, the POC phenomenon emerges, indicating that the
system converges to a limit with independent particles, where each solves the
MRBSDE. Beyond establishing the first POC result for doubly MRBSDEs, we achieve
distinct convergence speeds under different scenarios.
