  The paper studies a multi-dimensional mean-field reflected backward
stochastic differential equation (MF-RBSDE) with a reflection constraint
depending on both the value process $Y$ and its distribution $[Y]$. We
establish the existence, uniqueness and the stability of the solution of
MF-RBSDE. We also investigate the associated interacting particle systems of
RBSDEs and prove a propagation of chaos result. Lastly, we investigate the
relationship between MF-RBSDE and an obstacle problem for partial differential
equations in Wasserstein space within a Markovian framework. Our work provides
a connection between the work of Briand et al. (2020) on BSDEs with normal
reflection in law and the work of Gegout-Petit and Pardoux (1996) on classical
multi-dimensional RBSDEs.
