  By following the study in [24], we consider an inverse boundary problem for
the mean field game system where a probability density constraint is enforced
on the game agents. That is, we consider the case that reflective boundary
conditions are enforced and hence the population distribution of the game
agents should be treated as a probability measure which preserves both
positivity and the total population. This poses significant challenges for the
corresponding inverse problems in constructing suitable ``probing modes" which
should fulfill such a probability density constraint. We develop an effective
scheme in tackling such a case which is new to the literature.
