  This paper is concerned with the value function approach to multiobjective
bilevel optimization which exploits a lower level frontier-type mapping in
order to replace the hierarchical model of two interdependent multiobjective
optimization problems by a single-level multiobjective optimization problem. As
a starting point, different value-function-type reformulations are suggested
and their relations are discussed. Here, we focus on the situations where the
lower level problem is solved up to efficiency or weak efficiency, and an
intermediate solution concept is suggested as well. We study the
graph-closedness of the associated efficiency-type and frontier-type mappings.
These findings are then used for two purposes. First, we investigate existence
results in multiobjective bilevel optimization. Second, for the derivation of
necessary optimality conditions via the value function approach, it is inherent
to differentiate frontier-type mappings in a generalized way. Here, we are
concerned with the computation of upper coderivative estimates for the
frontier-type mapping associated with the setting where the lower level problem
is solved up to weak efficiency. We proceed in two ways, relying, on the one
hand, on a weak domination property and, on the other hand, on a scalarization
approach. Throughout the paper, illustrative examples visualize our findings,
the necessity of crucial assumptions, and some flaws in the related literature.
