On the equivalency between a linear bilevel programming problem and linear optimization over the efficient set

where x, c, c ∈ R1 , x, c, c ∈ R2 , b ∈ R, A1 is an m × n1 matrix, A2 is an m × n2 matrix, and T denotes the transposition. Such problems may arise when there are two decision makers at different hierarchical levels having joint constraints and different and possibly conflicting objectives. The decision-making process is sequential. The leader controlling the variables of x has the first choice restricting thus the decision space of the follower, who controls the variables of x. The second problem of the investigation connects with the multicriteria linear programming problem max Cx s.t. x ∈ P, (1.4)