optimizes his own objective. Two standard assumptions are considered in a Stackelberg game: *perfect knowledge*, that is each agent knows the problem solved by the other agent; *rationale behavior*, namely each agent has no interest in deviating from his own objective.\
Bilevel optimization considers Mixed-Integer Bilevel Linear Programs (MIBLP) where both the leader and the follower solve a combinatorial optimization problem with linear objective function and constraints and with either continuous or integer variables. The first generic Branch and Bound approach for MIBLP was provided in [@BaMo90]. Branch and Cut schemes were introduced in [@DeRa09], [@Den11]. Further approaches were proposed in [@CaMa15; @FiLjMoSi16; @XuWa14]. An improved generic MIBLP solver has been recently proposed in [@FiLjMoSi17]. We refer to [@FiLjMoSi17] and the references therein for an overview on MIBLP solvers and related applications.\
In this paper, we consider the Bilevel Knapsack with Interdiction Constraints (BKP), as introduced in [@Den11]. The problem is an extension of the classic 0-1 Knapsack Problem (KP) (see monographs [@KePfPi04] and [@MarTot90]) formulated as a Stackelberg game. More precisely, the leader and the follower choose items from a common set and hold their own private knapsacks. First, the leader selects some items to be interdicted for the 