relies on an ILP solver along its steps. We discuss the steps of the algorithm in the following. The corresponding pseudo code is then provided.

Step 1 {#TheStep1}
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### Handling the possible non-existence of a critical item {#NOcrit}

We first consider the case where there does not exist a critical item in $KP^{LP}(x^*)$. Thus, the follower will select all available items which are not interdicted by the leader and an optimal solution of BKP is found by solving the following problem $NCR$.\
$$\begin{aligned}
\text{min}\quad & \sum\limits_{i=1}^{n} p_{i}(1-x_{i})  \label{eq:ObjFirst}\\
    \text{subject to}\quad
    & \sum\limits_{i=1}^{n} v_{i}x_{i} \leq C_u \label{eq:capLFirst}\\
    & \sum\limits_{i=1}^{n} w_{i}(1-x_{i}) \leq C_l \label{eq:capFWmax}\\
& x_{i} \in\{0,1\} \qquad i= 1,\dots,n \label{eq:varDefXFirst}\end{aligned}$$ If problem $NCR$ is feasible, let denote by $x'$ the related optimal solution representing the leader’s strategy. The corresponding follower’s solution is denoted by $y'$, with $y'_i = 1 - x'_i$ $(i=1, \dots, n)$. The current best solution $(x^*, y^*)$ with value $z^*$ (which will be optimal at the end of the algorithm) is initialized accordingly (Lines \[NoC\]-\[endNoC\] of the pseudo code).

### Identifying the relevant critical items {#criticalitems}

We now assume that there exists a critical item $c$ in $KP^{LP}(x^*)$ (Lines \[CritItems\]-\[endCritItems\]) and estimate the first and last possible 