be modeled as follows:

$$\begin{aligned}
\text{min}\quad & \sum\limits_{i=1}^{n} p_{i}y_{i} \label{eq:ObjL}\\
    \text{subject to}\quad
    & \sum\limits_{i=1}^{n} v_{i}x_{i} \leq C_u \label{eq:capL}\\
    & x_{i} \in\{0,1\} \qquad i= 1,\dots,n \label{eq:varDefX} \\
    \text{where $y_1, \dots, y_n$ solve} \nonumber\\
    \text{the follower's problem:}\quad
    \text{max}\quad & \sum\limits_{i=1}^{n} p_{i}y_{i} \label{eq:ObjF}\\
    \text{subject to}\quad
    & \sum\limits_{i=1}^{n} w_{i}y_{i} \leq C_l \label{eq:capF}\\
    &y_{i} \leq 1 - x_{i} \qquad i= 1,\dots,n \label{eq:Interd} \\
    &y_{i} \in\{0,1\} \qquad i= 1,\dots,n \label{eq:varDefY} \end{aligned}$$

The leader’s objective function minimizes the profits of the follower through the interdiction constraints . These constraints ensure that each item $i$ can be selected by the follower, i.e. $y_i \leq 1$, only if the item is not interdicted by the leader, i.e. $x_i = 0$. Constraint represents the leader’s capacity constraint. The objective function maximizes the follower’s profits and constraint represents the follower’s capacity constraint. Constraints and define the domain of the variables.

The optimal solution value of model - is denoted by $z^*$. The optimal solution vectors of variables $x_i$ and $y_i$ are respectively denoted by $x^*$ and $y^*$. Notice that in model - there always exists an optimal solution for the leader which is maximal, namely where items are included in the leader’s knapsack until there is no enough capacity left. Let 