In this talk, we will discuss a bilevel problem with continuous outer variables and a mixed integer program for the inner optimisation problem. Both the leader and the follower are equipped with a budget. In addition, they have a set of projects with associated costs. The profits associated with these projects are perceived differently by the leader and the follower. The leader can provide subsidies to offset the costs of the projects, which will be modelled as the continuous outer variables. The follower solves a mixed integer knapsack problem with the subsidised costs. A special case of the problem, where in the inner problem has a sufficiently large budget results in a reformulation to a single level integer knapsack problem. For the general case, we introduce the notion of \epsilon-feasibility, where in we assume the follower accepts \epsilon-optimal solutions in favour of the leader and introduce reformulations. Finally, we discuss, a cutting plane approach, where we derive optimality cuts by dualising the inner problem.
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