Consider the usual bounded knapsack problem, with the extra twist: you know that $k$ of the chosen items will get spoiled after the sack is packed. And this happens adversarially, i.e. $k$ most valuable items will be gone.
Is there still a pseudo-polynomial time algorithm for such a problem? Anything else interesting that can be said about complexity in such a situation?
It looks very natural, but no relevant references turn up.