Selfish Routing: Knapsack-Like Equilibria

To be more precise, given n objects with weights w_i and profits p_i
and a capacity threshold b, we ask for the complexity of computing
a maximal knapsack with minimum profit (min-max knapsack).
We investigate this and other more general knapsack-like optimization
problems allowing different thresholds for different objects.
Our study is motivated by the complexity of best- and worst-case
microeconomical equilibria describing selfish customer allocations
for a service provider.