Selfish Knapsack

We study a strategic variant of the knapsack problem, in We emphasize that agents can misreport the existence of which there are n agents, each owning a set of items, where items, but not their properties--their size and value; that is, each item has a value and size. A social planner must design the planner has the power to verify the size and value of a mechanism to choose which items to include in a knapsack the reported items. One example of such a scenario is the of a certain capacity, where the total size of the chosen items allocation of a scientific resource, like time on a particle cannot exceed the capacity. Each agent gets a utility equal accelerator or NSF funding. Scientists submit research proposals, to the total value of her own items included in the knapsack, each requesting a certain amount of resource, which while the designer wishes to maximize social welfare (the would provide a certain expected scientific value. This expected sum of the utilities of the agents, which amounts to the total scientific value is evaluated/confirmed by an impartial value of the items in the knapsack).