Consider a combinatorial auction in which bidders can submit multiple bids under different names, unbeknownst to the mechanism. The allocation and payment of a bidder is the union and sum of the allocation and payments, respectively, assigned to all pseudonyms

a) Exhibit a combinatorial auction and bidder evaluation such that in the VCG mechanism, there is a bidder who can earn higher utility by submitting multiple bids than by bidding truthfully as a single agent (assuming other bid truthfully)

b) Can this ever happen in a second price single item auction?