We address the fundamental issue of revenue and efficiency in the combinatorial and simultaneous auction using a novel approach. Specifically, upper and lower bounds are constructed for the first-price sealed-bid setting of these two auctions.
The question of revenue is important yet very few results can be found in the literature. Only for very small instances with 2 items have comparisons been made. Krishna et. al. find that allowing combinatorial bids result in lower revenue compared to a second price simultaneous auction.
We formulate a lower bound on the first-price combinatorial auction and an upper bound on the first-price simultaneous auction for larger problems with several items and many bidders, in a model where bidders have synergies from winning a specific set of items. We show that the combinatorial auction is revenue superior to the simultaneous auction for a specific instance in pure symmetric equilibrium and give two generalized upper bounds on revenue for the simultaneous auction.
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