A New Analysis of Expected Revenue

Abstract

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 in a model where bidders have synergies from winning a specific set of items. With these bounds, we can (i) prove that asymptotically as the number of bidders increase, the combinatorial auction will be revenue-superior, and (ii) present a number of concrete examples where combinatorial auctions give higher expected revenue.