Core-pricing in large multi-object auctions: a market design for selling TV-ads

We introduce an auction design and computational methods to determine core payments for large markets with many objects such as the market for TV ads. Bidder optimal, core-selecting auctions have been introduced in spectrum auctions worldwide as a means to set incentives for truthful bidding, but at the same time avoid the problems of the Vickrey-Clarke-Groves mechanism. Many real-world markets involve large numbers of objects where such advanced designs cannot be applied any more for computational reasons, but also for the number of possible bundles available to bidders. An enumerative XOR bidding language (widely discussed in the literature and used in recent government spectrum auctions) grows too quickly to be practical. Market designs for large markets with many objects and similar incentive properties have received little attention in the literature. We propose a compact bidding language for coverage or demographic reach of TV ad slots, and investigate the resulting winner-determination problem and the computation of core payments. For realistic instances of the winner determination problem, very good solutions can be found relatively quickly, though closing the integrality gap to find marginally better solutions or prove optimality can take a prohibitively large amount of time. Our subsequent adaptation of a constraint-generation technique for the computation of bidder-optimal core paymants to this environment is a new, practically viable paradigm by which core-selecting auction designs can be applied to large markets with hundreds of items.