Compact Bid Languages and Core Pricing in Large Multi-item Auctions

Abstract

We introduce an auction design framework for large markets with hundreds of items and complex bidder preferences. Such markets typically lead to computationally hard allocation problems. Our new framework consists of compact bid languages for sealed-bid auctions and methods to compute second-price rules such as the Vickrey–Clarke–Groves or bidder-optimal, core-selecting payment rules when the optimality of the allocation problem cannot be guaranteed. To demonstrate the efficacy of the approach for a specific, complex market, we introduce a compact bidding language for TV advertising markets and investigate the resulting winner-determination problem and the computation of core payments. For realistic instances of the respective winner-determination problems, very good solutions with a small integrality gap can be found quickly, although 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 payments to this environment is a practically viable paradigm by which core-selecting auction designs can be applied to large markets with potentially hundreds of items. Such auction designs allow bidders to express their preferences with a low number of parameters, while at the same time providing incentives for truthful bidding. We complement our computational experiments in the context of TV advertising markets with additional results for volume discount auctions in procurement to illustrate the applicability of the approach in different types of large markets. Data, as supplemental material, are available at http://dx.doi.org/10.1287/mnsc.2014.2076 . This paper was accepted by Lorin Hitt, information systems.