Assignment Preferences and Combinatorial Auctions

Abstract

This paper considers auctions for several distinct items in which each bidder's valua- tion function is determined by an optimal assignment of goods among several agents, each with an independent valuation for each good. Given this preference structure, we demonstrate how to compute the set of lowest Walrasian equilibrium prices, gen- eralizing the work of Demange et al. (12), which considered the special case in which bidders are only interested in receiving a single item. In the more general combinatorial auction setting, where bidders may have arbitrary valuation functions, we propose that the resulting bid table bidding language pro- vides a useful communication format for use in a dynamic demand-revelation phase of a multi-stage hybrid auction. This new format for demand revelation results in unique linear item prices which can be computed in polynomial time, and with bidder input growing quadratically in the number of items. Relative to the simultaneous ascending auction used in combinatorial auctions by the FCC, this can be accomplished without the exposure to receiving substitute goods at additive prices, and without the ability for competitors to signal among themselves.