Reflections about pseudo-dual prices in combinatorial auctions

Combinatorial auctions permitting bids on bundles of items have been developed to remedy the exposure problem associated with single-item auctions. Given winning bundle prices a set of item prices is called market clearing or equilibrium if all the winning (losing) bids are greater (less) than or equal to the total price of the bundle items. However, the prices for individual items are not readily computed once the winner determination problem is solved. This is due to the duality gap of integer programming caused by the indivisibility of the items. In this paper we reflect on the calculation of approximate or pseudo-dual item prices. In particular, we present a novel scheme based on the aggregation of winning bids. Our analysis is illustrated by means of numerical examples.