Bidder Support in Multi-Item Multi-Unit Continuous Combinatorial Auctions : A Unifying Theoretical Framework

Despite known advantages of combinatorial auctions, wide adoption of this allocation mechanism, especially in consumer-oriented marketplaces, is limited partially by the lack of effective bidder support information that can assist bidders to make bidding decisions. In this paper, we study the bidder support problem for the general Multi-Item Multi-Unit (MIMU) combinatorial auctions, where multiple heterogeneous items are being auctioned and multiple homogeneous units are available for each item. Specifically, we consider continuous MIMU auctions, which impose minimal restrictions on bidding activities, thereby reducing the complexity of participation. Two prevalent bidding languages: OR bidding and XOR bidding, are discussed separately. For MIMU auctions with XOR bids, we derive theoretical results to calculate important bidder support metrics. We further demonstrate that bidder support results for MIMU auctions with OR bids can be derived directly from those with XOR bids, by viewing OR bids as XOR bids with each bid submitted by a unique bidder. Consequently, we establish MIMU auctions with XOR bids as the most general case, and unify the theoretical insights on bidder support problem for different bidding languages as well as different special cases of general MIMU auctions, namely the Single-Item Multi-Unit (SIMU) auctions and the Multi-Item Single-Unit (MISU) auctions. The derived theoretical results lead to algorithmic procedures that are capable of providing bidder support information efficiently in practice, which outperform the commonly used integer programming approach. Theoretical insights of the general MIMU auctions also extend to auctions with additional bidding constraints, including batch-based combinatorial auctions, hierarchical combinatorial auctions, and combinatorial reverse auctions