Bidder Support in Multi-item Multi-unit Continuous Combinatorial Auctions: A Unifying Theoretical Framework

Combinatorial auctions have seen limited applications in large-scale consumer-oriented marketplaces, partly due to the substantial complexity to keep track of auction status and formulate informed bidding strategies. 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. Under two prevalent bidding languages (OR bidding and XOR bidding), we derive theoretical results and design efficient algorithmic procedures to calculate important bidder support information, such as the winning bids of an auction and the minimum bidding value for a bid to win an auction either immediately or potentially in the future. Our results 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. We also consider auctions with additional bidding constraints, including batch-based combinatorial auctions and hierarchical combinatorial auctions, as well as the combinatorial reverse auctions, all of which have relevant practical applications (e.g., industrial procurements). Our results can be readily extended to solve the bidder support problems in these auction mechanisms.