Decision support for multi-unit combinatorial bundle auctions
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Many auctions involve selling several distinct items simultaneously, where bidders can bid on the whole or any part of the lot. Such auctions are referred to as combinatorial auctions. Examples of such auctions include truck delivery routes, industrial procurement, and FCC spectrum. Determining winners in such auctions is an NP-hard problem, and significant research is being conducted in this area. However, multiple-round (iterative) combinatorial auctions present significant challenges in bid formulations as well. Because the combinatorial dynamics in iterative auctions can make a given bid part of a winning and nonwinning set of bids without any changes in the bid, bidders are usually not able to evaluate whether they should revise their bid at a given point in time or not. Therefore, in this paper we address various computational problems that are relevant from the bidder's perspective. In particular, we introduce two bid evaluation metrics that can be used by bidders to determine whether any given bid can be a part of the winning allocation and explore their theoretical properties. Based on these metrics, we also develop efficient data structures and algorithms that provide comprehensive information about the current state of the auction atany time, which can help bidders in evaluating their bids and bidding strategies. Our approach uses exponential memory storage but provides fast incremental update for new bids, thereby facilitating bidder support for real-time iterative combinatorial auctions.