How to Bid Effectively in Multi-Unit Multi-Item Combinatorial Auctions

When a bid is placed on a package in a combinatorial auction (CA), the bid value must be large enough to ensure that the package remains in contention for inclusion in winning combinations in future. The Deadness Level (DL) of a package can serve as an ask price on a fresh bid that can be meaningfully placed on it. Package DL values in single-unit CAs are readily determined. In recent years, however, interest in multi-unit CAs has grown rapidly. The number of packages can be very large in this case, and bidders need greater guidance in estimating valuations. But the DL value of a package tends to creep upwards unsteadily as more bids are placed, and no closed form expression or computational method has been found for it as yet. Here we present for the first time an exact method for determining package DLs in the multi-unit case, assuming that an OR bidding language is being used. A dynamic programming implementation is described that enables fast incremental computations of ask prices after each bid. Experimental runs on simulated data and live data from a recent U.K. multi-unit spectrum auction show that the memory requirement is not excessive. Thus the proposed method could help to promote bidder participation in online multi-unit eBay-like CAs in the procurement and sale of commodities.