Bidder's Valuation Analysis

2.2.3.3 Sealed-Bid First-Price Auction
In both the English and Dutch auctions bidders are allowed an explicit insight into the valuation of their competitors i.e. in an English Auction a lack of activity suggests that a bidder’s valuation is less than the current winning bid and in Dutch auction a lack of activity suggests that a bidder’s valuation is below the current winning bid. This information can be misleading given the incentives for strategic behaviour apparent in both cases i.e. bidders have an incentive to bid below their true valuation. In an English auction, bidders have an incentive to bid below their true valuation in order to secure a preferable profit margin. Similarly in a Dutch auction, bidders have an incentive to allow the

auction the lots in series or in parallel. Up until now we have only considered the single lot auction (each individual lot is auctioned in isolation), this section will look to discuss the area of multi-lot auctions (multiple lots auctioned at once). A multi-lot auction is typically referred to as a combinatorial auction whenever bidders are allowed to express their cost efficiencies via package bidding. Package bidding in this context refers to the submission of a bid where the value of one lot is in some whey dependent on the receipt of another i.e. I only want A if I also get B. The appeal of combinatorial auctions is that they have the potential to enhance competition and improve market efficiency. However, these benefits come at a price. The allocation problem or winner determination problem in this setting is significantly more complex than its single lot counterpart. The computational complexity is introduced when a bid taker is forced to reason about packages of lots (rather than being allowed to focus on a bidder’s performance on an individual lot) when trying to find the optimal overall outcome. In a single lot setting the winning bidder will always submit the most competitive price on a lot, this assumption no longer holds in a multi-lot setting where a bid taker may be willing to forego profit on an individual lot in order to achieve a greater overall objective i.e. maximize social welfare across all bidders. This combinatorial allocation problem can be modelled as a set packing problem and is shown to be NP-hard.( Rothkopf M. H. et al, 1998) This allocation problem may be applied to a number of real-world problem such as scheduling, transport logistics and perhaps most notably in spectrum