As discussed in the literature review, combinatorial auctions are characterized by complexity. The winner determination is computationally complex, and the construction of bids requires the elicitation of complex preferences over a set of different items. Good bidding strategies are not easy to calculate, as good bids for one bidder depend not only on her preferences and cost structure, but also on bids made by other bidders. There is a lot of literature concerning the efficient solution of the WDP (see section 3.2.2.1), and recently there has also been some research into the elicitation of bidder preferences (section 3.2.2.2) and the design of auction mechanisms (section 3.2.3). The addition of multiple units of each item makes the mechanism design more complicated – and complicates further the bidders’ task of submitting bids. Also, only a few of the mechanisms are easily extended to the multi-unit setting. Bidder support has been neglected in existing literature. Thus, there is a need for a multi-unit auction combinatorial, which would be easy for bidders to participate in.
6.1 Need for Mechanisms for Multiple-Unit Combinatorial Auctions
Thus far, the extension of the combinatorial auction mechanisms for multiple-unit cases has not been discussed in literature much. Out of the mechanisms reviewed in section 3.2.3.2 five are easily extendable to the multi-unit setting: AUSM, PAUSE, RAD, the Endogenous Bidding Mechanism, and the combinatorial clock auction.
However, all of them have their shortcomings, one of them being that they compromise efficiency. In multiple unit auctions, the effect of linear ask prices on efficiency would be even worse because they remove the possibility of expressing economies of scale (i.e. quantity discounts). Using non-linear pricing improves efficiency, but it cannot really be used in multi-unit auctions, or large single-unit auctions for that matter. This is because auctions with multiple units, or a large number of items have too many possible combinations to be evaluated in reasonable time. Of course, not all combinations need to be considered – e.g. iBundle only considers combinations for which there are bids from previous rounds – but that
compromises efficiency. Thus, there is room for a different approach in combinatorial auction mechanism design.
6.2 Identification of the Puzzle Problem and Need for Quantity Support
Combinatorial auction literature recognizes the threshold problem – as noted in section 3.2.1.3 – but little has been done to try to alleviate it. In addition, I believe the threshold problem does not adequately describe all the problems facing the bidders bidding in a combinatorial auction. Firstly, the threshold problem refers to a situation in which a large number of “local” bidders – bidders bidding for single items or small packages – are trying to coordinate their bid prices to outbid a “global” bidder – a bidder bidding for the whole bundle (or a few big bidders). However, the bid price is only one dimension in the bid vector in a combinatorial auction. The bidder can also choose to vary the item combination associated with the price, and this, I believe, creates a whole new problem.
In combinatorial auctions, a successful bid complements existing bids, placing all of them among the winners (unless the winning bid is for the entire bundle). This brings a cooperative flavor into the auction even though bidders are still in competition with each other and are not allowed to collude. The threshold problem is one phenomenon arising from this cooperative nature of bidding. The threshold problem – the way it is presented in literature – is confined to price adjustments. However, in combinatorial auctions, the item combination in a bid plays as large a role in determining whether the bid is among the winners or not. A combinatorial auction is like a puzzle: in addition to the prices being right, the bids need to fit together to form the whole bundle like puzzle pieces fit together to form a complete puzzle. However, in a combinatorial auction, the size and shape of the puzzle pieces are not predetermined;
it is the task of the auction mechanism to endogenously determine them. The WDP is then analogous to the process of choosing which pieces to use to compile the puzzle.
Due to this very fitting analogy, I call the problem of finding and placing bids that complement other bidders’ bids (i.e. bids that will be chosen by the WDP), the puzzle problem. An implication of the puzzle problem is that even if a bidder has managed to
identify her most preferred combinations, it may not make sense to bid on them, if there are no complementing bids coming from other bidders.
In open-cry auctions, the puzzle problem is not more difficult to overcome than the threshold problem. But in sealed-bid auctions the puzzle problem becomes almost impossible to overcome, and it is a serious threat to allocative efficiency in such auctions. In sealed-bid auctions the bidders do not know the contents of the competing bids, and thus it is impossible for them to deliberately place complementing bids. The puzzle problem can thus arise without the coordination issues, which are at the heart of the threshold problem. A bidder could be able to place a bid that would make her (and a group of existing bids) winners, but does not know which bid it would be.
Most procurement auctions use a sealed-bid format, because they are preferred by the bidders (Jap, 2003). In sealed-bid auctions bidders do not have to worry what information their bids could reveal to their competitors. Also, for the auction owner a sealed-bid auction has the advantage that it removes the possibility of signaling, and jump bidding will not be as effective because competitors cannot observe it. The fact that combinatorial procurement auctions are often held in a sealed-bid format means that the concerns of auction outcomes being inefficient due to the puzzle problem are very relevant. The problems are aggravated in multiple-unit combinatorial auctions, because not only do the items in the bids complement each other, but the quantities also need to add up to the total demand. Thus, it can easily happen that a bidder with a low cost structure (in a reverse auction) loses, because she did not bid for the “right”
combination.
Even though winning in a combinatorial auction depends on other bidders’ bids, the support mechanisms presented in section 3.2.2.2 or the iterative auction mechanisms in section 3.2.3.2 do not attempt to find bids to form coalitions with other bidders.
Offering price information in an iterative auction guides the bidders to bid for items with a relatively high price, but it does not help in determining the quantities for each item (this is of course relevant only in multi-unit cases). I feel that this aspect of bidding in combinatorial auctions has been neglected in existing literature, and it is important that the puzzle problem be addressed.
6.3 Objectives and Methods of the Study
The objective of this study is to overcome the puzzle problem present in multi-unit sealed-bid and semi-sealed-bid12 combinatorial auctions. In this research project, we consider only iterative auctions, as one-shot auctions present very limited opportunities to a) gather any kind of information from the auction, and b) to support bidders. Also, our focus is on continuous, iterative auctions, and not on round-based auctions.
We try to reach the objective by developing support tools for bidders. The task of the support tools is to find bid suggestions that would complement the existing bids (that is, identify the size and shape of possible missing pieces of the puzzle). These bids should be beneficial for both the buyer (total cost should decrease), and the bidder (bidder should make a profit).
Our hypothesis is that providing this kind of “quantity support” the sealed-bid or semi-sealed-bid auction would reach a more efficient outcome. The support tools should also be considered fair by both the buyer and the sellers, because they try to maximize the bidders’ profit, all the while decreasing the total cost to the buyer. Also, providing support for the bidders – and thereby making bidding easier and less costly – the auction would be more attractive, and more bidders would participate. More competition should improve the buyer’s position, as she can expect to obtain the items for a lower total cost.
The main methods used in this study are simulations and laboratory experiments. The simulations were used to study the performance of the support tools. Through simulations we could observe the efficiency of the final allocations, as well as the total cost to the buyer. The laboratory experiment was used to study whether the simulated results could be reproduced with human users. The laboratory experiments were also used to observe bidders’ behavior in combinatorial auctions. Based on bidders’
behavior I identified different bidding strategies. In addition, I could draw conclusions on how difficult a bidding environment is for inexperienced bidders, and how good the usability of the user interface is.
12 A semi-sealed-bid auction is a sealed-bid auction in which the bidders know which of their own bids are among the provisional winners (= active) and which are not (= inactive).