Preference representation for multi-unit multiattribute auctions

The problem of multi-unit multiattribute trading, though useful in practical procurement settings, has been rarely addressed in auction literature. We present a general framework to structure specifications of preferences over multi-unit multiattribute outcomes, allowing flexible tradeoffs between expressiveness and compactness of representation. Next, we use this framework to propose an auction mechanism with useful economic and computational properties, applicable over a substantial part of the general preference domain. Background and introduction Procurement auctions typically involve various non-price aspects of a deal, such as quality measures, delivery and service information, and supplier qualification criteria. A multiattribute mechanism facilitates such negotiations, and potentially achieves higher welfare by picking contract configurations that are both valued by the buyer and less costly for the supplier. Various such mechanisms have been suggested in the auction literature (Che 1993; Bichler 2001; Parkes & Kalagnanam 2005; Engel & Wellman 2007). The design and implementation of a multiattribute auction presents several technical challenges, including preference extraction, compact preference representation, and a difficult optimization problem for clearing. Perhaps due to the inherent complexity of multiattribute auctions, nearly all prior proposals for multiattribute preference handling and mechanism design have assumed singlesourcing, where a single bidder is selected as supplier. As single-supplier relationships introduce a risk of cost overruns and supply disruptions or stock-outs, buyers often have a preference for multi-sourcing, where supply contracts are distributed among multiple winners. Limited supplier capacities may also contribute to the need for multi-sourcing. In practice, many procurement auctions have dealt with multiple units over multiattribute goods (Metti et al. 2005; Sandholm et al. 2006). To our knowledge, however, these do not support structured multiattribute preferences or provide efficiency guarantees across the space of configurations. To address multi-sourcing issues, we consider multi-unit multiattribute (MUMA) auctions. The MUMA problem Copyright c © 2007, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. combines the dimensionality of the single-unit multiattribute domain with the combinatorial complexity of multi-unit auctions of heterogeneous goods. Due to the complexity of this problem, we first restrict attention to the representation and expression of preferences over this domain. We consider the problem in its full generality, then suggest simplifications based on assumptions over preference structure. In prior work on MUMA double auctions (Engel, Wellman, & Lochner 2006), we reasoned directly from bid expressiveness to the computational complexity of clearing, finding constraints on the bidding language which led to tractable algorithms. Our current approach takes a preference representation perspective, rather than bid expressiveness, which brings several advantages. It lets us capture a fully general representation of this domain (whereas we previously did not represent complementarities), it lends itself easily to the expression of the welfare maximization problem, and most importantly allows the use of well-founded tools from multiattribute utility theory to simplify the preference representation. This framework lets us use meaningful preference structure in order to achieve value decomposition, which we apply to effectively decouple the multiattribute domain from the multi-unit problem. We then leverage this result to create an auction mechanism for multisourcing procurement. Some issues relevant to our work are explored in the literature on side constraints, which place hard constraints on the space of allocations acceptable to the bid taker in multiobject and combinatorial auctions. Work by Sandholm and Suri (2001) shows that most such constraints posed by the bid taker render the winner determination problem NPhard. Bichler and Kalagnanam (2005) explicitly consider the problem of multi-unit multiattribute procurement auctions, focusing on the winner determination problem given various buyer-imposed constraints. Our approach is a general framework to express preferences over the multi-unit multiattribute domain rather than hard constraints. In that sense another relevant work is from Boutilier, Sandholm and Shields (2004), which opts for a utility-based representation over hard constraints for allocation preferences in combinatorial auctions, and focuses on the elicitation of tradeoffs between constraints and cost. In the next section, we formally define the MUMA domain and introduce various simplifying assumptions over