Allocative efficiency in simulated multiple-unit combinatorial auctions with quantity support

We study the behavior of the Quantity Support Mechanism, a support tool, which suggests new bids for bidders in semi-sealed-bid combinatorial auctions. The support tool gives bidders a shortlist of provisionally winning bids (price–quantity combinations) they can choose from. We conducted a series of simulations to test the efficiency of the final allocations in the auctions. Our results indicate that quantity support auctions are more efficient than auctions without it, although the theoretical optimum is not always reached. Also, in our experiments, quantity support auctions led to a lower total cost to the buyer than non-combinatorial auctions, where the items were auctioned individually. The simulation results also show that the QSM cannot entirely overcome the threshold problem and what we call the “puzzle problem”.     

Compact bidding languages and supplier selection for markets with economies of scale and scope

Combinatorial auctions have been used in procurement markets with economies of scope. Preference elicitation is already a problem in single-unit combinatorial auctions, but it becomes prohibitive even for small instances of multi-unit combinatorial auctions, as suppliers cannot be expected to enumerate a sufficient number of bids that would allow an auctioneer to find the efficient allocation. Auction design for markets with economies of scale and scope are much less well understood. They require more compact and yet expressive bidding languages, and the supplier selection typically is a hard computational problem. In this paper, we propose a compact bidding language to express the characteristics of a supplier’s cost function in markets with economies of scale and scope. Bidders in these auctions can specify various discounts and markups on overall spend on all items or selected item sets, and specify complex conditions for these pricing rules. We propose an optimization formulation to solve the resulting supplier selection problem and provide an extensive experimental evaluation. We also discuss the impact of different language features on the computational effort, on total spend, and the knowledge representation of the bids. Interestingly, while in most settings volume discount bids can lead to significant cost savings, some types of volume discount bids can be worse than split-award auctions in simple settings.     

A new pricing scheme based on DEA for iterative multi-unit combinatorial auctions

Iterative Multi-unit Combinatorial Auctions are auctions in which: bidders can express bids in successive rounds until a stopping rule is held; there are multiple units of each item; and bids are bundles of items. Data Envelopment Analysis (DEA) is a nonparametric method for measuring the relative efficiency of a set of homogeneous units. In this work, we present an algorithm for solving an iterative multi-unit combinatorial auction in which the auctioneer computes at each round a linear anonymous price for each item by using a DEA model and pushes bidders to express bids according to them. A computational study is carried out in order to check the performance of the proposed design.      

All-pay auctions with pre- and post-bidding options

Motivated by the emergence of online penny or pay-to-bid auctions, in this study, we analyze the operational consequences of all-pay auctions competing with fixed list price stores. In all-pay auctions, bidders place bids, and highest bidder wins. Depending on the auction format, the winner pays either the amount of their bid or that of the second-highest bid. All losing bidders forfeit their bids, regardless of the auction format. Bidders may visit the store, both before and after bidding, and buy the item at the fixed list price. In a modified version, we consider a setting where bidders can use their sunk bid as a credit towards buying the item from the auctioneer at a fixed price (different from the list price). We characterize a symmetric equilibrium in the bidding/buying strategy and derive optimal list prices for both the seller and auctioneer to maximize expected revenue. We consider two situations: (1) one firm operating both channels (i.e. fixed list price store and all-pay auction), and (2) two competing firms, each operating one of the two channels.     

Non-linear anonymous pricing combinatorial auctions

In combinatorial auctions the pricing problem is of main concern since it is the means by which the auctioneer signals the result of the auction to the participants. In order for the auction to be regarded as fair among the various participants the price signals should be such that a participant that has won a subset of items knows why his bid was a winning bid and that agents that have not acquired any item easily can detect why they lost. The problem in the combinatorial auction setting is that the winner determination problem is a hard integer programming problem and hence a linear pricing scheme supporting the optimal allocation might not exist.     

Investigating buyer and seller strategies in online auctions

The annual turnover of online auctions is already in tens of billions of dollars and this amount is predicted to grow substantially over the next few years. Hence, it is important to know how buyers and sellers can influence their chances of success. Therefore, data were collected from eBay auctions for three different categories of collectible items, namely those with a published guide price, those with a rough guide price and those having no easily obtainable guide price. The options available to buyers and sellers of items were then analysed. It was found that it was hard for the seller to influence an item's achieved price significantly, apart from items with no guide price where the starting price could have an effect. Most bidders bid close to the current value and so there were insufficient data to determine the consequences of timing on the placing of high bids. For low bids, delaying a bid was found to improve significantly the chances of winning for one of the data sets.     

Combinatorial auctions

Combinatorial auctions are an important class of market mechanisms in which participants are allowed to bid on bundles of multiple heterogeneous items. In this paper, we discuss several complex issues that are encountered in the design of combinatorial auctions. These issues are related to the formulation of the winner determination problem, the expression of combined bids, the design of progressive combinatorial auctions that require less information revelation, and the need for decision support tools to help participants make profitable bidding decisions. For each issue, we survey the existing literature and propose avenues for further research. An earlier version of this paper appeared in 4OR 2, 1–33, 2004.     

Design issues for combinatorial auctions

Combinatorial auctions are an important class of market mechanisms in which participants are allowed to bid on bundles of multiple heterogeneous items. In this paper, we discuss several complex issues that are encountered in the design of combinatorial auctions. These issues are related to the formulation of the winner determination problem, the expression of combined bids, the design of progressive combinatorial auctions that require less information revelation, and the need for decision support tools to help participants make profitable bidding decisions. For each issue, we survey the existing literature and propose avenues for further research.Received: April 2003, Revised: July 2003, AMS classification: 91B26, 90BXX, 90C27All correspondence to:Jawad Abrache     

Comparing the Spanish and the discriminatory auction formats: A discrete model with private information

The Spanish Treasury is the only Treasury in the world that uses a hybrid system of discriminatory and uniform price auctions to sell government debt: winning bidders pay their bid price for each unit if this is lower than the weighted average price of winning bids (WAP), and pay the WAP otherwise. Following Gordy [Gordy, M., 1996. Multiple bids in a multiple-unit common-value auction. Board of Governors of the Federal Reserve System], we model the Spanish auction as a common value auction of multiple units with private information, allowing for multiple bids. Numerical analysis shows that bidders spread their bids more in the Spanish than in the discriminatory auction and bid higher for the first unit, and that the expected seller’s revenue is higher in the Spanish than in the discriminatory auction within a reasonable set of parameter values.     

Auctions with bidder-determined allowable combinations

Combinatorial auctions are desirable as they enable bidders to express the synergistic values of a group of assets and thus may lead to better allocations. Compared to other types of auctions, they keep bidders from being exposed to risks (of receiving only parts of combinations that would be valuable to them) or from being overly cautious (in order to minimize such risks). However, computation time needed to determine the set of optimal winning combinations in a general combinatorial auction may grow exponentially as the auction size increases, and this is sometimes given as a reason for not using combinatorial auctions. To determine the winning allocation in a reasonable time, a bid taker might try to limit the kinds of allowable combinations, but bidders may disagree on what combinations should be allowed, and this may make limiting the allowable combinations politically infeasible.This paper proposes and tests successfully a new approach to managing the computational complexity of determining the set of winning combinations. The main idea is to let bidders themselves determine and prioritize the allowable combinations. Using bidder-determined combinations has two nice properties. First, by delegating the decision on what is biddable to the bidders who know what combinations are important to them, the bid taker is able to be (and appear) fair. Second, since bidders know their economics and have the incentive to get important combinations included, bidder prioritization of combinations will tend to assure that the most economically-important combinations are included in determining the winning set of bids if the bid taker is not able to consider all of the combinations submitted by bidders. The proposed auction process is useful in situations, such as government auctions, in which the bid taker is reluctant to limit the allowable combinations.     

Configurable offers and winner determination in multi-attribute auctions

The theory of procurement auctions traditionally assumes that the offered quantity and quality is fixed prior to source selection. Multi-attribute reverse auctions allow negotiation over price and qualitative attributes such as color, weight, or delivery time. They promise higher market efficiency through a more effective information exchange of buyer’s preferences and supplier’s offerings. This paper focuses on a number of winner determination problems in multi-attribute auctions. Previous work assumes that multi-attribute bids are described as attribute value pairs and that the entire demand is purchased from a single supplier. Our contribution is twofold: First, we will analyze the winner determination problem in case of multiple sourcing. Second, we will extend the concept of multi-attribute auctions to allow for configurable offers. Configurable offers enable suppliers to specify multiple values and price markups for each attribute. In addition, suppliers can define configuration and discount rules in form of propositional logic statements. These extensions provide suppliers with more flexibility in the specification of their bids and allow for an efficient information exchange among market participants. We will present MIP formulations for the resulting allocation problems and an implementation.     

Anonymous sealed bid auction protocol based on a variant of the dining cryptographers’ protocol

Sealed bid auctions are a popular means of high-stakes bidding, as they eliminate the temporal element from the auction process, allowing participants to take less emotional, more thoughtful decisions. In this paper, we propose a digital communication protocol for conducting sealed bid auctions with high stakes, where the anonymity of bids as well as other aspects of fairness must be protected. The Dining Cryptographers?? Protocol (denoted by DC) was presented by David Chaum in 1988. The protocol allows the participants to broadcast a message anonymously. In a recent paper (Another Twist in the Dining Cryptographers?? Protocol, submitted to the Journal of Cryptology) the authors propose a variant of the original DC eliminating its main disadvantages. In this paper we present a cryptographic protocol realizing anonymous sealed bid auctions, such as first price or Vickrey auction, based on this variant. The proposed scheme allows to identify at least one dishonest participant violating the protocol without using of Trusted Third Parties. Additionally, we require that bids are binding. It is achieved by enabling all participants acting in concert (the so-called ??angry mob??) to find out the identity of the winner, in case the winner fails to make the purchase.     

Day-ahead market bidding for a Nordic hydropower producer: taking the Elbas market into account

In many power markets around the world the energy generation decisions result from two-sided auctions in which producing and consuming agents submit their price-quantity bids. The determination of optimal bids in power markets is a complicated task that has to be undertaken every day. In the present work, we propose an optimization model for a price-taker hydropower producer in Nord Pool that takes into account the uncertainty in market prices and both production and physical trading aspects. The day-ahead bidding takes place a day before the actual operation and energy delivery. After this round of bidding, but before actual operation, some adjustments in the dispatched power (accepted bids) have to be done, due to uncertainty in prices, inflow and load. Such adjustments can be done in the Elbas market, which allows for trading physical electricity up to one hour before the operation hour. This paper uses stochastic programming to determine the optimal bidding strategy and the impact of the possibility to participate in the Elbas. ARMAX and GARCH techniques are used to generate realistic market price scenarios taking into account both day-ahead price and Elbas price uncertainty. The results show that considering Elbas when bidding in the day-ahead market does not significantly impact neither the profit nor the recommended bids of a typical hydro producer.     

On the impact of low-balling: Experimental results in asymmetric auctions

The paper reports on a series of asymmetric auction experiments with private-independent values and two buyers. Maskin and Riley (2000) showed, under some conditions, that if one buyer has a greater probability than the other of not being able to bid, first-price auctions could yield lower revenues to the seller than second-price auctions. The data rejected this prediction because of an important overbidding when subjects received low values in first-price auctions. In this asymmetric setting, the observed overbidding cannot be explained by the usual risk aversion hypothesis and the detection of a learning pattern indicates that subjects used more an adaptive behaviour than a static one. An ad hoc bidding strategy for the buyers who are the most likely to bid explains the observed low bids better than the risk neutral equilibrium strategy. Finally, as subjects appear to have bid in equilibrium as if there were two other competitors instead of only one, their bidding behaviour can be thought to have displayed an over anxiousness about winning. Received: January 1999/Final version June 2001     

Competitive subset selection with two agents

We address an optimization problem in which two agents, each with a set of weighted items, compete in order to maximize the total weight of their winning sets. The latter are built according to a sequential game consisting in a fixed number of rounds. In every round each agent submits one item for possible inclusion in its winning set. We study two natural rules to decide the winner of each round.For both rules we deal with the problem from different perspectives. From a centralized point of view, we investigate (i) the structure and the number of efficient (i.e. Pareto optimal) solutions, (ii) the complexity of finding such solutions, (iii) the best-worst ratio, i.e. the ratio between the efficient solution with largest and smallest total weight, and (iv) existence of Nash equilibria.Finally, we address the problem from a single agent perspective. We consider preventive or maximin strategies, optimizing the objective of the agent in the worst case, and best response strategies, where the items submitted by the other agent are known in advance either in each round (on-line) or for the whole game (off-line).     

On being balanced in an unbalanced world

This paper examines the case of a procurement auction for a single project, in which the breakdown of the winning bid into its component items determines the value of payments subsequently made to bidder as the work progresses. Unbalanced bidding, or bid skewing, involves the uneven distribution of mark-up among the component items in such a way as to attempt to derive increased benefit to the unbalancer but without involving any change in the total bid. One form of unbalanced bidding for example, termed Front Loading (FL), is thought to be widespread in practice. This involves overpricing the work items that occur early in the project and underpricing the work items that occur later in the project in order to enhance the bidder's cash flow. Naturally, auctioners attempt to protect themselves from the effects of unbalancing—typically reserving the right to reject a bid that has been detected as unbalanced. As a result, models have been developed to both unbalance bids and detect unbalanced bids but virtually nothing is known of their use, success or otherwise. This is of particular concern for the detection methods as, without testing, there is no way of knowing the extent to which unbalanced bids are remaining undetected or balanced bids are being falsely detected as unbalanced. This paper reports on a simulation study aimed at demonstrating the likely effects of unbalanced bid detection models in a deterministic environment involving FL unbalancing in a Texas DOT detection setting, in which bids are deemed to be unbalanced if an item exceeds a maximum (or fails to reach a minimum) ‘cut-off’ value determined by the Texas method. A proportion of bids are automatically and maximally unbalanced over a long series of simulated contract projects and the profits and detection rates of both the balancers and unbalancers are compared. The results show that, as expected, the balanced bids are often incorrectly detected as unbalanced, with the rate of (mis)detection increasing with the proportion of FL bidders in the auction. It is also shown that, while the profit for balanced bidders remains the same irrespective of the number of FL bidders involved, the FL bidder's profit increases with the greater proportion of FL bidders present in the auction. Sensitivity tests show the results to be generally robust, with (mis)detection rates increasing further when there are fewer bidders in the auction and when more data are averaged to determine the baseline value, but being smaller or larger with increased cut-off values and increased cost and estimate variability depending on the number of FL bidders involved. The FL bidder's expected benefit from unbalancing, on the other hand, increases, when there are fewer bidders in the auction. It also increases when the cut-off rate and discount rate is increased, when there is less variability in the costs and their estimates, and when less data are used in setting the baseline values.     

Optimal bundle pricing with monotonicity constraint

We consider the problem of pricing (digital) items in order to maximize the revenue obtainable from a set of bidders. We suggest a natural monotonicity constraint on bundle prices, show that the problem remains NP-hard, and we derive a PTAS. We also briefly discuss the highway pricing problem.     

Multi-criteria auctions without full comparability of bids

The emergence of auction mechanisms that support bids characterized by several attributes is one of the most recent evolutions within auction theory. These mechanisms, referred to as multi-attribute, multiple issue or multi-dimensional auctions, are at the intersection between multi-criteria decision and auction theories. The purpose of this paper is to introduce multi-criteria auctions the originality of which is not to require full comparability between bids. We claim that this distinctive feature is of great interest, especially in procurement situations. Furthermore, the existence of potential incomparability between multi-dimensional offers will permit us to manage different bidding niches coexisting within the same bidding space. A theoretical framework based on a general preference structure will be introduced and then referenced to existing approaches such as multi-attribute auctions or new ones such as dominance based multi-criteria auctions or butterfly auctions.     

Sets in excess demand in simple ascending auctions with unit-demand bidders

This paper analyzes the problem of selecting a set of items whose prices are to be updated in the next iteration in so called simple ascending auctions with unit-demand bidders. A family of sets called “sets in excess demand” is introduced, and the main result demonstrates that a simple ascending auction always terminates at the minimum Walrasian equilibrium prices if and only if the selection belongs to this family.     

统计信息下在线反向拍卖的竞争分析

对于投标具有统计特征的在线反向拍卖问题,利用在线算法与平均情形竞争分析相结合的方法,讨论了单一定价策略的平均情形最优单一定价及其竞争性能,提出了无限可分商品在线反向拍卖的平均情形竞争分析策略,基于此策略建立了具有均匀分布特征的在线反向拍卖模型,通过对模型求解得到了采购商的竞争需要曲线。与不考虑投标的统计信息、只是利用常规的最坏情形竞争分析得到的在线反向拍卖的竞争策略进行对比分析,发现统计信息的利用提高了在线反向拍卖策略的竞争性能。