An optimal multiprocessor combinatorial auction solver

A combinatorial auction (CA) is an auction that permits bidders to bid on bundles of goods rather than just a single item. Unfortunately, winner determination for CAs is known to be NP-hard. In this paper, we propose a distributed algorithm to compute optimal solutions to this problem. The algorithm uses nagging, a technique for parallelizing search in heterogeneous distributed computing environments. Here, we show how nagging can be used to parallelize a branch-and-bound algorithm for this problem, and provide empirical results supporting both the performance advantage of nagging over more traditional partitioning methods as well as the superior scalability of nagging to larger numbers of processors.     

Visualizing combinatorial auctions

We propose a novel scheme to visualize combinatorial auctions; auctions that involve the simultaneous sale of multiple items. Buyers bid on complementary sets of items, or bundles, where the utility of securing all the items in the bundle is more than the sum of the utility of the individual items. Our visualizations use concentric rings divided into arcs to visualize the bundles in an auction. The arcs’ positions and overlaps allow viewers to identify and follow bidding strategies. Properties of color, texture, and motion are used to represent different attributes of the auction, including active bundles, prices bid for each bundle, winning bids, and bidders’ interests. Keyframe animations are used to show changes in an auction over time. We demonstrate our visualization technique on a standard testbed dataset generated by researchers to evaluate combinatorial auction bid strategies, and on recent Federal Communications Commission (FCC) auctions designed to allocate wireless spectrum licenses to cell phone service providers.     

MoRVAM: A reverse Vickrey auction system for mobile commerce

Internet auctions bring buyers and sellers together for the purpose of trading goods and services online. In order to get the goods, a buyer must search for items through several auction sites. When the auction starts, the buyer needs to connect to these auction sites frequently so that he/she can monitor the bid states and re-bid. In this paper, we propose an automated negotiation model between two participants, for mobile commerce, using collaborative mobile agents called MoRVAM, which mediates between the buyer and the sellers, and executes bidding asynchronously and autonomously. A new RVT protocol is also implemented to achieve unconditional bid privacy. Advantages of the RVT protocol are addressed as well. All the bidding process can be implemented without revealing losing bid and unnecessary information.     

A non-parametric estimator for setting reservation prices in procurement auctions

Electronic auction markets collect large amounts of auction field data. This enables a structural estimation of the bid distributions and the possibility to derive optimal reservation prices. In this paper we propose a new approach to setting reservation prices. In contrast to traditional auction theory we use the buyer’s risk statement for getting a winning bid as a key criterion to set an optimal reservation price. The reservation price for a given probability can then be derived from the distribution function of the observed drop-out bids. In order to get an accurate model of this function, we propose a nonparametric technique based on kernel distribution function estimators and the use of order statistics. We improve our estimator by additional information, which can be observed about bidders and qualitative differences of goods in past auctions rounds (e.g. different delivery times). This makes the technique applicable to RFQs and multi-attribute auctions, with qualitatively differentiated offers.     

Experiments with probabilistic quantum auctions

We describe human-subject laboratory experiments on probabilistic auctions based on previously proposed auction protocols involving the simulated manipulation and communication of quantum states. These auctions are probabilistic in determining which bidder wins, or having no winner, rather than always having the highest bidder win. Comparing two quantum protocols in the context of first-price sealed bid auctions, we find the one predicted to be superior by game theory also performs better experimentally. We also compare with a conventional first-price auction, which gives higher performance. Thus to provide benefits, the quantum protocol requires more complex economic scenarios such as maintaining privacy of bids over a series of related auctions or involving allocative externalities.      

Kombinatorische Auktionen in der betrieblichen BeschaffungEine Analyse grundlegender Entwurfsprobleme – An Analysis of Design Problems in Combinatorial Procurement Auctions

Traditional auction mechanisms support price negotiations on a single item. The Internet allows for the exchange of much more complex offers in real-time. This is one of the reasons for much research on multidimensional auction mechanisms allowing negotiations on multiple items, multiple units, or multiple attributes of an item, as they can be regularly found in procurement. Combinatorial auctions, for example, enable suppliers to submit bids on bundles of items. A number of laboratory experiments has shown high allocative efficiency in markets with economies of scope. For suppliers it is easier to express cost savings due to bundling (e. g., decreased transportation or production costs). This can lead to significant savings in total cost of the procurement manager. Procurement negotiations exhibit a number of particularities:

It is often necessary to consider qualitative attributes or volume discounts in bundle bids. These complex bid types have not been sufficiently analyzed.

The winner determination problem requires the consideration of a number of additional business constraints, such as limits on the spend on a particular supplier or the number of suppliers.

Iterative combinatorial auctions have a number of advantages in practical applications, but they also lead to new problems in the determination of ask prices.

In this paper, we will discuss fundamental problems in the design of combinatorial auctions and the particularities of procurement applications. Reprint of an article from WIRTSCHAFTSINFORMATIK 47(2)2005:126–134.     

An efficient Nash-implementation mechanism for network resource allocation

We propose a mechanism for auctioning bundles of multiple divisible goods in a network where buyers want the same amount of bandwidth on each link in their route. Buyers can specify multiple routes (corresponding to a source-destination pair). The total flow can then be split among these multiple routes. We first propose a one-sided VCG-type mechanism. Players do not report a full valuation function but only a two-dimensional bid signal: the maximum quantity that they want and the per-unit price they are willing to pay. The proposed mechanism is a weak Nash implementation, i.e., it has a non-unique Nash equilibrium that implements the social-welfare maximizing allocation. We show the existence of an efficient Nash equilibrium in the corresponding auction game, though there may exist other Nash equilibria that are not efficient. We then generalize this to arbitrary bundles of various goods. Each buyer submits a bid separately for each good but their utility function is a general function of allocations of bundles of various divisible goods. We then present a double-sided auction mechanism for multiple divisible goods. We show that there exists a Nash equilibrium of this auction game which yields the efficient allocation with strong budget balance.     

Designing Electronic Auctions: An Internet-Based Hybrid Procedure Combining Aspects of Negotiations and Auctions

We discuss design issues pertaining to multiple issue auctions in the WWW environment. Based on a critical evaluation of existing auctions, we propose NegotiAuction^tm, an algorithmic Internet-based auction procedure, which combines certain elements of negotiations and auctions. It can be used either in reverse or forward auctions. When defining a multiple issue (multiple attribute) auction, the auction owner has more control over the bidding process than is possible in traditional auctions, signaling bid requirements to the bidders individually. This will result in a preferred set of auction winners. It is believed to reduce the total transaction time and eliminate the necessity of holding subsequent negotiations with the set of winners.     

Tractable combinatorial auctions and b-matching

Auctions are the most widely used strategic game-theoretic mechanisms in the Internet. Auctions have been mostly studied from a game-theoretic and economic perspective, although recent work in AI and OR has been concerned with computational aspects of auctions as well. When faced from a computational perspective, combinatorial auctions are perhaps the most challenging type of auctions. Combinatorial auctions are auctions where agents may submit bids for bundles of goods. Given that finding an optimal allocation of the goods in a combinatorial auction is in general intractable, researchers have been concerned with exposing tractable instances of combinatorial auctions. In this work we expose the use of b-matching techniques in the context of combinatorial auctions, and apply them in a non-trivial manner in order to introduce polynomial solutions for a variety of combinatorial auctions.     

Exploring local search in winner determination problem

In Combinatorial Auctions, multiple goods (items) are available for auction simultaneously, and bidders bid for combinations of goods called bundles. In the single unit combinatorial auction problem, there is only single unit of each item present and the items are considered to be indivisible. This forms the supply side constraint resulting in a need by the seller to decide on which bundles to allocate for maximizing the revenue. Determining these winning bundles is an NP-complete problem and is known by the name of Winner Determination Problem (WDP) in literature. Combinatorial auction mechanism has a wide range of practical applications such as allocation of railroads, auction of adjacent pieces of real estate, auction of airport landing slots, distributed job shop scheduling etc. The optimal heuristic search algorithms like CASS and CABOB proposed for solving the WDP take a lot of CPU time for solving large problem instances. Though these algorithms give optimal solutions, they would be useful only in scenarios where time is not at all a constraint, and the bidding is a one time affair. This poses a limitation in conducting combinatorial auctions with multiple rounds of bidding and hence hinders the widespread use of combinatorial auctions on the patterns of traditional English auction and internet auctions. Thus faster solution of WDP holds the key to widespread use and popularity of combinatorial auctions. This paper attempts to address the above issue, and proposes a simple local search technique LSWDP (Local Search for Winner Determination Problem) that runs very fast and provides solutions quite close to optimal for a number of applications. It also outputs optimal solutions in many instances taking only a fraction of the CPU time taken by CASS. In addition LSWDP was found to outperform the anytime algorithm CASS given a time cutoff. This paper also presents an enhancement called LSCN (Local Search using Complimentary Neighborhood) that provides still better solutions in terms of close to optimal behavior and achieves a much better strike rate in hitting optimal solutions. LSCN runs slower than LSWDP but still takes only a fraction of the CPU time taken by CASS thus encouraging the use of local search for combinatorial auctions. Finally, an extension to multi-partition search has been proposed and analyzed.

An options-based solution to the sequential auction problem

The sequential auction problem is commonplace in open, electronic marketplaces such as eBay. This is the problem where a buyer has no dominant strategy in bidding across multiple auctions when the buyer would have a simple, truth-revealing strategy if there was but a single auction event. Our model allows for multiple, distinct goods and market dynamics with buyers and sellers that arrive over time. Sellers each bring a single unit of a good to the market while buyers can have values on bundles of goods. We model each individual auction as a second-price (Vickrey) auction and propose an options-based, proxied solution to provide price and winner-determination coordination across auctions. While still allowing for temporally uncoordinated market participation, this options-based approach solves the sequential auction problem and provides truthful bidding as a weakly dominant strategy for buyers. An empirical study suggests that this coordination can enable a significant efficiency and revenue improvement over the current eBay market design, and highlights the effect on performance of complex buyer valuations (buyers with substitutes and complements valuations) and varying the market liquidity.     

Real time prediction of closing price and duration of B2B reverse auctions

Nowadays, online auctions have become the most successful business model in the electronic marketplace. To the best of the authors’ knowledge, no other work has been devoted to the prediction of closing price and duration of Business-to-Business (B2B) English reverse online auctions in which goods or service providers compete with each other to win contracts by lowering offering prices with each bid, which is conducted on a virtual platform hosted on the Internet. This research designs and proposes a new methodology to predict closing prices and duration within the first few bids of the corresponding auctions based on real time bidding information rather than static auction information. In this article, we employ real time information and prediction rules to forecast the behavior of live auctions. This is in contrast to the static prediction approach that takes into consideration only information available at the beginning of an auction such as products, item features, or the seller’s reputation. This simulation is based on discretized auction data derived from a B2B online auction marketplace over a two-year period. Three measurements including accuracy, coverage, and benefit are used to evaluate the methodology. Results show that after observing the first 4 bids, this methodology can predict closing prices and duration with 84.6 and 71.9% accuracy, respectively.     

A secure multi-item e-auction mechanism with bid privacy

The recent focus within the auction field has been multi-item auctions where bidders are not restricted to buying only one item of the merchandise. It has been of practical importance in Internet auction sites and has been widely executed by them. In this paper, we concentrate on the use of the multi-item auction for task assignment scenarios and propose a novel PUPA auction protocol to solve the problem of bid privacy in multi-item auctions. A verifiable technique of shared key chain is proposed to find the winners without revealing the losing bid and bidder’s privacy. It can be shown that our new scheme is robust against cheating bidders.     

What Format for Multi-Unit Multiple-Bid Auctions?

This paper uses computational experiments where bidders learn over nonlinear bidding strategies to compare outcomes for alternative pricing format for multi-unit multiple-bid auctions. Multi-unit multiple-bid auctions, in which bidders are allowed to submit multiple price-quantity bids, are promising mechanisms for the allocation of a range of resources. The main advantage of such auctions is to avoid the lumpy bid problem which arises when bidders can only compete on the basis of one bid. However, there is great uncertainty about the best auction formats when multi-unit auctions are used. The theory can only supply the expected structural properties of equilibrium strategies and the multiplicity of potential equilibria makes comparisons across auction formats difficult. Empirical studies and experiments have improved our knowledge of multi-unit auctions but they remain scarce and most experiments are restricted to two bidders and two units. Moreover, they demonstrate that bidders have limited rationality and learn through experience. This paper constructs an agent-based computational model of bidders to compare the performance of alternative procurement auction formats under circumstances where bidders submit continuous bid supply functions and learn over time to adjust their bids in order to improve their net incomes. The setting is for independent private values. We show that bidding behaviour displays more interesting patterns than is depicted in the theoretical literature and that bidding patterns depend on the interplay between heterogeneity in the bidder population and the degree of rationing in the auction. Results indicate that the three auction formats have similar performance for most levels of competition but that their performances differ when competition is weak. This ranking is dependent on whether the population of bidders is homogenous or heterogeneous.     

Robust combinatorial auction protocol against false-name bids

This paper presents a new combinatorial auction protocol that is robust against false-name bids. Internet auctions have become an integral part of Electronic Commerce (EC) and a promising field for applying agent and Artificial Intelligence technologies. Although the Internet provides an excellent infrastructure for combinatorial auctions, we must consider the possibility of a new type of cheating, i.e., an agent tries to profit from submitting several bids under fictitious names (false-name bids). If there exists no false-name bid, the Generalized Vickrey Auction protocol (GVA) satisfies individual rationality, Pareto efficiency, and incentive compatibility. On the other hand, when false-name bids are possible, it is theoretically impossible for a combinatorial auction protocol to simultaneously satisfy these three properties.

Our newly developed Leveled Division Set (LDS) protocol, which is a modification of the GVA, utilizes reservation prices of auctioned goods for making decisions on whether to sell goods in a bundle or separately. The LDS protocol satisfies individual rationality and incentive compatibility even if agents can submit false-name bids, although it is not guaranteed to achieve a Pareto efficient social surplus. Simulation results show that the LDS protocol can achieve a better social surplus than that for a protocol that always sells goods in one bundle.     

A secure reverse Vickrey auction scheme with bid privacy

In recent years auctions have become more and more important in the field of multi-agent systems as useful mechanisms for resource allocations, task assignments and electronic commerce. In this paper, we concentrate on the use of the reverse Vickrey auction for task assignment scenarios and propose a novel RVP auction protocol as a method to solve problems to bid privacy in reverse Vickrey auctions. A verifiable technique of encryption key chain is used to find the second lowest bid without revealing the losing bid and unnecessary information. Through analysis, it is verified that our new scheme is robust against cheating bidders.     

Probabilistic Automated Bidding in Multiple Auctions

This paper presents an approach to develop bidding agents that participate in multiple auctions with the goal of obtaining an item with a given probability. The approach consists of a prediction method and a planning algorithm. The prediction method exploits the history of past auctions to compute probability functions capturing the belief that a bid of a given price may win a given auction. The planning algorithm computes a price and a set of compatible auctions, such that by sequentially bidding this price in each of the auctions, the agent can obtain the item with the desired probability. Experiments show that the approach increases the payoff of their users and the welfare of the market.     

The design and implementation of a secure auction service

We present the design and implementation of a distributed service for performing sealed bid auctions. This service provides an interface by which clients, or “bidders”, can issue secret bids to the service for an advertised auction. Once the bidding period has ended, the auction service opens the bids, determines the winning bid, and provides the winning bidder with a ticket for claiming the item bid upon. Using novel cryptographic techniques, the service is constructed to provide strong protection for both the auction house and correct bidders, despite the malicious behavior of any number of bidders and fewer than one third of the servers comprising the auction service. Specifically, it is guaranteed that: bids of correct bidders are not revealed until after the bidding period has ended; the auction house collects payment for the winning bid; losing bidders forfeit no money; and only the winning bidder can collect the item bid upon. We also discuss techniques to enable anonymous bidding     

Competitive analysis of incentive compatible on-line auctions

This paper studies auctions in a setting where the different bidders arrive at different times and the auction mechanism is required to make decisions about each bid as it is received. Such settings occur in computerized auctions of computational resources as well as in other settings. We call such auctions, on-line auctions.

We first characterize exactly on-line auctions that are incentive compatible, i.e. where rational bidders are always motivated to bid their true valuation. We then embark on a competitive worst-case analysis of incentive compatible on-line auctions. We obtain several results, the cleanest of which is an incentive compatible on-line auction for a large number of identical items. This auction has an optimal competitive ratio, both in terms of seller's revenue and in terms of the total social efficiency obtained.