A Double-Sided Multiunit Combinatorial Auction for Substitutes: Theory and Algorithms

Combinatorial exchanges have existed for a long time in securities markets. In these auctions buyers and sellers can place orders on combinations, or bundles of different securities. These orders are conjunctive: they are matched only if the full bundle is available. On business-to-business (B2B) exchanges, buyers have the choice to receive the same product with different attributes; for instance the same product can be produced by different sellers. A buyer indicates his preference by submitting a disjunctive order, where he specifies how much of the product he wants, and how much he values each attribute. Only the goods with the best attributes and prices will be matched. This article considers a doubled-sided multi-unit combinatorial auction for substitutes, that is, a uniform price auction where buyers and sellers place both types of orders, conjunctive and disjunctive. We prove the existence of a linear price which is both competitive and surplus-maximizing when goods are perfectly divisible, and nearly so otherwise. We describe an algorithm to clear the market, which is particularly efficient when the number of traders is large.Combinatorial auction, economic equilibrium

Combinatorial auctions for electronic business

Combinatorial auctions (CAs) have recently generated significant interest as an automated mechanism for buying and selling bundles of goods. They are proving to be extremely useful in numerous e-business applications such as e-selling, e-procurement, e-logistics, and B2B exchanges. In this article, we introduce combinatorial auctions and bring out important issues in the design of combinatorial auctions. We also highlight important contributions in current research in this area. This survey emphasizes combinatorial auctions as applied to electronic business situations

Preventing Strategic Manipulation in Iterative Auctions: Proxy Agents and Price-Adjustment

Iterative auctions have many computational advantages over sealed-bid auctions, but can present new possibilities for strategic manipulation. We propose a two-stage technique to make iterative auctions that compute optimal allocations with myopic best-response bidding strategies more robust to manipulation. First, introduce proxy bidding agents to constrain bidding strategies to (possibly untruthful) myopic bestresponse. Second, after the auction terminates adjust the prices towards those given in the Vickrey auction, a sealedbid auction in which truth-revelation is optimal. We present an application of this methodology to iBundle, an iterative combinatorial auction which gives optimal allocations for myopic best-response agents.Engineering and Applied Science

Multiattribute electronic procurement using goal programming

One of the key challenges of current day electronic procurement systems is to enable procurement decisions transcend beyond a single attribute such as cost. Consequently, multiattribute procurement have emerged as an important research direction. In this paper, we develop a multiattribute e-procurement system for procuring large volume of a single item. Our system is motivated by an industrial procurement scenario for procuring raw material. The procurement scenario demands multiattribute bids, volume discount cost functions, inclusion of business constraints, and consideration of multiple criteria in bid evaluation. We develop a generic framework for an e-procurement system that meets the above requirements. The bid evaluation problem is formulated as a mixed linear integer multiple criteria optimization problem and goal programming is used as the solution technique. We present a case study for which we illustrate the proposed approach and a heuristic is proposed to handle the computational complexity arising out of the cost functions used in the bids

Simulating digital dividend auctions: Service neutrality versus dedicated licences

The award of the digital dividend can consolidate auctions as the preferred mechanism for spectrum allocation. Knowing in advance an estimate of what the results of an auction with these characteristics could be would be unquestionably useful for those in charge of designing the process, even if at the end another method such as a beauty contest is chosen. This article provides a simulation of a digital dividend auction in a major-type European country. In one of the scenarios, the spectrum is not pre-allocated to any service in particular (service neutrality) while in the remaining four, blocks of spectrum are pre-allocated to DTT, mobile multimedia and mobile broadband communications. The results of the simulations reveal that the service neutrality scenario maximizes revenues for the seller and that, in general, DTT operators would seem to have fewer opportunities as the spectrum packaging is less protective for them

Average Sensitivity of the Knapsack Problem

In resource allocation, we often require that the output allocation of an algorithm is stable against input perturbation because frequent reallocation is costly and untrustworthy. Varma and Yoshida (SODA\u2721) formalized this requirement for algorithms as the notion of average sensitivity. Here, the average sensitivity of an algorithm on an input instance is, roughly speaking, the average size of the symmetric difference of the output for the instance and that for the instance with one item deleted, where the average is taken over the deleted item. In this work, we consider the average sensitivity of the knapsack problem, a representative example of a resource allocation problem. We first show a (1-?)-approximation algorithm for the knapsack problem with average sensitivity O(?^{-1}log ?^{-1}). Then, we complement this result by showing that any (1-?)-approximation algorithm has average sensitivity ?(?^{-1}). As an application of our algorithm, we consider the incremental knapsack problem in the random-order setting, where the goal is to maintain a good solution while items arrive one by one in a random order. Specifically, we show that for any ? > 0, there exists a (1-?)-approximation algorithm with amortized recourse O(?^{-1}log ?^{-1}) and amortized update time O(log n+f_?), where n is the total number of items and f_? > 0 is a value depending on ?

Computing Price Trajectories in Combinatorial Auctions with Proxy Bidding

Proxy bidding has proven useful in a variety of real auction formats---most notably eBay--- and has been proposed for the nascent field of combinatorial auctions. Previous work on proxy bidding in combinatorial auctions requires the auctioneer to run the auction with myopic bidders to determine the outcome. In this paper we present a radically different approach that computes the bidders' allocation of their attention across the bundles only at "inflection points." Inflections are caused by the introduction of a new bundle into an agent's demand set, a change in the set of currently competitive allocations, or the withdrawal of an agent from the set of active bidders. This approach has several advantages over alternatives, including that it computes exact solutions and is invariant to the magnitude of the bids

Exploring bidding strategies for market-based scheduling

A market-based scheduling mechanism allocates resources indexed by time to alternative uses based on the bids of participating agents. Agents are typically interested in multiple time slots of the schedulable resource, with value determined by the earliest deadline by which they can complete their corresponding tasks. Despite the strong complementarity among slots induced by such preferences, it is often infeasible to deploy a mechanism that coordinates allocation across all time slots. We explore the case of separate, simultaneous markets for individual time slots, and the strategic problem it poses for bidding agents. Investigation of the straightforward bidding policy and its variants indicates that the efficacy of particular strategies depends critically on preferences and strategies of other agents, and that the strategy space is far too complex to yield to general game-theoretic analysis. For particular environments, however, it is often possible to derive constrained equilibria through evolutionary search methods.http://deepblue.lib.umich.edu/bitstream/2027.42/50434/1/proof-dexter-dss.pd