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An Optimal Multi-Unit Combinatorial Procurement Auction with Single Minded Bidders  [PDF]
Sujit Gujar,Y Narahari
Computer Science , 2009,
Abstract: The current art in optimal combinatorial auctions is limited to handling the case of single units of multiple items, with each bidder bidding on exactly one bundle (single minded bidders). This paper extends the current art by proposing an optimal auction for procuring multiple units of multiple items when the bidders are single minded. The auction minimizes the cost of procurement while satisfying Bayesian incentive compatibility and interim individual rationality. Under appropriate regularity conditions, this optimal auction also satisfies dominant strategy incentive compatibility.
Efficiency Loss in Revenue Optimal Auctions  [PDF]
Vineet Abhishek,Bruce Hajek
Computer Science , 2010,
Abstract: We study efficiency loss in Bayesian revenue optimal auctions. We quantify this as the worst case ratio of loss in the realized social welfare to the social welfare that can be realized by an efficient auction. Our focus is on auctions with single-parameter buyers and where buyers' valuation sets are finite. For binary valued single-parameter buyers with independent (not necessarily identically distributed) private valuations, we show that the worst case efficiency loss ratio (ELR) is no worse than it is with only one buyer; moreover, it is at most 1/2. Moving beyond the case of binary valuations but restricting to single item auctions, where buyers' private valuations are independent and identically distributed, we obtain bounds on the worst case ELR as a function of number of buyers, cardinality of buyers' valuation set, and ratio of maximum to minimum possible values that buyers can have for the item.
Price of Anarchy for Auction Revenue  [PDF]
Jason Hartline,Darrell Hoy,Sam Taggart
Computer Science , 2014,
Abstract: This paper develops tools for welfare and revenue analyses of Bayes-Nash equilibria in asymmetric auctions with single-dimensional agents. We employ these tools to derive price of anarchy results for social welfare and revenue. Our approach separates the standard smoothness framework into two distinct parts, isolating the analysis common to any auction from the analysis specific to a given auction. The first part relates a bidder's contribution to welfare in equilibrium to their contribution to welfare in the optimal auction using the price the bidder faces for additional allocation. Intuitively, either an agent's utility and hence contribution to welfare is high, or the price she has to pay for additional allocation is high relative to her value. We call this condition value covering; it holds in every Bayes-Nash equilibrium of any auction. The second part, revenue covering, relates the prices bidders face for additional allocation to the revenue of the auction, using an auction's rules and feasibility constraints. Combining the two parts gives approximation results to the optimal welfare, and, under the right conditions, the optimal revenue. In mechanisms with reserve prices, our welfare results show approximation with respect to the optimal mechanism with the same reserves. As a center-piece result, we analyze the single-item first-price auction with individual monopoly reserves. When each distribution satisfies a regularity condition the auction's revenue is at least a $2e/(e-1) \approx 3.16$ approximation to the revenue of the optimal auction. We also give bounds for matroid auctions with first-price or all-pay semantics, and the generalized first-price position auction. Finally, we give an extension theorem for simultaneous composition, i.e., when multiple auctions are run simultaneously, with single-valued, unit-demand agents.
Optimal Auction Design with Quantized Bids  [PDF]
Nianxia Cao,Swastik Brahma,Pramod K. Varshney
Computer Science , 2015,
Abstract: This letter considers the design of an auction mechanism to sell the object of a seller when the buyers quantize their private value estimates regarding the object prior to communicating them to the seller. The designed auction mechanism maximizes the utility of the seller (i.e., the auction is optimal), prevents buyers from communicating falsified quantized bids (i.e., the auction is incentive-compatible), and ensures that buyers will participate in the auction (i.e., the auction is individually-rational). The letter also investigates the design of the optimal quantization thresholds using which buyers quantize their private value estimates. Numerical results provide insights regarding the influence of the quantization thresholds on the auction mechanism.
Revenue and Duration of Oral Auction  [PDF]
Junmin SHI, Ai-Chih CHANG
Journal of Service Science and Management (JSSM) , 2009, DOI: 10.4236/jssm.2009.24044
Abstract: This paper investigates the revenue and duration of a well-known hybrid oral auction (English auction and Dutch auction) that is extensively adopted in practice, for instance the Christie’s. Unlike sealed bid auction, oral auction is featured by its complexity of dynamic process. The bidding price varies as a stochastic time series. Therefore, the duration of oral auction as well as its revenue performs randomly. From the seller’s perspective, both the revenue and the duration are so important that extra attention and effort should be put on auction design. One of the most important issues is how to choose the starting bid price to maximize its revenue or minimize its duration. In this paper, the bidding process is decomposed into two phases: English auction (descending-bid) phase and the Dutch auction (ascending-bid) phase. For each phase, with the aid of Markov method, we derive the expected revenue and duration as a function of the starting bid. For an oral auction with a large number of bidder and each bidder behaves independently, we provide the limit results of the expected revenue and duration. The results of the auction model can be easily implemented in auction design.
Optimal Competitive Auctions  [PDF]
Ning Chen,Nick Gravin,Pinyan Lu
Computer Science , 2014,
Abstract: We study the design of truthful auctions for selling identical items in unlimited supply (e.g., digital goods) to n unit demand buyers. This classic problem stands out from profit-maximizing auction design literature as it requires no probabilistic assumptions on buyers' valuations and employs the framework of competitive analysis. Our objective is to optimize the worst-case performance of an auction, measured by the ratio between a given benchmark and revenue generated by the auction. We establish a sufficient and necessary condition that characterizes competitive ratios for all monotone benchmarks. The characterization identifies the worst-case distribution of instances and reveals intrinsic relations between competitive ratios and benchmarks in the competitive analysis. With the characterization at hand, we show optimal competitive auctions for two natural benchmarks. The most well-studied benchmark $\mathcal{F}^{(2)}(\cdot)$ measures the envy-free optimal revenue where at least two buyers win. Goldberg et al. [13] showed a sequence of lower bounds on the competitive ratio for each number of buyers n. They conjectured that all these bounds are tight. We show that optimal competitive auctions match these bounds. Thus, we confirm the conjecture and settle a central open problem in the design of digital goods auctions. As one more application we examine another economically meaningful benchmark, which measures the optimal revenue across all limited-supply Vickrey auctions. We identify the optimal competitive ratios to be $(\frac{n}{n-1})^{n-1}-1$ for each number of buyers n, that is $e-1$ as $n$ approaches infinity.
Optimal Auctions for Correlated Buyers with Sampling  [PDF]
Hu Fu,Nima Haghpanah,Jason Hartline,Robert Kleinberg
Computer Science , 2014,
Abstract: Cr\'emer and McLean [1985] showed that, when buyers' valuations are drawn from a correlated distribution, an auction with full knowledge on the distribution can extract the full social surplus. We study whether this phenomenon persists when the auctioneer has only incomplete knowledge of the distribution, represented by a finite family of candidate distributions, and has sample access to the real distribution. We show that the naive approach which uses samples to distinguish candidate distributions may fail, whereas an extended version of the Cr\'emer-McLean auction simultaneously extracts full social surplus under each candidate distribution. With an algebraic argument, we give a tight bound on the number of samples needed by this auction, which is the difference between the number of candidate distributions and the dimension of the linear space they span.
The Importance of Individual Characteristics on Consideration Sets for Online Auction Buyers
Drake,John R; Hall,Dianne J; Byrd,Terry Anthony;
Journal of theoretical and applied electronic commerce research , 2012, DOI: 10.4067/S0718-18762012000200003
Abstract: in this research, we extend online auction theory by considering set theory in terms of a staged buying process. success of online auction marketplaces depends on the efficacy of individual buyers searching for and finding desired items for bidding. searches that lead to consideration sets with too many or too few options may result in a suboptimal choice. results from this study suggest that certain personal characteristics may impact the number of auctions considered when filtering the awareness set to the consideration set. the findings suggest that design and management of online auction marketplaces should be refined to facilitate these individual traits such that individual search strategies are maximized.
The Auction and its Application in Multi-Agent System

JIN Xing SHI Chun-Yi,

计算机科学 , 2003,
Abstract: Auction, an operational and effective resource allocation method. generally results in economical efficiency allocation between buyers and sellers. As a negotiation method, auction can be used in Multi-Agent Systems. With the consideration of computation ability and communication ability of agents, superadditive and subadditive property of goods, requirements of agents' revenue and real*time ability, proper auction methods can be selected to achieve one-many or many-many task assignments or resource allocation. In this paper, we systematically summarize biding rules, buyers and sellers' strategies and the performances of current auction methods. A formal auction model, which fits most of the current auction methods, is also presented.
Revenue Optimization in Posted-Price Auctions with Strategic Buyers  [PDF]
Mehryar Mohri,Andres Mu?oz Medina
Computer Science , 2014,
Abstract: We study revenue optimization learning algorithms for posted-price auctions with strategic buyers. We analyze a very broad family of monotone regret minimization algorithms for this problem, which includes the previously best known algorithm, and show that no algorithm in that family admits a strategic regret more favorable than $\Omega(\sqrt{T})$. We then introduce a new algorithm that achieves a strategic regret differing from the lower bound only by a factor in $O(\log T)$, an exponential improvement upon the previous best algorithm. Our new algorithm admits a natural analysis and simpler proofs, and the ideas behind its design are general. We also report the results of empirical evaluations comparing our algorithm with the previous state of the art and show a consistent exponential improvement in several different scenarios.
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