车辆牌照拍卖模型

提出多个相同物品(如车辆牌照)同时密封拍卖的模型，给出对称均衡竞标策略；证明了该拍卖方式与第一价格密封连续拍卖产生相同的预期收益；对估价为均匀分布的拍卖预期收益进行了研究。     

All-pay auctions with risk-averse players

We study independent private-value all-pay auctions with risk-averse players. We show that: (1) Players with low values bid lower and players with high values bid higher than they would bid in the risk neutral case. (2) Players with low values bid lower and players with high values bid higher than they would bid in a first-price auction. (3) Players’ expected utilities in an all-pay auction are lower than in a first-price auction. We also use perturbation analysis to calculate explicit approximations of the equilibrium strategies of risk-averse players and the seller’s expected revenue. In particular, we show that in all-pay auctions the seller’s expected payoff in the risk-averse case may be either higher or lower than in the risk neutral case.     

Equilibrium and revenue in a family of common-value first-price auctions with differential information

We study a discrete common-value auction environment with two asymmetrically informed bidders. Equilibrium of the first-price auction is in mixed strategies, which we characterize using a doubly recursive solution method. The distribution of bids for the ex post strong player stochastically dominates that for the ex post weak player. This result complements Maskin and Riley’s (Rev Econ Stud 67:413–438, 2000) similar result for asymmetric private-value auctions. Finally, comparison with the dominance-solvable equilibrium in a second-price auction shows the Milgrom–Weber (Econometrica 50:1089–1122, 1982a) finding that the second-price auction yields at least as much revenue as the first-price auction fails with asymmetry: in some cases the first-price auction provides greater expected revenue, in some cases less.     

Ranking asymmetric auctions

We compare the expected revenue in first- and second-price auctions with asymmetric bidders. We consider “close to uniform” distributions with identical supports and show that in the case of identical supports the expected revenue in second-price auctions may exceed that in first-price auctions. We also show that asymmetry over lower valuations has a stronger negative impact on the expected revenue in first-price auctions than in second-price auctions. However, asymmetry over high valuations always increases the revenue in first-price auctions.     

How to bid in unified second-price auctions when requests are duplicated

In display advertising auctions, a unique display opportunity may trigger many bid requests being sent to the same buyer. Bid request duplication is an issue: programmatic bidding agents might bid against themselves. In a simplified setting of unified second-price auctions, the optimal solution for the bidder is to randomize the bid, which is quite unusual. Our results motivate the recent switch to a unified first-price auction by showing that a unified second-price auction could have been detrimental to all participants.     

Fraction auctions: The tradeoff between efficiency and running time

This paper studies the sales of a single indivisible object where bidders have continuous valuations. In Grigorieva et al. [14] it was shown that, in this setting, query auctions necessarily allocate inefficiently in equilibrium. In this paper we propose a new sequential auction, called the c-fraction auction. We show the existence of an ex-post equilibrium, called bluff equilibrium, in which bidders behave truthfully except for particular constellations of observed bids at which it is optimal to pretend a slightly higher valuation. We show c-fraction auctions guarantee approximate efficiency at any desired level of accuracy, independent of the number of bidders, when bidders choose to play the bluff equilibrium. We discuss the running time and the efficiency in the bluff equilibrium. We show that by changing the parameter c of the auction we can trade off efficiency against running time.     

Using bid data for the management of sequential,multi-unit,online auctions with uniformly distributed bidder valuations

Internet auctions for consumers’ goods are an increasingly popular selling venue. We have observed that many sellers, instead of offering their entire inventory in a single auction, split it into sequential auctions of smaller lots, thereby reducing the negative market impact of larger lots. Information technology also makes it possible to collect and analyze detailed bid data from online auctions. In this paper, we develop and test a new model of sequential online auctions to explore the potential benefits of using real bid data from earlier auctions to improve the management of future auctions. Assuming a typical truth-revealing auction model, we quantify the effect of the lot size on the closing price and derive a closed-form solution for the problem of allocating inventory across multiple auctions when bidder valuation distributions are known. We also develop a decision methodology for allocating inventory across multiple auctions that dynamically incorporates the results of previous auctions as feedback into the management of subsequent auctions, and updating the lot size and number of auctions. We demonstrate how information signals from previous auctions can be used to update the auctioneer’s beliefs about the customers’ valuation distribution, and then to significantly increase the seller’s profit potential. We use several examples to reveal the benefits of using detailed transaction data for the management of sequential, multi-unit, online auctions and we demonstrate how these benefits are influenced by the inventory holding costs, the number of bidders, and the dispersion of consumers’ valuations.     

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     

Dynamic lot-sizing in sequential online retail auctions

Retailers often conduct non-overlapping sequential online auctions as a revenue generation and inventory clearing tool. We build a stochastic dynamic programming model for the seller’s lot-size decision problem in these auctions. The model incorporates a random number of participating bidders in each auction, allows for any bid distribution, and is not restricted to any specific price-determination mechanism. Using stochastic monotonicity/stochastic concavity and supermodularity arguments, we present a complete structural characterization of optimal lot-sizing policies under a second order condition on the single-auction expected revenue function. We show that a monotone staircase with unit jumps policy is optimal and provide a simple inequality to determine the locations of these staircase jumps. Our analytical examples demonstrate that the second order condition is met in common online auction mechanisms. We also present numerical experiments and sensitivity analyses using real online auction data.     

Declining valuations in sequential auctions

We analyze an independent private values model where a number of objects are sold in sequential first- and second-price auctions. Bidders have unit demand and their valuation for an object is decreasing in the rank number of the auction in which it is sold. We derive efficient equilibria if prices are announced after each auction or if no information is given to bidders. We show that the sequence of prices constitutes a supermartingale. Even if we correct for the decrease in valuations for objects sold in later auctions we find that average prices are declining.Received June 2004We are grateful to Christian Groh, Wolfgang Köhler and Benny Moldovanu for helpful suggestions. Financial support from the German Science Foundation through SFB 504 and SFB/TR 15 at the University of Mannheim and the University of Bonn is gratefully acknowledged.     

Charity auctions for the happy few

Recent literature has shown that all-pay auctions raise more money for charity than either winner-pay auctions or lotteries. We demonstrate that first-price and second-price winner-pay auctions have a better revenue performance than first-price and second-price all-pay auctions when bidders are sufficiently asymmetric. Lotteries can also provide higher revenue than all-pay auctions. To prove this, we consider a framework with complete information. Complete information is helpful and may reflect events that occur, for instance, in a local service club (such as a voluntary organization) or at a show-business dinner.     

Hats,auctions and derandomization

We investigate derandomizations of digital good randomized auctions. We propose a general derandomization method which can be used to show that for every random auction there exists a deterministic auction having asymptotically the same revenue. In addition, we construct an explicit optimal deterministic auction for bi‐valued auctions. © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 46, 478–493, 2015     

First- and second-price sealed-bid auctions applied to push and pull supply contracts

We investigate a newsvendor-type retailer sourcing problem under demand uncertainty who has the option to source from multiple suppliers. The suppliers’ manufacturing costs are private information. A widely used mechanism to find the least costly supplier under asymmetric information is to use a sealed-bid reverse auction. We compare the combinations of different simple auction formats (first- and second-price) and risk sharing supply contracts (push and pull) under full contract compliance, both for risk-neutral and risk-averse retailer and suppliers. We show the superiority of a first-price push auction for a risk-neutral retailer. However, only the pull contracts lead to supply chain coordination. If the retailer is sufficiently risk-averse, the pull is preferred over the push contract. If suppliers are risk-averse, the first-price push auction remains the choice for the retailer. Numerical examples illustrate the allocation of benefits between the retailer and the (winning) supplier for different number of bidders, demand uncertainty, cost uncertainty, and degree of risk-aversion.     

Large auctions with risk-averse bidders

We study private-value auctions with n risk-averse bidders, where n is large. We first use asymptotic analysis techniques to calculate explicit approximations of the equilibrium bids and of the seller’s revenue in any k-price auction (k = 1, 2, . . .). These explicit approximations show that in all large k-price auctions the effect of risk-aversion is O(1/n ²) small. Hence, all large k-price auctions with risk-averse bidders are O(1/n ²) revenue equivalent. The generalization, that all large auctions are O(1/n ²) revenue equivalent, is false. Indeed, we show that there exist auction mechanisms for which the limiting revenue as ${n\longrightarrow \infty }We study private-value auctions with n risk-averse bidders, where n is large. We first use asymptotic analysis techniques to calculate explicit approximations of the equilibrium bids and of the seller’s revenue in any k-price auction (k = 1, 2, . . .). These explicit approximations show that in all large k-price auctions the effect of risk-aversion is O(1/n ²) small. Hence, all large k-price auctions with risk-averse bidders are O(1/n ²) revenue equivalent. The generalization, that all large auctions are O(1/n ²) revenue equivalent, is false. Indeed, we show that there exist auction mechanisms for which the limiting revenue as n? ￥{n\longrightarrow \infty } with risk-averse bidders is strictly below the risk-neutral limit. Therefore, these auction mechanisms are not revenue equivalent to large k-price auctions even to leading-order as n? ￥{n\longrightarrow \infty }.     

The communication complexity of private value single-item auctions

This paper is concerned with information revelation in single-item auctions. We compute how much data needs to be transmitted in three strategically equivalent auctions—the Vickrey auction, the English auction and the recently proposed bisection auction—and show that in the truth-telling equilibrium the bisection auction is the best performer.     

Auctions with synergy and resale

We study a sequential auction of two objects with two bidders, where the winner of the package obtains a synergy from the second object. If reselling after the two auctions occurs, it proceeds as either monopoly or monopsony take-it-or-leave-it offer. We find that a post-auction resale has a significant impact on bidding strategies in the auctions: Under the monopoly offer, there does not exist an equilibrium (symmetric or asymmetric) where bidders reveal their types with positive probability. Under the monopsony offer, however, we can identify symmetric increasing equilibrium strategies in auctions for both items. While allowing resale always improves efficiency, we demonstrate that the effect of resale on expected revenue and the probability of exposure are both ambiguous.     

Visualizing Online Auctions

Online auctions have been the subject of many empirical research efforts in the fields of economics and information systems. These research efforts are often based on analyzing data from Web sites such as eBay.com which provide public information about sequences of bids in closed auctions, typically in the form of tables on HTML pages. The existing literature on online auctions focuses on tools like summary statistics and more formal statistical methods such as regression models. However, there is a clear void in this growing body of literature in developing appropriate visualization tools. This is quite surprising, given that the sheer amount of data that can be found on sites such as eBay.com is overwhelming and can often not be displayed informatively using standard statistical graphics. In this article we introduce graphical methods for visualizing online auction data in ways that are informative and relevant to the types of research questions that are of interest. We start by using profile plots that reveal aspects of an auction such as bid values, bidding intensity, and bidder strategies. We then introduce the concept of statistical zooming (STAT-zoom) which can scale up to be used for visualizing large amounts of auctions. STAT-zoom adds the capability of looking at data summaries at various time scales interactively. Finally, we develop auction calendars and auction scene visualizations for viewing a set of many concurrent auctions. The different visualization methods are demonstrated using data on multiple auctions collected from eBay.com.     

Vickrey–Dutch procurement auction for multiple items

We consider a setting where there is a manufacturer who wants to procure multiple items from a set of suppliers each of whom can supply one or more of these items (bundles). We design an ascending price auction for such a setting which implements the Vickrey–Clarke–Groves outcome and truthful bidding is an ex post Nash equilibrium. Our auction maintains non-linear and non-anonymous prices throughout the auction. This auction has a simple price adjustment step and is easy to implement in practice. As offshoots of this auction, we also suggest other simple auctions (in which truthful bidding is not an equilibrium by suppliers) which may be suitable where incentives to suppliers are not a big concern. Computer simulations of our auction show that it is scalable for the multi-unit case, and has better information revelation properties than its descending auction counterpart.     

Core-selecting package auctions: a comment on revenue-monotonicity

Day and Milgrom (Int J Game Theory 36:393–407, 2008) argue that package auctions that select the seller’s minimum revenue in the Core are revenue-monotone. We show that no bidder-optimal Core-selecting auction can satisfy revenue-monotonicity for general preferences when there are at least three goods for sale, while the property holds for any bidder-optimal Core-selecting auction in environments with only two goods or if the characteristic function is submodular.