On the lowest-winning-bid and the highest-losing-bid auctions

Theoretical models of multi-unit, uniform-price auctions assume that the price is given by the highest losing bid. In practice, however, the price is usually given by the lowest winning bid. We derive the equilibrium bidding function of the lowest-winning-bid auction when there are k objects for sale and n bidders with unit demand, and prove that it converges to the bidding function of the highest-losing-bid auction if and only if the number of losers n−k gets large. When the number of losers grows large, the bidding functions converge at a linear rate and the prices in the two auctions converge in probability to the expected value of an object to the marginal winner.     

Selling shares to retail investors: auction vs. fixed price

We analyze the problem of selling shares of a divisible good to a large number of buyers when demand is uncertain. We characterize equilibria of two popular mechanisms, a fixed price mechanism and a uniform price auction, and compare the revenues. While in the auction truthful bidding is a dominant strategy, we find that bidders have an incentive to overstate their demand in the fixed price mechanism. For some parameter values we find that the fixed price mechanism outperforms the auction.     

Wars of attrition and all-pay auctions with stochastic competition

We extend the war of attrition and all-pay auction analysis of Krishna and Morgan (1997) to a stochastic competition setting. We determine the existence of equilibrium bidding strategies and discuss the potential shape of these strategies. Results for the war of attrition contrast with the characterization of the bidding equilibrium strategies in the first-price all-pay auction as well as the winner-pay auctions. Furthermore we investigate the expected revenue comparisons among the war of attrition, the all-pay auction and the winner-pay auctions and discuss the linkage principle as well. Our findings are applicable to future works on contests and charity auctions.     

基于拍卖的垄断型产品供应链的博弈分析

论文研究了基于拍卖交易的垄断型产品供应链中卖方和买方的博弈问题,成交价格同时取决于卖方向拍卖市场的供货数量和买方向拍卖市场的竞拍数量。博弈结果显示,在垄断供应的情况下,博弈的纳什均衡将会是买卖双方都不通过拍卖渠道来进行交易,只有在非常极端的条件下可以达成供货和竞拍等量的均衡。最后,论文引入一个新卖方作为买方参与拍卖后的补货来源,得到的新均衡解能使原买卖双方的收益提高,从而说明单纯的拍卖并不总是最好的交易方式,多渠道的销售方式有时更能保障买卖双方的利益。     

论几种特殊合同中的要约与承诺

文章指出,在招投标形式订立合同的过程中,招标属于合同上的要约邀请,投标为要约,定标是承诺,但招标属于必须经过的阶段,投标的撤回随意性比较大,定标采取投邮生效主义。在拍卖订立合同的过程中,各行为的性质视增价拍卖和减价拍卖而有所不同。增价拍卖也会因为有底价拍卖和无底价拍卖的区别而导致行为性质的差异。招股说明书的要式特征,使其虽然不满足要约的条件,但法定成为了要约,而且不可撤回和撤销。     

Descending price multi-item auctions

We propose a simultaneous descending price auction mechanism to sell multiple heterogeneous items, each owned by a distinct seller, to a number of buyers. Each buyer has known private valuations on items, and wants at most one item. We show that if the sellers follow a descending price offer procedure and the buyers follow a greedy strategy for accepting the offers, the auction results in a nearly efficient allocation, and terminates close to a competitive equilibrium price vector. The descending price offer strategy of the sellers is close to a Nash equilibrium. However, we show that the buyers are better off waiting in our auction. There is a maximum limit (corresponding to the minimum competitive equilibrium price vector) till which they can wait without running into the risk of not winning any item. If the buyers wait within this limit, the prices can be brought arbitrarily close to a uniquely defined competitive equilibrium price vector.     

我国海域使用权招标拍卖市场机制分析与完善

海域使用权招标拍卖作为国有海域资源配置的重要方式之一,是海域使用管理制度顺应市场经济发展需要的突出表现。本文从参与主体、适用范围以及市场规模方面对海域使用权招标拍卖市场机制进行了现状分析,从保留价格计算、创新招标拍卖方式、构建交易平台等方面,对现有的海域使用权招标拍卖市场交易机制进行了完善,以期丰富和发展海域使用权的招标拍卖机制,提高海域使用权的市场化配置效率。     

First price package auction with many traders

This paper studies a first price package auction in which multiple sellers participate in addition to multiple buyers. We generalize the notion of the profit-target strategy which is first introduced as a truthful strategy in a first price package auction with a single seller by Bernheim and Whinston (1986b). We then show that the set of equilibrium payoffs in profit-target strategies is equal to the bidder-optimal core, and is also equal to the set of coalition-proof Nash equilibria. Using this result, we find that any equilibrium payoff vector is weakly Pareto-dominated by the VCG payoff vector for buyers, and that the Walrasian competitive equilibrium payoff vector is weakly Pareto-dominated by some equilibrium payoff vector for buyers, even if goods are substitutes. This contrasts with the first price package auction with a single seller, in which it is shown that if goods are substitutes, then those three outcomes are payoff-equivalent.     

Revenue and efficiency ranking in large multi-unit and bundle auctions

Should a seller use a multi-unit auction for identical and indivisible units of a good? We show, under specific assumptions on the value distributions of the bidders, that in large markets the multi-unit format generates higher (lower) expected revenue compared to the bundled format when the supply is relatively scarce (abundant). In contrast, a large market is shown to be always more efficient under the multi-unit format than its bundled counterpart. Thus under these assumptions a profit maximizing seller is expected to choose the relatively efficient multi-unit format when supply is scarce.     

An experimental study of signaling in auctions with a flexible reserve price

This paper presents the results of an experimental study of preemptive jump bidding in English auctions with a flexible reserve price. While one of the possible explanations for jump bidding is based on signaling arguments, the ability of the seller to adjust his decision to accept an offer based on the bidding history makes the existence of a signaling equilibrium questionable. This paper shows that the seller's ability to set the reserve price after observing the opening bid reduces both jump bidding behavior and the use and interpretation of opening bids as a signaling device.     

佣金约束条件下排污权双边叫价拍卖机制设计

通过排污权交易提高环境资源的使用效率和配置效率,实现环境资源最优配置。排污权和排污权市场理论研究是环境资源可持续利用的重要研究课题,而排污权交易模型是排污权市场理论与实践中排污权交易的核心。本文采用双边叫价拍卖交易模式,建立了排污权交易双边叫价拍卖的不完全信息博弈模型,给出了双边叫价拍卖的机制设计。该机制具有有效性和激励相容性。     

上海市土地使用权出让机制改革研究——基于拍卖理论和上海市土地市场的实证检验

2007年上海市规定住宅用地挂牌出让的现场竞价规则由公开叫价改为一次性书面报价,旨在降低上海市住宅用地的价格.本文在价值相容和可显示信息的假设下,分别建立两阶段升价拍卖模型和混合拍卖模型,刻画改革前后的挂牌机制,指出:竞标者的均衡策略可解释土地挂牌出让中开发商集中在现场竞价阶段内出价,且更倾向在混合拍卖中隐藏信息的行为;当竞价过程中更易于显示信息时,混合拍卖的期望收入低于两阶段升价拍卖,这表明混合拍卖方式能够降低土地价格.上海市的土地交易数据也证明了这一结论.     

多单位网上拍卖中的托投标分析

在独立私有价值的多单位网上英式拍卖中，诚实的竞标者能够采用对抗性的竞标策略来降低卖者参与托投标的激励，然而即使考虑了诚实竞标者对于托投标的策略性响应，托投标对于卖者而言依然是有利可图的。更为有效地阻止托投标的措施可能包括吸引更多的潜在竞标者，并限制在单次拍卖中销售的物品数量。同时考虑了卖者对于这种对抗性竞标策略的策略响应，求解了卖者的最优托投标，结论表明无论最优的托投标是唯一的还是多重的，卖者的最优策略是在开始使用低的托投标，在观察到之前的竞标信息之后通过动态调整将托投标设定到最优水平。     

Anticipation of Auction Fever: Entry Decision,Reserve Price and the Choice of Auction Design

This paper analyzes the entry decision of rational bidders who expect to experience auction fever in English auctions. It shows that nonparticipation decision reduces seller's expected profit and this effect may outweigh the positive effect of the auction fever. We analyze the choice between English and second‐price sealed‐bid auctions and the optimal reserve price in English auctions. We show that it might be optimal for the seller to set a reserve price below her own valuation of the object. Finally, we show that the order in which bidders place their bids matters and the first bidder always has an advantage. Copyright © 2011 John Wiley & Sons, Ltd.     

基于边际成本递增的多属性反向拍卖最优策略

针对当前传统的基于单一价格属性的逆向拍卖机制已难以满足企业日益复杂的采购需求的现状,需要研究采购环境下的多属性英式拍卖机制。首先,文中提出了基于边际成本递增的多属性拍卖模型。然后运用多属性效用理论,进一步研究了在多属性英式拍卖机制下投标人的最优投标策略及拍卖人最优评分规则。最后,基于边际成本递增的多属性拍卖模型,研究了不同因素及边际成本对拍卖人最优评分规则的影响。     

First-price auctions where one of the bidders’ valuations is common knowledge

We analyze a private and independent valuation first-price auction under the assumption that one of the bidders’ valuations is common knowledge. We show that no pure strategy equilibrium exists and we characterize a mixed strategy equilibrium in which the bidder whose valuation is common knowledge randomizes her bid while the other bidders play pure strategies. In an example with the uniform distribution, we compare the expected profits of seller and buyers in this auction with those in a standard symmetric private valuation model.     

Delegation in first‐price all‐pay auctions

In a first‐price all‐pay auction buyers have an incentive to delegate the bidding to agents and to provide these agents with incentives to make bids that differ from the bids the buyers would like to make. Both buyers are better off in this strictly non‐cooperative delegation equilibrium and the delegation contracts are asymmetric, even if the buyers and the auction are perfectly symmetric. Copyright © 2004 John Wiley & Sons, Ltd.     

Auctions with asymmetric common-values: The first-price format

We study the performance of the first-price format in auctions with asymmetric common-values. We show that, contrary to the result for second-price auctions, a small advantage for one player translates only to small changes in bidders’ strategies, and the equilibrium remains close to the first-price equilibrium of the original game. We characterize the equilibrium bidding strategies and their behavior as the degree of asymmetry increases. Finally, we compare the revenues at the optimal auction, the first-price auction and the second-price auction.     

Econometric models of asymmetric ascending auctions

We develop econometric models of ascending (English) auctions which allow for both bidder asymmetries as well as common and/or private value components in bidders’ underlying valuations. We show that the equilibrium inverse bid functions in each round of the auction are implicitly defined (pointwise) by a system of nonlinear equations, so that conditions for the existence and uniqueness of an increasing-strategy equilibrium are essentially identical to those which ensure a unique and increasing solution to the system of equations. We exploit the computational tractability of this characterization in order to develop an econometric model, thus extending the literature on structural estimation of auction models. Finally, an empirical example illustrates how equilibrium learning affects bidding during the course of the auction.     

Auctions with endogenous participation

We study endogenous-participation auctions where bidders only know the number of potential participants. After seeing their values for the object, potential participants decide whether or not to enter the auction. They may not want to enter the auction since they have to pay participation costs. We characterize equilibrium bidding strategies and entry decisions for both first- and second-price sealed-bid auctions when participation is endogenous. We show that there is a pure strategy entry equilibrium where only bidders with values greater than a certain cut-off point actually bid. In this context, both types of auctions generate the same expected revenue. We also show that, contrary to the predictions of the fixed number of bidders literature, the seller's expected revenue may decrease when the number of potential participants increases. In addition, we show that it is optimal for the seller to charge an entry fee, which contrasts with results from the existing literature on auctions with entry. As in the fixed-n literature, we show that first-price auctions generate more expected revenue than second-price auctions when buyers are risk-averse. Finally, we characterize the optimal auction – the auction that maximizes the seller's expected revenue – by using a direct revelation mechanism. The optimal auction involves a reserve price larger than the optimal reserve price in the fixed-n literature. The winner's payment is the second highest bid less the participation cost and losers receive a subsidy equal to the participation cost. Received: 17 August 1998 / 21 September 1999