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.     

The participatory Vickrey–Clarke–Groves mechanism

This paper introduces the participatory Vickrey–Clarke–Groves mechanism, which satisfies both ex-ante budget balance and interim individual rationality. We bound the efficiency loss of this mechanism by a parameter that captures the structure of marginal contributions to the social welfare. We then apply the theory to quite general multiple unit double auction problems to show that the participatory VCG mechanism achieves asymptotic efficiency.     

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.     

Sealed bid auctions versus ascending bid auctions: an experimental study

This paper considers two multi-item auction formats (ascending and sealed bid) which both identify the minimum Walrasian equilibrium prices and where truthful preference revelation constitutes an equilibrium. Even though these auction formats share many theoretical properties, there are behavioral aspects that are not easily captured. To explore this issue in more detail, this paper experimentally investigates what role the design of the auction format has for its outcome. The results suggest that the sealed bid mechanism performs weakly better in all of the investigated measures (consistent reporting, efficiency etc.). In addition, we find that the performance of the ascending auction is increasing over time, whereas the sealed bid auction shows no such tendency.     

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.     

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.     

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。     

The condominium problem; auctions for substitutes

This paper considers the problem of designing selling procedures for substitutes (like condominium units). Oral, ascending auctions for the right to choose are efficient. This is a common type of auction used for the sale of real estate. Efficiency is not optimal from the seller’s viewpoint. An optimal procedure distorts the right-to-choose auction to favor in late rounds bidders whose preferred object has already been sold. This optimal auction is complex. A revenue improving departure from efficiency can be achieved by simply auctioning all the rights to choose before any of them is exerted.Received: 5 February 2003, Accepted: 15 February 2005, JEL Classification: D44I acknowledge very helpful comments by Joe Harrington, Ken Hendricks, and anonymous referees. Financial aid from the European Commission through the TMR Program (contract FMRX-CT98-0203) and the Spanish MCyT (Grants SEC 2002-02506 and SEC 2003-08080) is also gratefully acknowledged.     

Creating a winner’s curse via jump bids

We show that jump bids can be used by a bidder to create a winner’s curse and preserve an informational advantage that would otherwise disappear in the course of an open ascending auction. The effect of the winner’s curse is to create allocative distortions and reduce the seller’s expected revenue. Two novel features of equilibrium jump bids are derived. First, the jump bid may fail to hide completely the value of the common value component. Second, a bidder with a higher type might jump bid less frequently than a bidder with a lower type.     

Fear of losing in a clock auction

We examine bidding behavior in a clock auction in which price is set by the lowest-accepted bid and provisional winners are reported each round (the LABpw auction). This format was used in the India 3G spectrum auction. In the standard theory, the auction performs poorly. In particular it yields lower revenues and is less efficient than the more standard clock auction with exit bids and highest-rejected-bid pricing (the HRB auction). However, the LABpw auction performs well in the lab, achieving higher revenues than the HRB auction. We show how fear of losing provides one motivation for the overbidding that causes higher revenues in the LABpw auction.     

Stable matchings and the small core in Nash equilibrium in the college admissions problem

Both rematching proof and strong equilibrium outcomes are stable with respect to the true preferences in the marriage problem. We show that not all rematching proof or strong equilibrium outcomes are stable in the college admissions problem. But we show that both rematching proof and strong equilibrium outcomes in truncations at the match point are all stable in the college admissions problem. Further, all true stable matchings can be achieved in both rematching proof and strong equilibrium in truncations at the match point. We show that any Nash equilibrium in truncations admits one and only one matching, stable or not. Therefore, the core at a Nash equilibrium in truncations must be small. But examples exist such that the set of stable matchings with respect to a Nash equilibrium may contain more than one matching. Nevertheless, each Nash equilibrium can only admit at most one true stable matching. If, indeed, there is a true stable matching at a Nash equilibrium, then the only possible equilibrium outcome will be the true stable matching, no matter how different are players' equilibrium strategies from the true preferences and how many other unstable matchings are there at that Nash equilibrium. Thus, we show that a necessary and sufficient condition for the stable matching rule to be implemented in a subset of Nash equilibria by the direct revelation game induced by a stable mechanism is that every Nash equilibrium profile in that subset admits one and only one true stable matching. Received: 30 December 1998 / Accepted: 12 October 2001 This paper is a revision of the paper “Manipulation and Stability in a College Admissions Problem” circulated since 1994. I thank Rich McLean, Abraham Neyman, Mark Satterthwaite, Sang-Chul Suh, and Tetsuji Yamada for helpful discussions. I thank the associate editor and the two anonymous referees for their helpful comments that have greatly improved the paper. I am grateful to the Kellogg G.S.M. at the Northwestern University for the hospitality for my visit. Any errors are mine.     

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     

Risk neutrality regions

An Expected Utility maximizer can be risk neutral over a set of nondegenerate multivariate distributions even though her NM (von Neumann Morgenstern) index is not linear. We provide necessary and sufficient conditions for an individual with a concave NM utility to exhibit risk neutral behavior and characterize the regions of the choice space over which risk neutrality is exhibited. The least concave decomposition of the NM index introduced by Debreu (1976) plays an important role in our analysis as do the notions of minimum concavity points and minimum concavity directions. For the special case where one choice variable is certain, the analysis of risk neutrality requires modification of the Debreu decomposition. The existence of risk neutrality regions is shown to have important implications for the classic consumption–savings and representative agent equilibrium asset pricing models.     

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。     

Personalized Pricing and Quality Customization

We embed the principal–agent model in a model of spatial differentiation with correlated consumer preferences to investigate the competitive implications of personalized pricing and quality allocation (PPQ), whereby duopoly firms charge different prices and offer different qualities to different consumers, based on their willingness to pay. Our model sheds light on the equilibrium product-line pricing and quality schedules offered by firms, given that none, one, or both firms implement PPQ. The adoption of PPQ has three effects in our model: it enables firms to extract higher rents from loyal customers, intensifies price competition for nonloyal customers, and eliminates cannibalization from customer self-selection. Contrary to prior literature on one-to-one marketing and price discrimination, we show that even symmetric firms can avoid the well-known Prisoner's Dilemma problem when they engage in personalized pricing and quality customization. When both firms have PPQ, consumer surplus is nonmonotonic in valuations such that some low-valuation consumers get higher surplus than high-valuation consumers. The adoption of PPQ can reduce information asymmetry, and therefore sellers offer higher-quality products after the adoption of PPQ. Overall, we find that while the simultaneous adoption of PPQ generally improves total social welfare and firm profits, it decreases total consumer surplus.     

Job auctions and hold-ups

We consider a labor market with search frictions in which firms need to invest in capital before they can post a vacancy. This assumption creates a natural scope for hold-up problems, but the innovation of our study is that we allow for competition among the applicants who apply for the same job. In our economy all applicants are paid their actual marginal product. Nonetheless, with random search there exists a hold-up problem, leading to underinvestment in capital. On the contrary, if workers can direct their search towards firms with different capital levels, the equilibrium is efficient. This result contrasts sharply with the predictions of models with ex-post bargaining that never yield an efficient allocation. Moreover, our results extend the efficiency of auction mechanisms to an environment with non-contractible investments.     

Optimal procurement mechanisms for divisible goods with capacitated suppliers

Procurement auction literature typically assumes that the suppliers are uncapacitated [see, e.g. Dasgupta and Spulber in Inf Econ Policy 4:5–29, 1990 and Che in Rand J Econ 24(4):668–680, 1993]. Consequently, the auction mechanisms award the contract to a single supplier. We study mechanism design in a model where suppliers have limited production capacity, and both the marginal costs and the production capacities are private information. We provide a closed-form solution for the revenue maximizing direct mechanism when the distribution of the cost and production capacities satisfies a modified regularity condition [Myerson in Math Oper Res 6(1):58–73, 1981]. We also present a sealed low bid implementation of the optimal direct mechanism for the special case of identical suppliers. The results in this paper extend to other principle-agent mechanism design problems where the agents have a privately known upper bound on allocation. The authors would like to thank the anonymous referees for valuable suggestions and comments.     

A sufficiency result for constrained economies

This paper presents a general sufficiency result for constrained economies. The result shows that, when an equilibrium allocation satisfies the first order necessary conditions for hybrid efficiency (a new type of constrained efficiency), there exists a marginal cost pricing equilibrium in an associated economy. If this equilibrium is Pareto efficient in the associated economy, then the original equilibrium allocation is hybrid efficient. Hence. the necessary conditions are also sufficient.     

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.     

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.