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.     

Auction Theory: A Guide to the Literature

This paper provides an elementary, non-technical, survey of auction theory, by introducing and describing some of the critical papers in the subject. (The most important of these are reproduced in a companion book, The Economic Theory of Auctions , Paul Klemperer (ed.), Edward Elgar (pub.), forthcoming.); We begin with the most fundamental concepts, and then introduce the basic analysis of optimal auctions, the revenue equivalence theorem, and marginal revenues. Subsequent sections address risk-aversion, affiliation, asymmetries, entry, collusion, multi-unit auctions, double auctions, royalties, incentive contracts, and other topics. Appendices contain technical details, some simple worked examples, and a bibliography for each section.     

Partial identification and testable restrictions in multi-unit auctions

Bidders’ values in discriminatory and uniform-price auctions are not necessarily point-identified under the assumptions of equilibrium bidding and independent private values, but meaningful policy analysis can proceed from bounds on bidder values. This paper provides upper and lower bounds on the set of values that can rationalize a given distribution of bids, under the additional (and standard) assumption of non-increasing marginal values. Novel testable implications of the best response hypothesis are also provided, again under the assumption of non-increasing marginal values.     

Capacity constraints and the winner's curse in multi-unit common value auctions

We explore the role of capacity constraints in establishing efficient pricing in multi-unit common value auctions in a setting relevant to auction-based equity IPOs. The method of inquiry is experimental economics. We find that sufficiently large capacity constraints mitigate the overbidding that plagues single-unit auctions and is one of the most robust laboratory findings. We also uncover a puzzling propensity for most bidders to place a portion of their bids at prices above their signals. This disequilibrium behavior persists with experience and in cases with substantial losses in previous auctions. Our results suggest caution is warranted in promoting auction based IPOs that allow unrestricted access by the non-professional investing public.     

On the strictly descending multi-unit auction

We analyze the bidding behavior in a strictly descending multi-unit auction where the price decreases continuously without going back to the initial start price once an object is sold. We prove that any equilibrium in the multi-unit descending auction is inefficient. We derive a symmetric equilibrium for general distribution functions as well as an arbitrary number of bidders and objects. Moreover, equilibrium bidding is characterized by a set of initial value problems. Our analysis thus generalizes previous results in the literature.     

AUCTIONS: AN INTRODUCTION

Abstract. This is a detailed introduction to auction theory. It begins with a simple analysis of standard auctions and then uses a strikingly simple general solution of symmetric private values auctions to prove the payoff equivalence of many auction rules. The basic framework is then modified to admit risk aversion, multi-unit and repeated auctions as well as collusion. Then follows an introduction to optimal auctions, with and without stochastic entry, and to common value auctions and the winner's curse problem. The survey closes with a sample of applications, from the regulation of natural monopolies to price competition in oligopoly and the government securities market.     

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.     

Preemptive bidding in takeover auctions with affiliated values

This paper extends Fishman's (1988) model of preemptive bidding in takeover auctions to auctions with affiliated values. It shows that preemptive bidding transfers wealth from the seller to the first bidder without affecting the profit of the second bidder and social welfare. It also shows that higher correlation between bidders’ values leads to higher preemption rates but has an ambiguous effect on the size of the opening bid. Finally, it shows that in auctions with affiliated values, even infinitesimal entry costs may lead to a preemptive jump bidding that allows the reallocation of the entire surplus from the seller to the first bidder.     

Preemptive Bidding in Takeover Auctions: An Experimental Study

This paper presents the results of an experimental study on jump bidding in takeover auctions with entry costs. It provides support for signaling hypothesis behind jump bidding and analyzes how the size of the entry costs affects the bidders' behavior and their expected profits. It also shows that jump bidding allows the reallocation of the surplus from the seller to the first bidder but has little effect on the social surplus and the profits of the second bidder. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

Preemptive bidding in common value takeover auctions: Social surplus and the target’s revenue

This paper develops a model of preemptive jump bidding in common value takeover auctions. It shows that, in a case of common values, jump bidding increases the social surplus and, under certain conditions, can lead to a higher expected target’s revenue. It also demonstrates that an increase in investigation costs may improve social efficiency even if it leads to larger direct social costs. Based on the results, the paper provides several implications related to legal fees and the length of the takeover contest.     

在线拍卖中的代理研究综述

在线拍卖站点的不断增加给在线竞买人提出了具大的挑战,竞买人需要从大量的拍卖站点中选择一个恰当的拍卖站点,以保证在满足他们偏好的前提下得到他们希望的物品。不同的拍卖站点采用的拍卖方式和竞价策略是不同的,因此,不同的拍卖站点其竞价代理的设计策略也不同。本文主要对目前在线拍卖代理研究进行综述。     

Multiple and last-minute bidding in competing internet auctions

The present paper proposes a theoretical model of the equilibrium bidding behavior in simultaneous competing private-value Internet auctions such as those on eBay. It shows that last-minute bidding and multiple bidding, two commonly observed bidding strategies, arise in equilibrium. It also suggests that last-minute bidding may lead to inefficient outcomes.     

Can preemptive bidding in takeover auctions be socially optimal? Yes it can

This paper analyzes a model of preemptive jump bidding in private value takeover auctions with entry costs. It shows that when the second bidder owns a fraction of the target firm preemptive jump bidding leads to a higher social surplus, improves the expected profit of both bidders and reduces the expected final price. Such a toehold also leads to higher jump bids. The model implies that preemptive bidding hurts the minority shareholders but benefits the large shareholder of the target firm.     

Asymmetry in first‐price auctions with affiliated private values

Collusion and heterogeneity across firms may introduce asymmetry in bidding games. A major difficulty in asymmetric auctions is that the Bayesian Nash equilibrium strategies are solutions of an intractable system of differential equations. We propose a simple method for estimating asymmetric first‐price auctions with affiliated private values. Considering two types of bidders, we show that these differential equations can be rewritten using the observed bid distribution. We establish the identification of the model, characterize its theoretical restrictions, and propose a two‐step non‐parametric estimation procedure for estimating the private value distributions. An empirical analysis of joint bidding in OCS auctions is provided. Copyright © 2003 John Wiley & Sons, Ltd.     

Identification and estimation in sequential,asymmetric, English auctions

Within the independent private-values paradigm, we derive the data-generating process of the winning bid for the last unit sold at multi-unit, sequential, asymmetric, English auctions. When the identity of the winner and the number of units won by each bidder in previous stages of the auction are observed, we demonstrate nonparametric identification and propose a semi-nonparametric estimation strategy based on orthogonal polynomials. We apply our estimator to daily data from fish auctions in Denmark. For single-unit supply, we use our estimates to compare the revenues a seller could expect to earn were a Dutch auction employed instead.     

Maximizing bidder surplus in simultaneous online art auctions via dynamic forecasting

This paper presents a novel intelligent bidding system, called SOABER (Simultaneous Online Auction BiddER), which monitors simultaneous online auctions of high-value fine art items. It supports decision-making by maximizing bidders’ surpluses and their chances of winning an auction. One key element of the system is a dynamic forecasting model, which incorporates information about the speed of an auction’s price movement, as well as the level of competition both within and across auctions. Other elements include a wallet estimator, which gauges the bidders’ willingness to pay, and a bid strategizer, which embeds the forecasting model into a fully automated decision system. We illustrate the performance of our intelligent bidding system on an authentic dataset of online art auctions for Indian contemporary art. We compare our system with several simpler ad-hoc approaches, and find it to be more effective in terms of both the extracted surplus and the resulting winning percentage.     

A final price prediction model for english auctions: a neuro-fuzzy approach

Online auction has now been a popular mechanism in setting prices for internet users. However, auction price prediction, involving the modeling of uncertainty regarding the bidding process, is a challenging task primarily due to the variety of factors changing in auction settings. Even if all the factors were accounted for, there still exist uncertainties in human behavior when bidding in auctions. In this paper, three models, regression, neural networks and neuro-fuzzy, are constructed to predict the final prices of English auctions, using real-world online auction data collected from Yahoo-Kimo Auction. The empirical results show that the neuro fuzzy system can catch the complicated relationship among the variables accurately much better than the others, which is of great help for the buyers to avoid overpricing and for the sellers to facilitate the auction. Besides, the knowledge base obtained from neuro fuzzy provides the elaborative relationship among the variables, which can be further tested for theory building.     

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。