EQUILIBRIA EXISTENCE AND CHARACTERIZATION IN AUCTIONS: ACHIEVEMENTS AND OPEN QUESTIONS

Abstract Establishing existence and characterizing equilibria are both important achievements in the study of auctions. However, we recognize that equilibria existence results form the basis for well accepted characterizations. In this survey, we review the landmark results and highlight open questions regarding equilibria existence and characterizations in auctions. In addition, we review the standard assumptions underlying these results, and discuss the suitability of the Nash equilibrium solution concept. We focus our review on single‐object auctions, but also review results in multi‐unit, divisible, combinatorial and double auctions.     

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.     

The FCC Spectrum Auctions: An Early Assessment

This paper analyzes six spectrum auctions conducted by the Federal Communications Commission from July 1994 to May 1996. These auctions were simultaneous multiple-round auctions in which collections of licenses were auctioned simultaneously. This auction form proved remarkably successful. Similar items sold for similar prices, and bidders successfully formed efficient aggregations of licenses. Bidding behavior differed substantially in the auctions. The extent of bidder competition and price uncertainty played an important role in determining behavior. Bidding credits and installment payments also played a major role in several of the auctions.     

Replacing Sample Trimming with Boundary Correction in Nonparametric Estimation of First‐Price Auctions

Two‐step nonparametric estimators have become standard in empirical auctions. A drawback concerns boundary effects which cause inconsistencies near the endpoints of the support and bias in finite samples. To cope, sample trimming is typically used, which leads to non‐random data loss. Monte Carlo experiments show this leads to poor performance near the support boundaries and on the interior due to bandwidth selection issues. We propose a modification that employs boundary correction techniques, and we demonstrate substantial improvement in finite‐sample performance. We implement the new estimator using oil lease auctions data and find that trimming masks a substantial degree of bidder asymmetry and inefficiency in allocations. Copyright © 2014 John Wiley & Sons, Ltd.     

User acceptance of complex electronic market mechanisms: Role of information feedback

This paper broadens the scope of evaluating the design of economic mechanisms that is traditionally done solely from an economic perspective. We introduce and demonstrate the application of acceptability to evaluate complex economic mechanisms. In particular, we apply our approach to the evaluation of continuous combinatorial auctions, which represent a complex, sophisticated market mechanism that has not been generally available in the online marketplace but has the potential to enhance the economic efficiency of trade for assets with interdependent values. Such auctions are being increasingly used in industry, e.g., to procure logistical services. Intuitively, acceptance and usage of a complex mechanism can be fostered by a design that provides information and tools that meet the users’ task demands. Based on prior research and an analysis of the auction tasks, we discuss practical and innovative information feedback schemes for reducing the cognitive burden of formulating bids in combinatorial auctions. Then, we use constructs from the technology acceptance model (TAM) – which have been consistently shown to be key determinants of technology acceptance in the extant literature – to compare the acceptability of the mechanism under three different information regimes. In addition, we borrow constructs from marketing theory to assess the potential growth in adoption of the mechanism. We compare user perceptions of the three alternative designs in a laboratory experiment with over 130 subjects. Our study constitutes a complementary and novel approach in evaluating the design of complex economic mechanisms. Results indicate a higher adoption and usage potential of the mechanism with advanced information feedback, supporting the potential of combinatorial auctions as a user-acceptable market mechanism with appropriate feedback.     

Synergies in Wireless Telephony: Evidence from the Broadband PCS Auctions

We examine bid data from the first two broadband PCS spectrum auctions for evidence of value synergies. First, we estimate a benchmark regression for the determinants of final auction prices. Then, we include variables reflecting the extent to which bidders ultimately won or already owned the adjacent wireless properties. Consistent with geographic synergies in an ascending-bid auction, prices were higher when the highest losing bidder had adjacent licenses. The footprints of winning bidders suggest that they were often successful in realizing these synergies.     

Existence of optimal auctions in general environments

We provide a unified approach to the problem of existence of optimal auctions for a wide variety of auction environments. We accomplish this by first establishing a general existence result for a particular Stackelberg revelation game. By systematically specializing our revelation game to cover various types of auctions, we are able to deduce the existence of optimal Bayesian auction mechanisms for single and multiple unit auctions, as well as for contract auctions with moral hazard and adverse selection. In all cases, we allow for risk aversion and multidimensional, stochastically dependent types.     

Dynamic pricing in subsidized performing arts

While current pricing strategies in public theaters are mostly based on static schemes, this paper analyzes the potential of dynamic pricing. Subsidized performing arts organizations face the challenge of selling a fixed capacity (available seats of a venue) to a broad and varied audience. Based on the literature and on empirical evidence from a survey among Swiss theaters, we discuss whether and to what extent yield management and uniform‐price auctions—two widespread dynamic pricing mechanisms in the Internet age—can be applied to public theaters in view of the particular goals and targets imposed by their source of funding and by subsidy contracts. Our analysis suggests that although the application of yield management may not be advantageous in the current environment, the introduction of dynamic elements (including auctions) to prevailing pricing strategies can help public theaters respond to temporal demand fluctuations and fill up performances with a varied audience. Copyright © 2015 John Wiley & Sons, Ltd.     

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     

Broadcasting-Auctions, Competition and Policy

How efficient is the Government at regulating the radio spectrum? Dr Cento Velianovski argues that its current system of TV franchises should be replaced by auctions.     

Learning through Simultaneous Play: Evidence from Penny Auctions

This paper contributes to the emerging empirical literature on penny auctions, a particular type of all‐pay auctions. We focus on the potential learning effects that bidders may experience over time but also (and particularly) across auctions as a result of their auction participation. Using detailed bid‐level information, we find that, similarly to earlier literature, bidders suffer from a sunk cost fallacy, whereby their probability of dropping out of an auction is decreasing in the number of bids they have already placed in that auction. Although we do find that learning through repeated participation alleviates the sunk cost fallacy, participation in simultaneous penny auctions emerges as a much more effective learning mechanism, ultimately contributing toward bidders earning higher individual surpluses.     

Empirical implementation of nonparametric first-price auction models

Nonparametric estimators provide a flexible means of uncovering salient features of auction data. Although these estimators are popular in the literature, many key features necessary for proper implementation have yet to be uncovered. Here we provide several suggestions for nonparametric estimation of first-price auction models. Specifically, we show how to impose monotonicity of the equilibrium bidding strategy; a key property of structural auction models not guaranteed in standard nonparametric estimation. We further develop methods for automatic bandwidth selection. Finally, we discuss how to impose monotonicity in auctions with differing numbers of bidders, reserve prices, and auction-specific characteristics. Finite sample performance is examined using simulated data as well as experimental auction data.     

The Structure and Conduct of Corporate Lobbying: How Firms Lobby the Federal Communications Commission

This paper examines the amount and organization (individual vs. collective) of lobbying by firms in administrative agencies. It explores the power and limitations of the collective-action theories and transaction-cost theories in explaining lobbying. It introduces a dataset of over 900 lobbying contacts covering 101 issues at the Federal Communications Commission (FCC) in early 1998. It finds that the structure and conduct of large-firm lobbying at the FCC is consistent with the predictions of theories of transaction costs and the main results of theories of collective action. Small firms show little sensitivity to collective-action issues or transaction-cost issues in the organization of their lobbying, but they do lobby less when having to reveal proprietary information. In sum, large firms behave in a manner largely consistent with theoretical predictions, while small firms do not.     

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.     

Sudden Termination Auctions—An Experimental Study

The design of online markets has become a major issue due to the capability of operators to implement almost any set of market rules overnight. With this study we contribute to the literature of auction market design by presenting a theoretical and experimental analysis of sudden termination auctions. Our main focus is on the candle auction that has a positive termination probability at any time in the course of the auction. Candle auctions prove to be a much faster, but equally efficient alternative to standard hard close auctions.     

Characterization of bidding behavior in multi-unit auctions

This paper considers a very general class of single or multi-unit auctions of indivisible objects. The model allows for interdependent values, multidiminensional types and any attitude towards risk. Assuming only optimal behavior, we prove that each bid is chosen in order to equalize the marginal benefit to the marginal cost of bidding. This generalizes many existing results in the literature. We use this characterization to obtain sufficient conditions for truthful bidding, monotonic best reply strategies and identification results for multi-unit auctions.     

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.     

The use of bundling in B2B online reverse auctions

In industrial purchasing a request for quotation (RFQ) can consist of a single item, but is most often composed of two or more products and/or services bundled together. While such bundles are used in offline purchase negotiations, their criticality is heightened in online auctions due to their usual short duration and constrained bidding environment. Despite this importance, little systematic discussion or evaluation has taken place concerning bundling practice, especially as it relates to the individual items included in the bundle, the overall bundle composition, and the resulting supply base and ultimate bundle performance. This study investigates these issues by developing a conceptual model and testing it with a large-scale survey completed by purchasing professionals practicing bundling in B2B online auctions. Results indicate that crafting a more homogeneous bundle is most important in achieving a successful outcome. Furthermore, more complex or difficult-to-specify items do not impact perceived bundle performance, but do influence the supply base that is willing and able to bid on the business.     

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.     

A dynamic analysis of collusive networks

This paper investigates the strategic formation of collusive networks in a dynamic framework. A collusive network is a set of market sharing agreements between firms in oligopolistic markets and auctions. Belleflamme and Bloch (Int Econ Rev 45(2):387–411, 2004) fully characterize the pairwise stable collusive networks in their symmetric model. In contrast, we characterize the collusive networks to which a dynamic network formation process converges with positive probability in the symmetric model. We provide a complete characterization for the case of the process that starts from a network with sufficiently few links. Moreover, we show that the process never cycles but always converges to a stable network. In addition, we discuss an asymmetric model where firms enjoy a home country advantage. We show that the expected number of collusive agreements may be reduced by an increase in the degree of the home country advantage. This implies that policies for discouraging entry may fail, and may lead to a decrease in expected social surplus.