Risk-averse Bidders Research Articles

How Risk Sharing May Enhance Efficiency of English Auctions

We investigate the possibility of enhancing efficiency by awarding premiums to a set of highest bidders in an English auction - in a setting that extends Maskin and Riley (1984, Econometrica 52: 1473-1518) in three aspects: (i) the seller can be risk averse, (ii) the bidders can have heterogeneous risk preferences, and (iii) the auction can have a binding reserve price. Our analysis reveals that the premium has an intricate joint effect on risk sharing and expected revenue, which in general benefits risk averse bidders. When the seller is more risk averse than the pivotal bidder - a condition often verifiable by deduction prior to the auction - the premium also benefis the seller and therefore leads to a Pareto improvement of the English auction. The advantage of such premium tactics is directly related to (a) the seller's degree of risk aversion, (b) the reserve price, (c) the riskiness of the object for sale, (d) the degree of heterogeneity in risk preferences among the bidders, and (e) the number of the potential bidders.

Ascending Combinatorial Auctions with Risk Averse Bidders

Ascending combinatorial auctions are being used in an increasing number of spectrum sales worldwide, as well as in other multi-item markets in procurement and logistics. Much research has focused on pricing and payment rules in such ascending auctions. However, recent game-theoretical research has shown that such auctions can even lead to inefficient perfect Bayesian equilibria with risk-neutral bidders. There is a fundamental free-rider problem without a simple solution, raising the question whether ascending combinatorial auctions can be expected to be efficient in the field. Risk aversion is arguably a significant driver of bidding behavior in high-stakes auctions. We analyze the impact of risk aversion on equilibrium bidding strategies and efficiency in a threshold problem with one global and several local bidders. Due to the underlying free-rider problem, the impact of risk-aversion on equilibrium bidding strategies of local bidders is not obvious. We characterize the necessary and sufficient conditions for the perfect Bayesian equilibria of the ascending auction mechanism to have the local bidders to drop at the reserve price. Interestingly, in spite of the free-riding opportunities of local bidders, risk-aversion reduces the scope of the non-bidding equilibrium. The results help explain the high efficiency of ascending combinatorial auctions observed in the lab.

Secret versus public reserve price in an “outcry” English procurement auction: Experimental results

In a set of human experiments, we analyze the impact of the buyer׳s reserve price policy in an online open outcry reverse auction. We measure the impact of revealing or not the reserve price on the buyer׳s expected cost when suppliers may be risk-averse. Results confirm that the optimal public reserve price policy dominates for the buyer when the lowest cost supplier is weakly risk-averse but in contrast with theory, the secret reserve price policy does not dominate when he becomes very risk-averse. Analysis of strategic suppliers׳ bidding behavior shows, in conformity with theory, that they react to the secret reserve price and are more aggressive when they are more risk-averse. This explains why the optimal public reserve price does not perform better in this context but is equivalent to the secret one. However, strongly risk-averse bidders are less aggressive than predicted by theory. That is why the secret reserve price policy does not strictly dominate.

Nonparametric Estimation of Large Auctions with Risk Averse Bidders

This article studies the robustness of Guerre et al.'s (2000) two-step nonparametric estimation procedure in a first-price, sealed-bid auction with n (n ≫ 1) risk averse bidders. Based on an asymptotic approximation with precision of order O(n −2) of the intractable equilibrium bidding function, we establish the uniform consistency with rates of convergence of Guerre et al.'s (2000) two-step nonparametric estimator in the presence of risk aversion. Monte Carlo experiments show that the two-step nonparametric estimator performs reasonably well with a moderate number of bidders such as six.

Identification and Estimation in a Third-Price Auction Model

We show global identification of the private values distribution in a sealed-bid third-price auction model using a fully nonparametric methodology. The second novelty of the paper comes from the study of the identification and estimation of the model using a quantile approach. We consider an i.i.d. private values environment with risk-averse bidders. In a first place, we consider the case where the risk-aversion parameter is known. We show that the speed of convergence in process of our nonparametric estimator produces at the root-n parametric rate and we explain the intuition behind this apparently surprising result.Although the model is globally identified, we also present the functional local approach, which is useful when the model is not globally tractable. This is the case when one searches to identify also the risk-aversion parameter. Moreover there is a recent interest of local treatment of nonparametric models. Using the exogenous variation in the number of participants we are able to achieve the local identification of the unknown risk-aversion parameter. Not only this methodology is more rigorous, but it can also be applied for different types of games, which involve complicated nonlinear inverse problems.We extend our procedure to the case where we observe only the bids corresponding to the transaction prices and we generalize the model as to account for the presence of exogenous variables.The methodological toolbox used for analyzing local and global identification of the third-price auction model can be employed in the study of other games of incomplete information. Moreover, our results are interesting also from a policy perspective, as some authors recommend the use of the third-price auction format for some Internet auctions.

How Risk Sharing May Enhance Efficiency in English Auctions

We investigate the possibility of enhancing efficiency by awarding premiums to a set of highest bidders in an English auction - in a setting that extends Maskin and Riley (1984, Econometrica 52: 1473-1518) in three aspects: (i) the seller can be risk averse, (ii) the bidders can have heterogeneous risk preferences, and (iii) the auction can have a binding reserve price. Our analysis reveals that the premium has an intricate joint effect on risk sharing and expected revenue, which in general benefits risk averse bidders. When the seller is more risk averse than the pivotal bidder - a condition often verifiable by deduction prior to the auction - the premium also benefits the seller and therefore leads to a Pareto improvement of the English auction. We discuss how this finding is related to the seller’s degree of risk aversion, the reserve price, the riskiness of the object for sale, the degree of heterogeneity in risk preferences among the bidders, and the number of the potential bidders.

Bidding in Private-Value Auctions with Uncertain Values

Auctions are often used to sell idiosyncratic goods that may be difficult for potential bidders to value ex ante. In a laboratory experiment with uncertainty over final values, 18% and 27% of bids in private-value first-price and English auctions, respectively, were above the expected value of item. This overbidding cannot be explained by learning, mistakes, or risk preferences as measured on an individual decision task. The evidence suggests that overbidding is due to some bidders who are prone to overbidding. The stylized fact from the experimental literature that bids in first-price auctions with certain values are above the risk-neutral Nash equilibrium but below the bidder's value is often explained by modeling risk-averse bidders, but the overbidding with uncertain values provides strong evidence that risk aversion is not a good explanation for the bidding behavior in first-price auctions. In English auctions, the size and frequency of overbids are significantly larger than in first-price auctions, while more bidders overbid in more English auctions and more English auctions are won by overbidders than first-price auctions. This behavior is consistent with popular notions of 'auction fever,' which has not been observed in laboratory experiments with certain values.

Structural Econometric Methods in Auctions: A Guide to the Literature

Auction models have proved to be attractive to structural econometricians who, since the late 1980s, have made substantial progress in identifying and estimating these rich game-theoretic models of bidder behavior. We provide a guide to the literature in which we contrast the various informational structures (paradigms) commonly assumed by researchers and uncover the evolution of the field. We highlight major contributions within each paradigm and benchmark modifications and extensions to these core models. Lastly, we discuss special topics that have received substantial attention among auction researchers in recent years, including auctions with risk-averse bidders, unobserved auction-specific heterogeneity, accounting for an unobserved number of bidders as well as endogenous entry, auction dynamics, testing informational paradigms, and auctions for multiple objects.

Two-Stage Buy-It-Now Auctions

This paper studies second-price auctions with a temporary Buy-It-Now price (BIN auctions) using a two-stage model, in which two groups of bidders enter the auction at different times. The early bidders are offered a Buy-It-Now (BIN) option to purchase the item immediately at a listed price (BIN price). If no early bidder accepts the BIN option, an additional group of bidders (late bidders) enter the auction and both groups of bidders participate in a second-price sealed-bid auction without BIN option. When bidders are risk averse with concave utility functions, we establish the existence and uniqueness of a cutoff equilibrium such that an early bidder will accept the BIN option if his valuation is higher than the cutoff valuation. Moreover, bidders are more likely to accept the BIN option when fewer bidders are offered the BIN option. We show that when facing risk averse bidders, the seller can obtain higher expected revenue in BIN auctions than in standard second-price auctions. Furthermore, the expected seller revenue decreases with the number of early bidders. Consequently, the expected seller revenue is higher in the auctions with BIN only available to a subset of bidders than in the auctions with BIN available to all bidders. These results may help explain the popularity of temporary BIN auctions on eBay and the observed high acceptance frequencies of BIN prices in experimental and field studies.

Semiparametric Estimation of First-Price Auctions with Risk-Averse Bidders

In view of the non-identification of the first-price auction model with risk-averse bidders, this paper proposes some parametric identifying restrictions and a semiparametric estimator for the risk aversion parameter(s) and the latent distribution of private values. Specifically, we exploit heterogeneity across auctioned objects to establish semiparametric identification under a conditional quantile restriction of the bidders’ private value distribution and a parameterization of the bidders’ utility function. We develop a multistep semiparametric method and we show that our semiparametric estimator of the utility function parameter(s) converges at the optimal rate, which is slower than the parametric one but independent of the dimension of the exogenous variables thereby avoiding the curse of dimensionality. We then consider various extensions including a binding reserve price, affiliation among private values, and asymmetric bidders. The method is illustrated on U.S. Forest Service timber sales, and bidders’ risk neutrality is rejected.

Semiparametric Estimation of First-Price Auctions with Risk-Averse Bidders

Semiparametric Estimation of First-Price Auctions with Risk-Averse Bidders

Auctions with resale when private values are uncertain: Evidence from the lab and field

Auction theory represents one of the richest areas of research in economics over the past three decades. Yet, whether, and to what extent, the introduction of secondary resale markets influences bidding behavior in sealed-bid first-price auctions remains under researched. This study begins by examining field data from a unique data set that includes nearly 3000 auctions (over 10,000 individual bids) for cutting rights of standing timber in British Columbia from 1996 to 2000. In comparing bidding patterns across agents who are likely to have resale opportunities with those who likely do not, we find evidence that is consistent with theory. Critical evaluation of the reduced-form bidding model, however, reveals that sharp tests of the theoretical predictions are not possible because several other differences may exist across these bidder types. We therefore use a laboratory experiment to examine if the resale opportunity by itself can have the predicted theoretical effect. We find that while it does have the predicted effect, a theoretical model based on risk-averse bidders explains the overall data patterns more accurately than a model based on risk-neutral bidders. Beyond testing theory, the paper highlights the inferential power of combining naturally occurring data with laboratory data.

Designing bidding strategies in sequential auctions for risk averse agents

Designing efficient bidding strategies for sequential auctions represents an important, open problem area in agent-mediated electronic markets. In existing literature, a variety of bidding strategies have been proposed and have been shown to perform with varying degrees of efficiency. However, most of strategies proposed so far do not explicitly model bidders' attitudes towards risk which, in mainstream economic literature, is considered an essential attribute in modeling agent preferences and decision making under uncertainty. This paper studies the effect that risk profiles (modeled through the standard Arrow-Pratt risk aversion measure), have on the bidders' strategies in sequential auctions. First, the sequential decision process involved in bidding is modeled as a Markov Decision Process. Then, the effect that a bidder's risk aversion has on her decision theoretic optimal bidding policy is analyzed, for a category of expectations of future price distributions. This analysis is performed separately for the case of first price and second-price sequential auctions. Next, the bidding strategies developed above are simulated, in order to study the effect that an agent's risk aversion has on the chances of winning a set of complementary-valued items. The paper concludes with an experimental study of how the presence of risk-averse bidders affects both bidder profits and auctioneer revenue, for different market scenarios of increasing complexity.

On the Existence of Monotone Pure Strategy Equilibria in Bayesian Games

We generalize Athey's (2001) and McAdams' (2003) results on the existence of monotone pure strategy equilibria in Bayesian games. We allow action spaces to be compact locally-complete metrizable semilattices and type spaces to be partially ordered probability spaces. Our proof is based upon contractibility rather than convexity of best reply sets. Several examples illustrate the scope of the result, including new applications to multi-unit auctions with risk-averse bidders.

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 oftheequilibriumbidsandoftheseller'srevenueinany k-priceauction(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 bid- ders 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 mech- anisms for which the limiting revenue as n −→ ∞ 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 −→ ∞.

Market performance and bidders' bidding behavior in the New York Transmission Congestion Contract market

Using publicly available bidder level bids data for Transmission Congestion Contracts (TCCs) and the realized awards of TCCs in the NYISO monthly reconfiguration auctions from June 2000 to December 2004, we examine both market performance and bidders' bidding behavior in the auctions. The data show significant under-pricing in the realized awards of TCCs. Theories suggest that under-pricing may arise from risk-aversion, monopsonistic market power or winner's curse. Our empirical analysis illustrates that all of the three effects play a role in the NYISO TCCs market. Both market performance and bidders' bidding strategies can be best explained by the theoretical model with asymmetric information and risk-averse bidders.

Hybrid auctions revisited

We examine hybrid auctions with affiliated private values and risk-averse bidders, and show that the optimal hybrid auction trades off the benefit of information extraction in the ascending-bid phase and the cost of reduced competition in the sealed-bid phase.

Endogenous entry and self-selection in private value auctions: An experimental study

This paper presents the results of an experimental study of endogenous entry in first-price independent private value auctions. N potential bidders simultaneously decide whether to participate in an auction or receive a known outside option. In the second stage, entrants submit bids after learning their own private values and the number of entrants. An equilibrium model of heterogeneous risk averse bidders implies a self-selection effect, where bidding in the auction is lower with endogenous entry because only less risk averse bidders enter. This effect is confirmed by the experiment. We also observe excessive entry relative to the theoretical model.

Uniqueness in symmetric first-price auctions with affiliation

The first-price auction has a unique monotone pure strategy equilibrium when there are n symmetric risk-averse bidders having affiliated types and interdependent values.

Regret, Learning and Risk Aversion in First Price Sealed Bid Auctions

Understanding bidding behavior in Sealed Bid First Price (SBFP) auctions for a single unit in the independent private value setting is important because it can provide relevant insights into what to expect in complex real world settings. Laboratory experiments are used to test existing theory, and provide insights for developing new theory. One fundamental puzzle about SBFP auctions that received a great deal of attention in the experimental economics literature is why do participants generally bid above the Risk Neutral Nash Equilibrium (RNNE). This result has been replicated numerous times by different researchers at different laboratories and under a variety of environments, but the reason for overbidding has never been fully understood. According to Kagel (1995), . . risk aversion is one element, but far from the only element, generating bidding above the RNNE. (p. 525). Engelbrecht-Wiggans (1989) suggested that the desire to avoid regret may be motivating bidders in SBFP auctions. Although the theory of regret has been used to explain some well-known anomalies in expected utility theory, this notion has never been applied to auctions prior to Engelbrcht-Wiggans (1989), and has never been tested in the auction context. The aim of our proposal is to systematically test the Engelbrecht-Wiggans (1989) theory of regret in auctions, with the specific view of separating the role of regret from that of risk aversion. As we gain a better understanding of behavior in SBFP auctions, we will also extend and refine the theory to incorporate the new insights and to explain some of the existing puzzles. In the sequence of experiments we propose, human bidders will compete against computerized bidders programmed to play risk-neutral Nash equilibrium (RNNE). Human bidders will have the same values for a number of rounds, thus allowing them to learn, and bidding strategies will be restricted in a variety of ways. It is our conjecture that this setting will be more conducive to learning than the traditional setting, and therefore, if overbidding relative the RNNE is due to errors, we should see a substantial trend towards lower bids. If we find that overbidding persists, we will conduct the second study, aimed at separating the regret and the risk-aversion explanations by having bidders bid in a number of auctions simultaneously while restricting their actual bids to be the same for all auctions. Risk averse bidders should overbid substantially less when they are paid based on the outcome of several auctions than when they are paid based on the outcome of a single auction. But bidders who are motivated by the desire to avoid regret should continue to overbid relative to RNNE because regret is cumulative and does not cancel out. Implications of our work go beyond the laboratory because over the past two decades auction theory has been used extensively to help design real world auctions and exchanges. Examples of these new auctions include the FCC auctions for spectrum licenses, electric power auctions, auctions for transportation services, and different types of procurement auctions. These mechanisms are complex, and designers must make decisions about many aspects of auction rules that are likely to have a profound effect on the auction's efficiency,the sellers' revenue and the buyers' profits. To make good design decisions in the real world we need to further our knowledge about the basic forces behind bidding behavior, and understanding why people bid above RNNE in SBFP auctions is an important step towards bridging the gap between auction theory and the practice or market design.