Risk-averse Bidders Research Articles

Signaling Equilibria in Takeovers with Risk-averse Bidders

Signaling Equilibria in Takeovers with Risk-averse Bidders

Signalling in auctions for risk-averse bidders.

We study risk-averse equilibrium bidding in first-price and second-price sealed-bid auctions where bidders have signalling concerns, i.e., they care about how the auction outcome is interpreted by an outside observer. We find that when the winner’s identity and her payment are revealed to the outside observer, risk aversion yields less aggressive bidding behaviour in the second-price sealed-bid auction than in the risk-neutral case. Our analysis explains various revenue ranking reversals relative to the risk-neutral equilibrium observed in a recent experiment by Bos (2021).

Nonparametric identification and estimation of all-pay auction and contest models

AbstractIn this paper, I study the nonparametric identification and estimation of multi-unit all-pay auctions of incomplete information. First, I consider the setting where multiple goods are allocated among several risk-neutral participants with independent private values (IPV). I prove the nonparametric identification of the model and derive two different consistent estimators of the distribution of bidder valuations. The first estimator is based on the classical structural approach similar to that of Guerre et al. (Econometrica 68(3):525–574, 2000). The second estimator, instead, allows estimation of the quantile function of the bidders’ valuations directly using the quantile density of the bids. Monte Carlo simulations show good small sample property under various assumptions of the number of players and goods. Next, I consider a variety of model extensions: the case of affiliated private values (APV), asymmetric players, the addition of random noise, as well as the case of risk-averse bidders. In contrast to all other scenarios, I prove that the general model with risk-averse bidders is not identified even in the semi-parametric case in which utility function is restricted to belong to the class of functions with constant absolute risk aversion (CARA). On the other hand, I show that the model with risk aversion can be identified if the distribution of valuations is restricted to having fixed support.

Sovereign Debt Auctions in Turbulent Times

We use a model of multiunit discriminatory auctions with asymmetrically informed risk-averse bidders to analyze Mexican sovereign bond auctions during periods of macroeconomic stress. We argue that the discriminatory protocol provides insurance benefits to the government in bad times because it allows for uninformed bids above the marginal price to be executed at the bid price. Uninformed investors are willing to make such bids if the inframarginal risk premium is large enough to offset the winner's curse. In crisis periods, we infer 1 p.p. lower borrowing costs in the worst states of the world, but 2.2 p.p. higher average costs.

Competing Sellers in Security-Bid Auctions under Risk-Averse Bidders

Competing Sellers in Security-Bid Auctions under Risk-Averse Bidders

Leveling the Playing Field for Risk-Averse Agents in Security-Bid Auctions

We introduce risk-averse bidders in a security-bid auction to analyze how the security design affects bidders’ equilibrium behavior and, as a result, the revenue and efficiency of the auction. We show that steeper securities provide more insurance because they allow bidders to smooth payoffs across realizations. Such insurance levels the playing field for more-risk-averse bidders, inducing them to bid more aggressively. As a consequence, the auction’s allocative efficiency weakly increases when the seller switches from a flatter to a steeper security. Furthermore, we prove that when bidders are homogeneously and sufficiently risk averse, the only security that guarantees Pareto efficiency is the steepest, that is, a call option. We also determine the relationship between the security design and the auction format. In particular, we show that for convex and superconvex families of securities, the first-price auction yields higher expected revenues, provided a technical condition, whereas for subconvex families, the second price yields higher expected revenues, provided that bidders are moderately risk averse. Finally, we show that steeper securities also attract higher entry from an ex ante perspective, when entry is costly, and discuss the effects that the presence of risk aversion has on informal auctions. This paper was accepted by Gustavo Manso, finance.

Adversarial Risk Analysis for Auctions Using Mirror Equilibrium and Bayes Nash Equilibrium

In this paper, we use the adversarial risk analysis (ARA) methodology to model first-price sealed-bid auctions under quite realistic assumptions. We extend prior work to find ARA solutions for mirror equilibrium and Bayes Nash equilibrium solution concepts, not only for risk-neutral but also for risk-averse and risk-seeking bidders. We also consider bidders having different wealth and assume that the auctioned item has a reserve price.

Risk aversion and auction design: Theoretical and empirical evidence

Auctions are inherently risky: bidders face uncertainty about their prospects of winning and payments, while sellers are unsure about revenue and chances of a successful sale. Auction rules influence the allocation of risk among agents and the behavior of risk-averse bidders, leading to a breakdown of payoff and revenue equivalence and a heightened significance of auction design decisions by sellers. In this paper, we review the literature on risk aversion in auctions, with an emphasis on what can be learned about auction design from theoretical modeling and empirical studies. We survey theoretical results relating to the behavior of risk-averse agents in auctions, the comparison of standard auction formats in the presence of risk aversion and implications for auction design. We discuss standard and more recent approaches to identifying risk preferences in empirical studies and evidence for the significance of risk aversion in auction applications. Finally, we identify areas where existing evidence is relatively scant and ask what questions empirical research might ask given the theory and where further theoretical research may be beneficial given existing empirical results.

Quantile regression methods for first-price auctions

The paper proposes a quantile-regression inference framework for first-price auctions with symmetric risk-neutral bidders under the independent private-value paradigm. It is first shown that a private-value quantile regression generates a quantile regression for the bids. The private-value quantile regression can be easily estimated from the bid quantile regression and its derivative with respect to the quantile level. This also allows to test for various specification or exogeneity null hypothesis using the observed bids in a simple way. A new local polynomial technique is proposed to estimate the latter over the whole quantile level interval. Plug-in estimation of functionals is also considered, as needed for the expected revenue or the case of CRRA risk-averse bidders, which is amenable to our framework. A quantile-regression analysis to USFS timber is found more appropriate than the homogenized-bid methodology and illustrates the contribution of each explanatory variable to the private-value distribution. Linear interactive sieve extensions are proposed and studied in the Appendices.

Taking Orders and Taking Notes: Dealer Information Sharing in Treasury Auctions

The use of order-flow information by financial firms has come to the forefront of the regulatory debate. Should a dealer who acquires information by taking client orders be allowed to use or share that information? We explore how information sharing affects dealers, clients, and issuer revenues in US Treasury auctions, in a model calibrated to auction results data, which we use to quantify counterfactuals. Sharing information reduces uncertainty about future value. With less uncertainty, risk-averse bidders bid more. For investors, the welfare effects of information sharing depend on how information is shared and how it affects asymmetry. The model shows that investors can benefit when dealers share information with each other, not when they share more with clients.

Identification and Estimation in First-Price Auctions with Risk-Averse Bidders and Selective Entry

We study identification and estimation in first-price auctions with risk averse bidders and selective entry, building on a flexible entry and bidding framework we call the Affiliated Signal with Risk Aversion (AS-RA) model. This framework extends the AS model of Gentry and Li (2014) to accommodate arbitrary bidder risk aversion, thereby nesting a variety of standard models as special cases. It poses, however, a unique methodological challenge – existing results on identification with risk aversion fail in the presence of selection, while the selection-robust bounds of Gentry and Li (2014) fail in the presence of risk aversion. Motivated by this problem, we translate excludable variation in potential competition into identified sets for AS-RA primitives under various classes of restrictions on the model. We show that a single parametric restriction – on the copula governing selection into entry – is typically sufficient to restore point identification of all primitives. In contrast, a parametric form for utility yields point identification of the utility function but only partial identification of remaining primitives. Finally, we outline a simple semiparametric estimator combining Constant Relative Risk Aversion utility with a parametric signal-value copula. Simulation evidence suggests that this estimator performs very well even in small samples, underscoring the practical value of our identification results.

Optimal Auctions for Dual Risk Averse Bidders: Myerson meets Yaari

We study auction design for bidders equipped with non-expected utility preferences that exhibit constant risk aversion (CRA). The CRA class is large and includes loss-averse, disappointment-averse, mean-dispersion and Yaari's dual preferences as well as coherent and convex risk measures. The optimal mechanism offers full-insurance in the sense that each agent's utility is independent of other agents' reports. The seller excludes less types than under risk neutrality, and awards the object randomly to intermediate types. Subjecting intermediate types to a risky allocation while compensating them when losing allows the seller to collect larger payments from higher types. Relatively high types are anyway willing to pay more, and their allocation is efficient. (A previous version has been circulated under the title Optimal Auctions for Dual Risk Averse Bidders: Myerson meets Yaari.)

Identification and Inference in First-Price Auctions with Risk Averse Bidders and Selective Entry

We study identification and inference in first-price auctions with risk averse bidders and selective entry, building on a flexible entry and bidding framework we call the Affiliated Signal with Risk Aversion (AS-RA) model. Assuming that the econometrician observes either exogenous variation in the number of potential bidders (N) or a continuous instrument (z) shifting opportunity costs of entry, we provide a sharp characterization of the nonparametric restrictions implied by equilibrium bidding. Given variation in either competition or costs, this characterization implies that risk neutrality is nonparametrically testable in the sense that if bidders are strictly risk averse, then no risk neutral model can rationalize the data. In addition, if both instruments (discrete N and continuous z) are available, then the model primitives are nonparametrically point identified. We then explore inference based on these identification results, focusing on set inference and testing when primitives are set identified. Keywords: Auctions, entry, risk aversion, identification, set inference.

The Effect of a Right-of-First-Refusal Clause in a First-Price Auction with Heterogeneous Risk-Averse Bidders

Considering the sale of an asset by a first-price sealed-bid auction, we analyze the effect of a right-of-first-refusal (ROFR) clause, under which a buyer can match the highest bidder. When the buyers do not exactly know their competitors' degree of risk aversion, we compare their optimal bidding strategies with and without an ROFR. Then, when the seller does not exactly know each buyer's degreeof risk aversion, we determine some sufficient conditions under which an ROFR cannot increase the seller's expected revenue. However, when she knows that information and when two buyers compete, we show that granting an ROFR can increase her expected revenue.

Revenue in first-price auctions with a buy-out price and risk-averse bidders

Abstract We model the “Buy-It-Now or Best Offer” eBay listing option as a first-price auction with a buy-out price and consider seller revenue when bidders are risk-averse. In this model we consider a discrete setting and a continuous setting. We show that a buy-out price in a first-price auction can increase seller revenue in the discrete setting but not in the continuous setting. Furthermore, we prove that in either setting a second-price auction with an optimally chosen buy-out price will never generate more expected revenue than a first-price auction with an optimally chosen buy-out price. These theoretical results support the thesis that a first-price mechanism is superior in expected revenue generation to a second-price mechanism in an online marketplaces where sellers are risk-neutral and buyers are risk-averse and explain the prevalence of “Buy-It-Now or Best Offer” listings on eBay over the traditional eBay auction.

Bidding with Securities under Risk Aversion: The Role of Steepness as Insurance

In a security-bid auction, the stochastic revenue of the project being auctioned is used as an asset to securitize the winner's payment to the seller. De Marzo et al. (2005) show that in an environment with risk-neutral seller and bidders, steeper securities increase the seller's expected revenue but do not affect the efficiency of the auction. We introduce risk-averse bidders to analyze the insurance role of steepness and its implications for revenue, efficiency and bidders' endogenous participation. Steeper securities provide more insurance because they allow bidders to smooth payoffs across realizations: asking for lower payments when revenue realizations are low and for higher payments when realizations are high. We show that such insurance levels the field for more risk-averse bidders, inducing them to bid more aggressively and improving the revenue and the allocative efficiency of the auction. In addition, we present two results that are novel to the auction literature. We show that if bidders are homogeneously and sufficiently risk-averse (i) a call option is the only security that guarantees Pareto efficiency; and (ii) steeper securities attract more entry when bidders do not know their signals and entry is costly.

IDENTIFICATION AND ESTIMATION IN A THIRD-PRICE AUCTION MODEL

The first novelty of this paper is that 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 the 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. Next, we consider that the risk-aversion parameter is unknown, and we locally identify it using exogenous variation in the number of participants. We extend our procedure to the case where we observe only the bids corresponding to the transaction prices, and we generalize the model so as to account for the presence of exogenous variables. The methodological toolbox used to analyse identification of the third-price auction model can be employed in the study of other games of incomplete information. Our results are interesting, also from a policy perspective, as some authors recommend the use of the third-price auction format for certain Internet auctions. Moreover, we contribute to the econometric literature on auctions using a quantile approach.

Competing first-price and second-price auctions

This paper theoretically investigates which auctions are selected by competing sellers when they can choose between first-price auctions and second-price auctions, and when homogeneously risk averse bidders endogenously enter one of the auctions. In order to study this, we first consider bidders’ entry decisions between exogenously given auctions. We find that there exists a symmetric entry equilibrium that is unique and is characterized by a mixed strategy, which depends on whether bidders exhibit constant, decreasing or increasing absolute risk aversion. In a next step, we endogenize the sellers’ choice of auctions. We show that competing sellers have a dominant strategy to select first-price auctions if bidders exhibit nondecreasing absolute risk aversion. If bidders exhibit decreasing absolute risk aversion, other equilibria may exist in which sellers select second-price auctions as well. For instance, we demonstrate that sellers may select second-price auctions if the distribution of private values is sufficiently skewed.

Combinatorial and Simultaneous Descending Auctions for Electricity Transmission Concessions

Many countries use auctions to select agents to which transmission concessions are awarded. Where multiple concessions are auctioned each year, there are potential benefits, for transcos and grid users, in using auction protocols allowing risk-averse bidders to explicitly consider complementary packages of transmission facilities: combinatorial and simultaneous descending auctions. We investigate the use of these protocols for transmission auctions, with aid of mixed-integer linear optimization models developed for this task and realistic case studies, while focusing on the treatment of the exposure problem.

Nonparametric estimation of first-price auctions with risk-averse bidders

This paper proposes nonparametric estimators for the bidders’ utility function and density of private values in a first-price sealed-bid auction model with independent valuations. I study a setting with risk-averse bidders and adopt a fully nonparametric approach by not placing any restrictions on the shape of the utility function beyond regularity conditions. I propose a population criterion function that has a unique minimizer, which characterizes the utility function and density of private values. The resulting estimators emerge after replacing the population quantities by sample analogues. These estimators are uniformly consistent and their convergence rates are established. I further suggest an estimator for the optimal reserve price. Monte Carlo experiments show that the proposed estimators perform well in finite samples.