Risk-neutral Bidders Research Articles

Auctions Where Incomes are Private Information and Preferences (Non Quasi-Linear) are Common Knowledge

We consider a two good world where an individual i with income mi has utility function u (x, y), where x ∈ [0, ∞) and y ∈ {0, 1}. We first derive the valuation (maximum price that he is willing to pay for the object) for good y as a function of his income. Then we consider the following problem. Suppose good x is available in a store at a fixed price 1. Good y can be obtained in an auction. In such a situation we show that bidding ones own valuation is an equilibrium in a second-price auction. With risk neutral bidders and high enough incomes we derive the symmetric equilibrium in first-price and all-pay auctions and show that revenue equivalence fails to hold. With risk neutrality we also show that under mild restrictions, the revenue maximising reserve price is zero for all the three auctions and the all-pay auction with zero reserve price fetches the highest expected revenue. With low enough incomes, we show that under some restrictions, bidding ones own valuation is a symmetric equilibrium even for first-price and all-pay auctions. Here also, the expected revenue is the highest with all-pay auctions.

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.

Participation Costs and Inefficiency in Takeover Contests

We consider a takeover in which risk neutral bidders incur private costs to participate to the auction. Supposing that valuations for target firm are common knowledge, we study the optimal strategy of bidders and analyze the takeover result when they get or not toeholds in the target firm. We found that bidder's decision of participation is endogenous. By analyzing bidder's condition of participation, we found that the probability that the potential bidder with the highest valuation will not participate to the control, exists. We show that this probability increases with the size of toeholds possessed by the bidder with low valuation. Nevertheless, the size of toeholds possessed by the bidder with the highest valuation increases the probability of his participation to the auction. Asymmetric toeholds between potential bidders can accentuate inefficient allocation when participation costs are private information. However, if bidder with toeholds deters completely bidders without toeholds to participate when valuation are private information, the phenomenon of fully deterring is destroyed when valuations are common knowledge.

Budget-constrained sequential auctions with incomplete information

I study a budget-constrained, private-valuation, sealed-bid sequential auction with two incompletely-informed, risk-neutral bidders in which the valuations and income may be non-monotonic functions of a bidder's type. Multiple equilibrium symmetric bidding functions may exist that differ in allocation, efficiency and revenue. The sequence of sale affects the competition for a good and therefore also affects revenue and the prices of each good in a systematic way that depends on the relationship among the valuations and incomes of bidders. The sequence of sale may affect prices and revenue even when the number of bidders is large relative to the number of goods. If a particular good, say α, is allocated to a strong bidder independent of the sequence of sale, then auction revenue and the price of good α are higher when good α is sold first.

Optimal auctions with asymmetrically informed bidders

The paper analyzes a problem of optimal auction design when the seller faces asymmetrically informed bidders. Specifically, we consider a continuum of risk-neutral uninformed bidders taking part into the auction along with n risk-averse informed bidders. The contribution of the paper is threefold. First, we fully characterize the optimal auction in this non standard environment and in a very general set-up. We find that when informed bidders reveal “bad news” about the value of the good, the seller optimally awards the object to the uninformed bidders. Secondly, we show that the seller is better off in presence of uninformed bidders because this allows to lower the informational rents paid to the informed bidders. Last, we find that, with bi-lateral risk neutrality, the seller always awards the good to the uninformed bidders thereby keeping all the surplus.

Bidding behavior at sequential first-price auctions with(out) supply uncertainty: A laboratory analysis

We report on a series of experiments that test the effects of an uncertain supply on bidding behavior and prices in sequential first-price auctions with private-independent values and unit-demands. Supply is assumed uncertain when buyers do not know the exact number of units to be sold (i.e., the length of the sequence). We observe an important overbidding in all but the last stage of a sequence, no matter whether supply is certain, and a non-monotone behavior when supply is certain. Yet, the data qualitatively support most stage-to-stage bid predictions and the price trend predictions for risk neutral bidders.

The role of varying risk attitudes in an auction with a buyout option

An auction with a buyout option is modelled. Such an option allows a bidder to purchase the item being auctioned at a pre-specified buyout price, instead of attempting to obtain the item through the traditional auction procedure. This analysis is motivated by internet auctions where such options are present. If all auction participants are risk neutral, the seller will choose a buyout price high enough so that the option is never exercised. However, a risk averse seller facing risk neutral bidders will choose a price low enough so that the option is exercised with positive probability. Further, if bidders are risk neutral and the seller is risk averse, this option may result in a Pareto improvement compared to a sealed bid second price auction.

Field experiments on the effects of reserve prices in auctions: more Magic on the Internet

I present experimental evidence on the effects of minimum bids in first‐price, sealed‐bid auctions. The auction experiments manipulated the minimum bids in a preexisting market on the Internet for collectible trading cards from the game Magic: the Gathering. I examine a number of outcomes, including the number of participating bidders, the probability of sale, the levels of individual bids, and the auctioneer's revenues. The benchmark theoretical model is one with symmetric, risk‐neutral bidders with independent private values. The results verify a number of the predictions concerning equilibrium bidding. Many bidders behave strategically, anticipating the effects of the reserve price on others' bids.

Effect of Buyer and Seller Experience on Buy It Now Pricing

ABSTRACT Although auctions have been around for centuries, online auctions are still a relatively new phenomenon. This paper examines the phenomenon of online auctions, specifically on a pricing option known as “Buy It Now.” With this option, a buyer can purchase merchandise immediately at a stated price and truncate the auction process. Auction items sold with a Buy It Now price tend to be at a higher price than the high bid price for an identical item sold through an ascending-bid auction. In addition, Buy It Now prices tend to attract risk averse bidders while high bidders of ascending-bid auctions tend to be less risk averse or risk neutral bidders. On the other hand, we found more experienced sellers sell their items with a Buy It Now price while less experienced sellers sell their items through an ascending-bid process. Thus, experience and risk are factors in choosing a Buy It Now price for the seller and buyer.

Asymptotic and small sample analysis of the stochastic properties and certainty equivalents of winning bids in independent private values auctions $\!$

This paper investigates the stochastic properties of the first price and second price winning bids in auctions with risk neutral bidders with independent and identically distributed valuations. In such an environment, the winning first price bids second order stochastically dominate the second price winning bids. A key result of this paper is that the ratio of the variance of the winning first price bid to that of the winning second price bid is strictly less than one even as the number of bidders goes to infinity. This suggests that the stochastic dominance of the winning first price bids does not vanish even in the limit. Both the asymptotic and small sample properties of winning bids are investigated. In particular, the small sample results suggest that the identification power of econometric procedures that rely on winning bids can decline rapidly as the number of bidders increases. This paper also includes a systematic evaluation of the difference in certainty equivalents between the two auction formats for several common distributions and number of bidders for the case of auctioneers with constant coefficient of absolute risk aversion. These results are presented in a form that makes it easy to apply them to a specific auction of interest.

Ignorance Promotes Competition: An Auction Model with Endogenous Private Valuations

We study a situation in which an auctioneer wishes to sell an object toone of N risk-neutral bidders with heterogeneous preferences. Theauctioneer does not know bidders preferences but has private informationabout the characteristics of the ob ject, and must decide how muchinformation to reveal prior to the auction. We show that the auctioneerhas incentives to release less information than would be efficient andthat the amount of information released increases with the level ofcompetition (as measured by the number of bidders). Furthermore, in aperfectly competitive market the auctioneer would provide the efficientlevel of information.

Ignorance Promotes Competition: An Auction Model with Endogenous Private Valuations

We study a situation in which an auctioneer wishes to sell an object to one of N risk-neutral bidders with heterogeneous preferences. The auctioneer does not know bidders' preferences but has private information about the characteristics of the object, and must decide how much information to reveal prior to the auction. We show that the auctioneer has incentives to release less information than would be efficient and that the amount of information released increases with the level of competition (as measured by the number of bidders). Furthermore, in a perfectly competitive market the auctioneer would provide the efficient level of information.

Monotone Equilibrium in Multi-Unit Auctions

In a large class of multi-unit auctions of identical objects that includes the uniform-price, as-bid (or discriminatory), and Vickrey auctions, a Bayesian Nash equilibrium exists in monotone pure strategies whenever there is a finite price / quantity grid and each bidder's interim expected payoff function satisfies single-crossing in own bid and type. A stronger condition, non-decreasing differences in own bid and type, is satisfied in this class of auctions given (a) independent types and (b) risk-neutral bidders with marginal values that are (c) nondecreasing in own type and have (d) non-increasing differences in own type and others' quantities. A key observation behind this analysis is that each bidder's valuation for what he wins is always modular in own bid in any multi-unit auction in which the allocation is determined by market-clearing. This paper also provides the first proof of pure strategy equilibrium existence in the uniform-price auction when bidders have multi-unit demand and values that are not private.

Posterior odds comparison of a symmetric low-price, sealed-bid auction within the common-value and the independent-private-values paradigms

I attempt to decide, using the posterior odds ratio, whether the symmetric common-value paradigm or the symmetric independent-private-values paradigm is a more probable explanation of the low-price, sealed-bid auctions conducted by the Indian Oil Corporation to purchase crude-oil from the international market. The estimation approach is structural parametric. The auctions are modelled as static non-cooperative games of incomplete information with risk neutral bidders. I conclude that the symmetric independent-private-values paradigm is more probable. Copyright © 1999 John Wiley & Sons, Ltd.

Multiple unit auctions with strategic price-quantity decisions

I study a multiple unit auction where symmetric risk-neutral bidders choose prices and quantities endogenously. In the model, bidders (a) may place non-linear valuations on the auctioned units, and (b) bid for several units at the same price (“lumpy” bids). I characterize quantity-symmetric and strictly monotone-increasing price equilibria for discriminatory and competitive auctions, and show that (i) if quantity strategy profiles are equal across auctions revenue- equivalence holds, (ii) expected revenue is higher if bidders bid for the entire supply rather than for shares of it, and (iii) equilibrium allocations may fail to be Pareto-optimal.

Auction Form Preferences of Risk-Averse Bid Takers

We analyze the preferences of a risk-averse seller over the class of auctions with symmetric and risk-neutral bidders. Assuming that buyers' private signals are independently distributed, we find that a sealed-bid first-price auction with an appropriately set reserve price is preferred by all risk-averse sellers to any other standard auction. In first- and second-price auctions, the more risk averse a seller, the lower the seller's optimal reserve price. Given two first-price auctions with reserve prices and entry fees such that both have the same screening level, all risk-averse sellers prefer the auction with the lower entry fee.

Bid shading and risk aversion in multi-unit auctions with many bidders

We extend the analysis of optimal price taking bidding in multi-unit auctions to allow for risk aversion and a continuous random stop-out price. We show that in a discriminatory auction risk averse bidders should bid less aggressively than risk neutral bidders. However, bid shading is optimal at each price, which implies, with complete certainty, inefficient trade. This is in sharp contrast to competitive auctions where truthful bidding is optimal even under risk aversion.

Seller surplus in first price auctions

In a first-price sealed-bid discriminatory auction with M winners, the surplus gained by the seller from constant relative and constant absolute risk-averse bidders is defined. For sufficiently high risk aversion in these cases, the seller gains all the surplus. It is also shown that constant relative risk-averse bidders are equivalent to risk-neutral bidders with a transformed distribution of private values.

Ambiguity aversion in first-price sealed-bid auctions

Experiments on first-price sealed-bid auctions with independent private values have shown that submitted bids typically exceed Nash-equilibrium predictions for risk-neutral bidders. Existing bidding models explain this phenomenon by assuming that the bidders are risk-averse and capable of drawing complete and correct inferences about their winning probabilities. In this article, we use the Choquet expected utility (CEU) theory to demonstrate that the observed bidding behavior can also be attributed to ambiguity aversion which causes the bidders to underestimate their chances of winning the auction. Empirical support for CEU bidding models is given through an analysis of recent bidding data.

Revenue Equivalence and Bidding Behavior in a Multi-Unit Auction Market: An Empirical Analysis

Revenue-equivalence of competitive and discriminatory formats is a major result for private-value multiunit auctions with risk-neutral bidders. Among the factors that may cause this result to break down, the most notorious ones are risk-aversion, value-affiliation, and endogenous bidder participation. Using data from competitive and discriminatory auctions undertaken in the Zambian foreign exchange market, the author analyzes revenue-equivalence and other bidding phenomena. The results indicate that (1) competitive auctions were revenue-superior due to higher participation; (2) high bidders adjusted with delay to an auction format change; and (3) a reservation bid was used as a policy instrument. Copyright 1993 by MIT Press.