Bidding behavior in asymmetric auctions: An experimental study

We review an asymmetric auction experiment. Based on Plum (Int. J. Game Theory 20 (1992) 393) private valuations of the two bidders are independently drawn from distinct but commonly known distributions, one of which first-order stochastically dominates the other. We test the qualitative properties of that model of asymmetric auctions, in particular whether the weak bidder behaves more aggressively than the strong, and then test bidders’ preference for first- vs. second-price auctions.     

Strategic ignorance in a second-price auction

Suppose that bidders may publicly choose not to learn their values prior to a second-price auction with costly bidding. All equilibria with truthful bidding exhibit bidder ignorance when the number of bidders is sufficiently small. Ignorance considerations also affect the optimal reserve price.     

First-price auctions with resale: the case of many bidders

We study first-price auctions with resale when there are many bidders and derive existence and characterization results under the assumption that the winner of the initial auction runs a second-price auction with an optimal reserve price. The fact that symmetrization fails when there are more than two bidders has been observed before, but we also provide the direction: weaker bidders are less likely to win than stronger ones. For a special class of distributions and three bidders, we prove that the bid distributions are more symmetric with resale than without. Numerical simulations suggest that the more bidders there are, the more similar the allocation is to the case without resale, and thus, the more asymmetric the bid distributions are between strong and weak bidders. We also show in an example that the revenue advantage of first-price auctions over second-price auctions is positive, but decreasing in the number of bidders.     

Risky procurement with an insider bidder

Procurement auctions carry substantial risk when the value of the project is highly uncertain and known only to insiders. This paper reports the results from a series of experiments comparing the performance of three auction formats in such complex and risky settings. In the experiment, every bidder knows the private value for the project but only a single insider bidder knows the common-value part. In addition to the standard second-price and English auctions we test the “qualifying auction,” a two-stage format commonly used in the sale of complex and risky assets. The qualifying auction has a fully “revealing” equilibrium that implements the revenue-maximizing outcome but it also has an uninformative “babbling” equilibrium in which bidders place arbitrarily high bids in the first stage. In the experiments, the latter equilibrium has more drawing power, which causes the qualifying auction to perform worse than the English auction and only slightly better than a sealed-bid second-price auction. Compared to the two other formats, the English auction is roughly 40% more efficient, yields 50% more revenues, avoids windfall profits for the insider, while protecting uninformed bidders from losses.     

Auctions in which losers set the price

We study auctions of a single asset among symmetric bidders with affiliated values. We show that the second-price auction minimizes revenue among all efficient auction mechanisms in which only the winner pays, and the price only depends on the losers' bids. In particular, we show that the kth price auction generates higher revenue than the second-price auction, for all k>2. If rationing is allowed, with shares of the asset rationed among the t highest bidders, then the (t+1)st price auction yields the lowest revenue among all auctions with rationing in which only the winners pay and the unit price only depends on the losers' bids. Finally, we compute bidding functions and revenue of the kth price auction, with and without rationing, for an illustrative example much used in the experimental literature to study first-price, second-price and English auctions.     

An experiment on auctions with endogenous budget constraints

We perform laboratory experiments comparing auctions with endogenous budget constraints. A principal imposes a budget limit on a bidder (an agent) in response to a principal-agent problem. In contrast to the existing literature where budget constraints are exogenous, this theory predicts that tighter constraints will be imposed in first-price auctions than in second-price auctions, tending to offset any advantages attributable to the lower bidding strategy of the first-price auction. Our experimental findings support this theory: principals are found to set significantly lower budgets in first-price auctions. The result holds robustly, whether the principal chooses a budget for human bidders or computerized bidders. We further show that the empirical revenue difference between first- and second-price formats persists with and without budget constraints.     

Bidding for the future: signaling in auctions with an aftermarket

This paper considers auctions where bidders compete for an advantage in future strategic interactions. When bidders wish to exaggerate their private information, equilibrium bidding functions are biased upwards as bidders attempt to signal via the winning bid. Signaling is most prominent in second-price auctions where equilibrium bids are “above value.” In English and first-price auctions, signaling is less extreme since the winner incurs the cost of her signaling choice. The opportunity to signal lowers bidders’ payoffs and raises revenue. When bidders understate their private information, separating equilibria need not exist and the auction may not be efficient.     

Bidding behavior in competing auctions: Evidence from eBay

Much of the existing auction literature treats auctions as running independently of one another, with each bidder choosing to participate in only one auction. However, in many online auctions, a number of substitutable goods are auctioned concurrently and bidders can bid on several auctions at the same time. Recent theoretical research shows how bidders can gain from the existence of competing auctions, the current paper providing the first empirical evidence in support of competing auctions theory using online auctions data from eBay. Our results indicate that a significant proportion of bidders do bid across competing auctions and that bidders tend to submit bids on auctions with the lowest standing bid, as the theory predicts. The paper also shows that winning bidders who cross-bid pay lower prices on average than winning bidders who do not.     

Bidder collusion

We analyze bidder collusion at first-price and second-price auctions. Our focus is on less than all-inclusive cartels and collusive mechanisms that do not rely on auction outcomes. We show that cartels that cannot control the bids of their members can eliminate all ring competition at second-price auctions, but not at first-price auctions. At first-price auctions, when the cartel cannot control members’ bids, cartel behavior involves multiple cartel bids. Cartels that can control bids of their members can suppress all ring competition at both second-price and first-price auctions; however, shill bidding reduces the profitability of collusion at first-price auctions.     

Beyond chopsticks: Symmetric equilibria in majority auction games

Majority auction games are simultaneous sealed-bid auctions of identical objects among identical bidders who each want to win a specified fraction (more than a half) of the objects. Each bidder receives no benefit from winning less than the specified fraction and no additional benefit from winning more than it. Symmetric equilibria having simple, intuitive forms are shown to exist in first-price, second-price and all-pay versions of such games when the number of bidders is sufficiently large. This contrasts with earlier results for the two-bidder “pure chopstick” majority auction games where the only known equilibria are more complicated.     

Asymmetric information about rivals'' types in standard auctions

We study auctions in which bidders may know the types of some rival bidders but not others. This asymmetry in bidders' knowledge about rivals' types has different effects on the two standard auction formats. In a second-price auction, it is weakly dominant to bid one's valuation, so the knowledge of rivals' types has no effect, and the good is allocated efficiently. In a first-price auction, bidders refine their bidding strategies based on their knowledge of rivals' types, which yields an inefficient allocation. We show that the inefficient allocation in the first-price auction translates into a poor revenue performance. Given a standard regularity condition, the seller earns higher expected revenue from the second-price auction than from the first-price auction, whereas the bidders are better off from the latter.     

Learning to bid: The design of auctions under uncertainty and adaptation

We examine auction design in a context where symmetrically informed adaptive agents with common valuations learn to bid for a good. Despite the absence of private valuations, asymmetric information, or risk aversion, bidder strategies do not converge to the Bertrand–Nash equilibrium strategies even in the long run. Deviations from equilibrium strategies depend on uncertainty regarding the value of the good, auction structure, the agents? learning model, and the number of bidders. Although individual agents learn Nash bidding strategies in isolation, the learning of each agent, by flattening the best-reply correspondence of other agents, blocks common learning. These negative externalities are more severe in second-price auctions, auctions with many bidders, and auctions where the good has an uncertain value ex post.     

Optimal auctions with asymmetric financial externalities

This paper studies optimal auction design with asymmetric linear financial externalities among bidders. When the matrix Γ that relates bidders? payoffs to their payments is nonsingular, the payment-related component in the design objective must equal a unique linear combination of its counterparts in bidder?s payoffs. If all multipliers of the linear combination are nonnegative, a modified Myerson procedure is discovered for deriving the optimal design. If any multiplier is negative, an arbitrarily high value can be achieved for design objective by setting proper fixed transfers to bidders. When the matrix Γ is singular, the unbounded optimum result typically prevails. We applied our method to auctions with cross shareholdings and charity auctions for revenue-maximizing and efficient designs.     

A common value auction model with endogenous entry and information acquisition

Summary Much of the auction literature assumes both a fixed number of bidders and a fixed information setting. This sidesteps the important and often costly decisions a potential bidder must make prior to an auction: Should I enter and, if I do, what level of resources should I expend evaluating the good prior to bidding? We answer these questions for a stylized information model of a common value auction. The expected selling price is shown to be the expected value of the good minus the expected aggregate entry and information costs of the bidders. Thus, the seller indirectly pays for these costs to the bidders. There are auctions where the seller seemingly restricts the bidders' information expenditures. While this restriction does influence the entry decision, we demonstrate that the overall effect can be to improve the selling price. Finally, the probability of entry and the chosen accuracy of the information are never more in the second-price auction than in the first-price auction, and the seller prefers the second-price auction.We are grateful for the comments and suggestions of seminar participants at the University of British Columbia, Dartmouth College, the University of Wisconsin, Yale University, and the International Conference on Game Theory and Economics at SUNY Stony Brook.     

Bidding in a possibly common-value auction

We analyze a second-price auction with two bidders in which only one of the bidders is informed as to whether the object is valued commonly. We show that any equilibrium strategy of the bidder who is uninformed must be part of an equilibrium when both bidders instead know that the auction is not common value, regardless of the way in which the values are different. We derive sufficient conditions for equilibrium existence.     

The high/low divide: Self-selection by values in auction choice

Most prior theoretical and experimental work involving auction choice has assumed bidders find out their value after making a choice of which auction to enter. We examine whether or not bidders knowing their value prior to making a choice of which among multiple alternative auction formats to enter impacts their choice decision and/or the outcome of the auctions. The results show a strong impact on auction choice. Subjects with low values choose the first price sealed bid auction more often while subjects with high values choose the ascending auction more often. The number of bidders in each auction, revenue, efficiency and average bidder surplus all end up equalized.     

Standard Auctions with Financially Constrained Bidders

We develop a methodology for analyzing the revenue and efficiency performance of auctions when buyers have private information about their willingness to pay and ability to pay. We then apply the framework to scenarios involving standard auction mechanisms. In the simplest case, where bidders face absolute spending limits, first-price auctions yield higher expected revenue and social surplus than second-price auctions. The revenue dominance of first-price auctions over second-price auctions carries over to the case where bidders have access to credit. These rankings are explained by differences in the extent to which financial constraints bind in different auction formats.     

Collusion in one-shot second-price auctions

Summary. Most of the literature on collusive behavior in auctions ignores two important issues that make collusion difficult to sustain at least in one-shot interactions: the detection of cheating and the verification of bids. Colluding bidders may deceive each other by using shill bidders. Also, if the identities of the bidders and their bids are not published then it would be difficult to verify the bid of a colluding bidder. This paper addresses these problems in one shot second price auctions where one bidder offers another bidder a side payment in exchange for not participating in the auction, while the number of other bidders is stochastic. In spite of the barriers to collusion mentioned above, a simple side payment mechanism which depends only on the auction price is introduced. It induces a successful collusion, eliminates the verification problem, provides no incentive for the use of shill bidders and guarantees that the proponent obtains ex-post non-negative payoff. The colluding bidders are ex-ante strictly better off compared with the competitive case, irrespective of their types.Received: 27 November 2002, Revised: 28 January 2005, JEL Classification Numbers: C72, D44, D82.Yair Tauman: Correspondence toWe would like to thank an anonymous referee for very valuable comments and suggestions that significantly improved the paper. We thank Shmuel Zamir for a helpful discussion.     

A non-expected utility model and its application in practical auctions

ABSTRACT

This article presents a non-expected utility decision model which is nonlinear in the winning probabilities. The model not only explicitly expresses bidders’ attitudes to risk, but also addresses their preference over the bidding criteria. To demonstrate how to apply the model in the practical auction design, the first- and second-price auctions with both commission rate and reserve price are examined, respectively. For nonrisk-neutral bidders, the equilibrium bidding strategies are characterized, in which the commission rate has a significant influence on the bidding strategy through the critical valuation. However, the existence of the optimal commission rate is uncertain, but once it exists, it depends on the information rent of the highest or second highest order valuation in terms of the inverse hazard rate. With risk-aversion bidders, the only difference to the optimal reserve price is a constant between the first- and second-price auctions. The revenue comparisons show that the classical Revenue Equivalence Theorem fails in practical auctions with the commission rate. This article extends the application of the decision-making model in the auction design in theory and provides some guidance for the auction house and the seller to make their decisions in reality.     

Large common value auctions with risk averse bidders

We analyze large symmetric auctions with conditionally i.i.d. common values and risk averse bidders. Our main result characterizes the asymptotic equilibrium price distribution for the first- and second-price auctions. As an implication, we show that with constant absolute risk aversion (CARA), the second-price auction raises significantly more revenue than the first-price auction. While this ranking seems robust in numerical analysis also outside the CARA specification, we show by counterexamples that the result does not generalize to all risk averse utility functions.