Expected revenue of all-pay and first-price sealed-bid auctions with affiliated signals

In the general symmetric auction framework of Milgrom and Weber (1982) it is shown—as a new manifestation of thelinkage principle—that the all-pay sealed-bid auction yieldshigher expected revenue than the standard first-price sealed-bid auction. This raises the question why sealed-bid auctions of the standard first-price variety are observed in practice whereas the all-pay variety is not.     

On the continuous equilibria of affiliated-value,all-pay auctions with private budget constraints

We consider all-pay auctions in the presence of interdependent, affiliated valuations and private budget constraints. For the sealed-bid, all-pay auction we characterize a symmetric equilibrium in continuous strategies for the case of N bidders. Budget constraints encourage more aggressive bidding among participants with large endowments and intermediate valuations. We extend our results to the war of attrition where we show that budget constraints lead to a uniform amplification of equilibrium bids among bidders with sufficient endowments. An example shows that with both interdependent valuations and private budget constraints, a revenue ranking between the two auction formats is generally not possible. Equilibria with discontinuous bidding strategies are discussed.     

Simultaneous ascending auctions with complementarities and known budget constraints

We study simultaneous ascending auctions of two identical objects when bidders are financially constrained and their valuations exhibit complementarities. We assume the budget constraints are known but the values for individual objects are private information, and characterize noncollusive equilibria. Equilibrium behavior is affected by the exposure problem. Bidders with higher budgets are more reluctant to bid, because opponents with lower budgets may end up pursuing a single object, thus preventing the realization of complementarities. Therefore poor bidders may win both objects when they do not have the highest valuation. We gratefully acknowledge comments by Marco Battaglini, Benny Moldovanu and participants at seminars held at Montreal, Yale, Texas A&M, Washington St. Louis and at the Workshop on Mechanism Design with Budget Constraints held at SUNY - Stony Brook. Sandro Brusco acknowledges financial support from the Ministerio de Educacion y Ciencias D.G.E.S., proyecto SEC2001-0445.     

Multi-stage sequential all-pay auctions

We study multi-stage sequential all-pay contests (auctions) where heterogeneous contestants are privately informed about a parameter (ability) that affects their cost of effort. We characterize the perfect Bayesian equilibrium of these contests and analyze the effect of the number of contestants and their types on the contestants׳ expected highest effort.     

Bribing in first-price auctions: Corrigendum

We clarify the sufficient condition for a trivial equilibrium to exist in the model of Rachmilevitch (2013).     

Tie-breaks and bid-caps in all-pay auctions

We revisit the two bidder complete information all-pay auction with bid-caps introduced by Che and Gale (1998), dropping their assumption that tie-breaking must be symmetric. Any choice of tie-breaking rule leads to a different set of Nash equilibria. Compared to the optimal bid-cap of Che and Gale we obtain that in order to maximize the sum of bids, the designer prefers to set a less restrictive bid-cap combined with a tie-breaking rule which slightly favors the weaker bidder. Moreover, the designer is better off breaking ties deterministically in favor of the weak bidder than symmetrically.     

Pre-auction offers in asymmetric first-price and second-price auctions

We consider first-price and second-price auctions with asymmetric buyers, and examine whether pre-auction offers to a subset of buyers are profitable. A single offer is never profitable prior to a second-price auction, but may be profitable prior to a first-price auction. However, a sequence of offers is profitable in either type of auction. In our model, suitably chosen pre-auction offers work because they move the assignment when bidder valuations are “near the top” closer to the optimal, revenue-maximizing assignment.     

The symmetric multiple prize all-pay auction with complete information

This paper extends the analysis of the n-player all-pay auction with complete information to cover the case of m≤n prizes, valued in weakly decreasing order, but symmetrically across players. We provide a complete characterization of the Nash equilibrium distributions for this class of auctions and provide an exact expression for the expected revenue generated.     

The value of information in asymmetric all-pay auctions

This note analyzes a two-player all-pay auction with incomplete information. More precisely, one bidder is uncertain about the size of the initial advantage of his rival modeled as a head start in the auction.I derive the unique Bayesian Nash equilibrium outcome for a large class of cumulative distribution functions of the head start. The stronger player generates an informational rent if and only if his head start distribution is not stochastically dominated by a uniform distribution. I identify why my results for an uncertain head start differ qualitatively from uncertainty about a cost function or a valuation.     

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.     

Asymmetry and revenue in first-price auctions

We show by an example that in first-price IPV auctions, asymmetry in bidders' valuations need not reduce the revenue compared to a benchmark symmetric model with the same amount of social surplus. Asymmetry need not reduce competition in first-price auctions.     

Bidding ‘as if’ risk neutral in experimental first price auctions without information feedback

Experimental research on first price sealed bid auctions has usually involved repeated settings with information feedback on winning bids and payoffs after each auction round. Relative to the risk neutral Nash equilibrium, significantly higher bidding has been reported. The present paper reports the results of experimental first price auctions with n=7 where feedback on payoffs and winning bids is withheld. Under these conditions, average bidding is below the risk neutral Nash equilibrium prediction but converges to it with repetition.

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Electronic Supplementary Material  The online version of this article () contains supplementary material, which is available to authorized users.      

An elementary proof of the common maximal bid in asymmetric first-price and all-pay auctions

We prove that the maximal bid in asymmetric first-price and all-pay auctions is the same for all bidders. Our proof is elementary, and does not require that bidders are risk neutral, or that the distribution functions of their valuations are independent or smooth.     

A note on budget balance under interim participation constraints: the case of independent types

We provide a simple proof of the equivalence between ex ante and ex post budget balance constraints in Bayesian mechanism design with independent types when participation decisions are made at the interim stage. The result is given an interpretation in terms of efficient allocation of risk.     

Competition in the economic crisis: Analysis of procurement auctions

We study the effects of the recent economic crisis on firms׳ bidding behavior and markups in sealed bid auctions. Using data from Austrian construction procurements, we estimate bidders׳ construction costs within a private value auction model. We find that markups of all bids submitted decrease by 1.5 percentage points in the recent economic crisis, markups of winning bids decrease by 3.3 percentage points. We also find that without the government stimulus package this decrease would have been larger. These two pieces of evidence point to pro-cyclical markups.     

Risk aversion in auctions with asymmetrically informed bidders: A “desensitizer” from uncertainty

In the context of first-price auctions with asymmetrically informed bidders, we show that risk aversion not only increases a player’s bid, but also makes him less sensitive to the probability that other bidders are informed about his private valuation.     

Revenue ranking of first-price auctions with resale

When the price setter in post-auction resale is chosen according to exogenous probabilities, Hafalir and Krishna (2008) [2] showed that the first-price auction brings more expected revenues than the second-price auction with truth-bidding bidders. We complete their revenue ranking by proving that the first-price auction produces higher expected revenues the higher the probability the auction winner sets the resale price.     

State enterprise performance and soft budget constraints: The case of Bulgaria

This paper analyses the performance of state enterprises in Bulgaria during 1992-94. Consistent with the literature on other transitional economies, this paper finds that one key factor underlying (the lack of) enterprise adjustment in Bulgaria during this period was the availability of financing. Empirically, the (lack of) past adjustment and the softness of finance are the best predictors of current adjustment. Many state enterprises, mostly smaller ones, appear to have adjusted to the new economic structure, partly in response to tighter budget constraints. However, a number of large, hard-core lossmaking state enterprises did not adjust, due primarily to the soft budget constraints that they faced. These enterprises crowded out profitable enterprises, both public and private, through their large financing requirements, adversely affecting economic growth. Moreover, continued bank financing of these large loss-makers decapitalized the banking system, and budgetary financing of their losses, largely through tax arrears, has undermined fiscal policy. This lack of enterprise adjustment and the resulting financial indiscipline lies at the core of the macroeconomic difficulties that Bulgaria has recently faced.     

Information aggregation in auctions with an unknown number of bidders

Information aggregation, a key concern for uniform-price, common-value auctions with many bidders, has been characterized in models where bidders know exactly how many rivals they face. A model allowing for uncertainty over the number of bidders is essential for capturing a critical condition for information to aggregate: as the numbers of winning and losing bidders grow large, information aggregates if and only if uncertainty about the fraction of winning bidders vanishes. It may be possible for the seller to impart this information by precommitting to a specified fraction of winning bidders, via a proportional selling policy. Intuitively, this could make the proportion of winners known, and thus provide all the information that bidders need to make winner's curse corrections.