Distribution Of Bids Research Articles

On joint distribution of bids in some k-th price auction model

In the era of increasingly widespread use of electronic communication tools, constant growth of e-commerce turnover is hardly surprising. One of its mechanisms are online auctions whose turnover, on a global scale, is enormous. This paper proposes a stochastic model of the value of subsequent actual bids appearing in the course of a dynamic internet k-th price auction. On this basis, it was possible to determine unconditional joint probability distributions, as well as univariate marginal distributions of successive bids appearing in the course of the auction type under consideration.

Nonparametric Identification and Inference of First-Price Auctions with Heterogeneous Bidders

In the auction literature, it is well established that bidders’ asymmetry plays an important role in determining auction revenues. In this article, we propose a nonparametric methodology to analyze first-price auctions with two popularly adopted asymmetries: heterogeneous risk preferences and asymmetric value distributions. We find that the two competing models provide distinct implications for the bid distributions conditional on heterogeneity. By modeling bidders’ asymmetry as unobserved heterogeneity, we show that the conditional bid distributions are identified nonparametrically. These results enable researchers to test the two competing models. In an application using the US Forest Service timber auction data, we find that the data supports the model with heterogeneity in risk preference.

It’s all relative: consistent marginal effects with willingness to pay and willingness to accept framing in experimental auctions

ABSTRACT When eliciting consumer preferences for controversial products – an increasing number of which exist due to increasing demographic diversity and political polarization – conventional assumptions that all individuals derive positive marginal utility from consumption are challenged. It is relatively easy to adjust hypothetical stated preference questionnaires to include negative willingness to pay (WTP), but few studies on controversial products investigate how individuals behave using incentive-compatible revealed preference techniques. Using a framed field experiment with 292 adult subjects, we fill this gap by comparing the differences and similarities between a set of results that arise from the Becker-DeGroot-Marschak (BDM) mechanism between WTP versus willingness to accept (WTA) elicitation methods. This study has two main findings. First, in economic experiments eliciting preferences for controversial products, neither the WTP nor the WTA method fully discovers the true valuation range across all participants. Second, despite framing effects that give rise to different bid distributions, relative revealed preferences for the examined products are consistent under various interventions, indicating that WTP and WTA estimates have consistent policy implications.

A Machine Learning Approach for Flagging Incomplete Bid-Rigging Cartels

AbstractWe propose a detection method for flagging bid-rigging cartels, particularly useful when cartels are incomplete. Our approach combines screens, i.e., statistics derived from the distribution of bids in a tender, with machine learning to predict the probability of collusion. As a methodological innovation, we calculate such screens for all possible subgroups of three or four bids within a tender and use summary statistics like the mean, median, maximum, and minimum of each screen as predictors in the machine learning algorithm. This approach tackles the issue that competitive bids in incomplete cartels distort the statistical signals produced by bid rigging and it outperforms previously suggested methods in applications to incomplete cartels based on empirical data from Switzerland.

Transnational Machine Learning with Screens for Flagging Bid-Rigging Cartels

Abstract We investigate the transnational transferability of statistical screening methods originally developed using Swiss data for detecting bid-rigging cartels in Japan. We find that combining screens with machine learning (either a random forest or an ensemble method consisting of six different algorithms) to classify collusive versus competitive tenders entails (depending on the model) correct classification rates of 88%–97% when training and testing the method on the Okinawa bid-rigging cartel. As in Switzerland, bid rigging in Okinawa reduced the variance and increased the asymmetry in the distribution of bids. When training the models in data from one country to test their performance in the data from the other country, imbalance increases between the correct prediction of truly collusive and competitive tenders for all machine learners and classification rates go down substantially when using the random forest as machine learner, due to some screens for competitive Japanese tenders being similar to those for collusive Swiss tenders. Demeaning the screens reduces such distortions due to institutional differences across countries such that correct classification rates based on training in one and testing in the other country amount to 85% and to 90% when using the ensemble method as machine learner, which generally outperforms the random forest.

On Joint Distribution of Bids in Some k-th Price Auction Model

On Joint Distribution of Bids in Some k-th Price Auction Model

A common‐value auction with state‐dependent participation

This paper analyzes a common‐value, first‐price auction with state‐dependent participation. The number of bidders, which is unobservable to them, depends on the true value. For participation patterns with many bidders in each state, the bidding equilibrium may be of a “pooling” type—with high probability, the winning bid is the same across states and is below the ex ante expected value—or of a “partially revealing” type—with no significant atoms in the winning bid distribution and an expected winning bid increasing in the true value. Which of these forms will arise is determined by the likelihood ratio at the top of the signal distribution and the participation across states. We fully characterize this relation and show how the participation pattern determines the extent of information aggregation by the price.

Standard Deviation of Bids for Construction Contract Auctions

AbstractPrevious research has confirmed that the distribution of bids for construction auctions can be reasonably modeled with Lognormal distribution. The location parameter of this distribution (t...

A Market-Inspired Bidding Scheme for Peer Review Paper Assignment

We propose a market-inspired bidding scheme for the assignment of paper reviews in large academic conferences. We provide an analysis of the incentives of reviewers during the bidding phase, when reviewers have both private costs and some information about the demand for each paper; and their goal is to obtain the best possible k papers for a predetermined k. We show that by assigning `budgets' to reviewers and a `price' for every paper that is (roughly) proportional to its demand, the best response of a reviewer is to bid sincerely, i.e., on her most favorite papers, and match the budget even when it is not enforced. This game-theoretic analysis is based on a simple, prototypical assignment algorithm. We show via extensive simulations on bidding data from real conferences, that our bidding scheme would substantially improve both the bid distribution and the resulting assignment.

Nonparametric Identification of First-Price Auctions with Heterogenous Bidders

In the auction literature, it is well established that bidders' asymmetry plays an important role in determining auction revenues. In this paper, we propose a nonparametric methodology to analyze first-price auctions with two popularly adopted asymmetries: heterogeneous risk preferences and asymmetric value distributions. We find that the two competing models provide distinct implications for the bid distributions conditional on heterogeneity. By modeling bidders' asymmetry as unobserved heterogeneity, we show that the conditional bid distributions are identified nonparametrically. These results enable researchers to distinguish between the two competing models. The Monte Carlo experiments demonstrate the good performance of the proposed method. In an application using the US Forest Service timber auction data, we find that the data support the model with heterogeneity in risk preference.

Strategic Overbidding in Dynamic Auctions: Structural Estimation of Value of Synergy

In this study, we formulate and estimate a dynamic procurement auction game where bidder asymmetry due to synergy is endogenous. The seller sells multiple goods via a sequence of first‐price auctions. While bidders are ex‐ante symmetric, the first‐period winner has a valuation advantage as a result of such synergy in the second‐period bidding game and becomes a strong bidder. This endogenous synergy creation leads to overbidding in the first‐period auction relative to a static bidding game. We characterize the equilibrium in terms of the observed bid distribution and suggest a two‐step estimation procedure. We apply our method to data on OCS oil‐tract auctions. We find that the federal government recovers 52% of the “strong” buyers’ willingness to pay in the second period. Bidders perceive the value of synergy to be about 5% of their first period’s informational rent. Counterfactual experiments show that government revenue could have increased by about 27% under alternative selling mechanisms.

Identification in Auction Models with Interdependent Costs

This paper provides a nonparametric identification result for procurement models with asymmetric bidders, dependent private information, and interdependent costs. For risk-neutral bidders, the model’s payoff-relevant primitives are the joint distribution of private information and each bidder’s full-information expected cost. The joint distribution of bids identifies the joint distribution of signals. First-order conditions identify the expected cost conditional on tying with at least one competitor for the lowest bid. I show identification of each bidder’s full-information cost, using variation in competitors’ cost shifters that are excludable from bidders’ own full-information costs, and generate variation in the set of competitors’ signals that induce a tie for the lowest bid. I estimate the relevant payoff primitives using data from Michigan highway procurements and evaluate policies that affect the winner’s curse’s severity.

A Mean Field Game Approach to Scheduling in Cellular Systems

There has been much work done on designing cellular scheduling algorithms. These algorithms are set up in the manner of a direct mechanism in which the queues reveal their states (backlog), and the scheduler chooses an allocation. In policies such as longest queue first (LQF), scheduling can be shown to yield short queue lengths. However, these algorithms are reliant on truthful declarations of state. Our goal in this article is to determine if a Vickrey–Clarke–Groves (VCG)-type mechanism (a second price auction) that elicits truthful value will also possess the desired LQF-like behavior in a system of dynamically evolving queues. Our approach is to use the concept of a mean field game under which at each time instant, a queue chooses its bid as a best response to its belief that the bids of the others will be drawn independently from a common bid distribution. If this best response is itself a sample from the belief bid distribution, a mean field equilibrium (MFE) is said to exist. We show the existence of the MFE and find it using its structure that the results of the allocation policy are the same as LQF. Thus, the desired LQF-like behavior arises naturally under the second-price auction mechanism. We also present results on the accuracy of the model as the number of agents (queues) becomes large. Finally, using simulations with a large number of queues, we show that computation of the MFE is straightforward.

Challenges of Electronic Reverse Auctions in Construction Industry—A Review

The innovation of construction procurement by means of electronic reverse auctions is a controversial subject of discussion among both researchers and practitioners. This paper consolidates and critically discusses current knowledge concerning the adoption and use of electronic reverse auctions in the light of specific features of the construction industry. A systematic literature review has been employed to select papers indexed in Scopus and Web of Science databases. The findings of the study indicate that studies are addressing especially five main areas, i.e., suitability of electronic reverse auction (eRA) for construction tenders, related drivers and barriers, ethical considerations, savings potential and bidding behavior, and bid distribution. Accordingly, the authors are suggesting three directions in which future research should focus on mutual interaction of electronic reverse auctions and long-term effects on construction project outcomes.

Private and common value auctions with ambiguity over correlation

We analyze auctions when individuals have ambiguity over the joint information structures generating the valuations and signals of players. We analyze how two standard auction effects interact with the ambiguity of bidders over correlation structures. First, a “competition effect” arises when different beliefs about the correlation between bidders' valuations imply different likelihoods of facing competitive bids. Second, a “winner's value effect” arises when different beliefs imply different inferences about the winner's value. In the private values case, only the first effect exists and this implies that the distribution of bids first order stochastically dominates the distribution of bids in the absence of ambiguity. In common value auctions both effects exist and we show that compared to the canonical model, both in the first-price and second-price auctions, these effects combine to imply that the seller's revenue decreases with ambiguity (in contrast with the private values case). We then characterise the optimal auction in both the private and common value cases. A novel feature that arises in the optimal mechanism in the common values case is that the seller only partially insures the high type against ambiguity.

A First Price Auction with an Arbitrary Number of Asymmetric Bidders

Abstract We examine an auction setting with private values and $n\geq 2$ bidders, which differ in the probability to have a low (high) value. We prove that for the first price auction, the equilibrium strategies can be written in closed form and there are gaps in the equilibrium bid distribution of each bidder except the strongest two. Our equilibrium characterization allows to prove that in this setting the seller prefers the second price auction to the first price auction for each $n\geq 2$.

Machine learning with screens for detecting bid-rigging cartels

We combine machine learning techniques with statistical screens computed from the distribution of bids in tenders within the Swiss construction sector to predict collusion through bid-rigging cartels. We assess the out of sample performance of this approach and find it to correctly classify more than 84% of the total of bidding processes as collusive or non-collusive. We also discuss tradeoffs in reducing false positive vs. false negative predictions and find that false negative predictions increase much faster in reducing false positive predictions. Finally, we discuss policy implications of our method for competition agencies aiming at detecting bid-rigging cartels.

Nonparametric Estimation of the Diamond-Dybvig Banking Model

I propose a nonparametric structural estimator for the distribution of liquidity needs in a version of the Diamond and Dybvig (1983) model when only the aggregate level of withdrawals is observed. The model is an extension of Peck and Shell (2003) with a continuum of depositors. I show how the characterization of the optimal contract proposed in Sultanum (2014) can be used to estimate the distribution of aggregate liquidity needs. The method builds on the literature of estimation of auctions. More precisely, it uses the indirect approach proposed by Guerre et al. (2000). Guerre et al. (2000) use the differential equation associated with the first-order condition for the optimal bid to recover the unobserved distribution of agents' valuations from the distribution of bids in an auction. The method I propose uses the differential equation associated with the first-order condition for an optimal bank contract to recover the unobserved distribution of liquidity needs from the observed distribution of total bank withdrawals. I use a numerical simulation to illustrate the estimation procedure

Test‐Retesting in Experimental Valuation of Perishable Food Products: Unstable Individual Bids and Reliable Market Demand

AbstractOne important property of a preference measure is its reliability. In this article, we explore the reliability of experimental auctions in measuring the market demand for five types of fish. We use the test‐retest method to compare demand curves from two Becker–DeGroot–Marschak experiments with the same 116 participants conducted 7 months apart in time. The individual bids are not stable for these perishable products, but the distributions of the individual bids are stable. We find that the unsystematic individual variations cancel out in the aggregation of bids in a typical sample size for experimental valuation studies. Our results suggest that experimental auctions provide reliable market demand estimates even though the individual bids may change substantially over time.

Large all-pay auctions with IPV bidders

This note analyzes different types of all-pay auctions when the number of bidders becomes large. We compute the distributions of the highest bids for the first-price all pay auction and we show that the expected payment made by the winning bidder converges to half of the total payments. In the second-price all-pay auction (the war of attrition), the highest bid amounts to about 35.5% of the total revenues. We also compute the payments for all-pay auctions with multiple prizes.