Number Of Bidders Research Articles

Cartels in Public Procurement

Public procurement markets differ from all others because quantities do not adjust with prices, but are fixed by the bidding authority. As a result, there is a high incentive for organizing cartels (the price elasticity of demand is zero below the base price) that are quite stable because there are no lasting benefits for cheaters. In such circumstances leniency programs are unlikely to help discovering cartels. Since all public procurement cartels operate through some form of bid rotation, public procurement officials have all the information necessary (but they have to collect evidence on a number of bids) to discover them, contrary to what happens in normal markets where customers are not aware of the existence of a cartel. However in order to promote reporting, the structure of incentives has to change. For example, the money saved from a carte, should at least in part remain with the administration that helped discovering it and the reporting official should have some career advantages. In any case, competition authorities should create a channel of communication with public purchasers, so that they would know that informing the Authority on any suspicion they may have on bid rigging is easy and does not require them to provide a full proof.

Simultaneous Allocation of Bundled Goods Through Auctions: Assessing the Case for Joint Bidding

We use the experimental method to study the costs and benefits of allowing joint bidding in simultaneous multi-unit first price sealed bid auctions for bundled goods. The research has immediate applications to the sale of public forest stands that arbor a mixture of species. Joint bidding and communication raise the prospect of higher allocative efficiency, but also of collusive bidding through a reduction in the number of bidders and a greater scope for the formation of bidding rings. However, we find that allowing joint bidding has a significant positive impact on efficiency and reduces collusion significantly. We also explore the robustness of the results to characteristics of the auction environment that are relevant to timber auctions.

Charity Art Auctions

Using a unique panel data set of art auctions on eBay, we conduct an empirical analysis of the impact of charity status on the outcome of an auction and find it to be substantial. Charity status increases the probability of sale by 46%, the observed number of bidders by 111% and the sale price by 45%. In addition, charity status substantially lowers the auction's opening price. Interestingly, the effect of charity status declines over time indicating that charity auctions may be susceptible to donor fatigue.

What Impact Does Antitrust Intervention Have on Competition? The Case of Public Drug Procurement in Russia

In this paper we study antitrust intervention in long-term relationships between public procurer and his preferred supplier in one of the Russian regions. We presume that antitrust control of auctions held by affiliated procurer increases the risks of implementing long-term relationships with his preferred supplier. However we found out that after the intervention of antitrust agency the number of bidders in the auctions increased, but relative contract prices remained the same. We argue that procurer and preferred bidder invited firm with passive bidding strategy to decrease the risks of antitrust punishment. Thereby, antitrust intervention led to fake competition, but not to honest non-corrupt behavior in public auctions.

Discrete Rule Learning and the Bidding of the Sexes

We present a hidden Markov model of discrete strategic heterogeneity and learning in first price independent private values auctions. The model includes three latent bidding rules: constant absolute mark-up, constant percentage mark-up, and strategic best response. Rule switching probabilities depend upon a bidder's past auction outcomes. We apply this model to a new experiment that varies the number of bidders, the auction frame between forward and reverse, and includes the collection of saliva samples - used to measure subjects' sex hormone levels. We find the proportion of bidders following constant absolute mark-up increases with experience, particularly when the number of bidders is large. The primary driver here is subjects' increased propensity to switch strategies when they experience a loss (win) reinforcement when following a strategic (heuristic) rule. This affect is stronger for women and leads them spend more time following boundedly rational rules. We also find women in the Luteal and Menstrual phases of their menstrual cycle bid less aggressively, in terms of surplus demanded, when following the best response rule. This combined with spending more time following simple rules of thumbs explains gender differences in earnings.

Multiple-round timber auction design and simulation

This paper presents a multiple-round timber auction simulation, developed in order to study various configurations of auction design. In this study, simultaneous sequential timber auctions are modelled and analysed using agent-based simulation technology. As there are many individual items in the auction to be sold, the auction designer defines several rounds that are sequential at pre-defined intervals. At each round, the auction designer announces several simultaneous auctions. Since bidders are offered different items at each round, a mathematical linear programing model for selecting the best set of items to bid for is presented. Different bidding patterns are simulated and compared in various setup configurations. The most advanced of these strategies are adaptive and use agent-learning capability. The comparisons include the success rate of winning the auction and the winning price per m3. This study suggests an efficient bidding pattern for bidders to bid in order to achieve to their goal and increase their profit. Similarly, in order to increase profit, the auctioneer (i.e. the government) needs to control several auction parameters including the number of auctions per year, the lot size, the auction periodicity, and the number of bidders. This study also suggests parameters configurations that to maximise revenue for the auctioneer.

Identification and Estimation of First-Price Auctions Under Ambiguity

This paper studies identification and estimation of first-price auctions if the bidders face ambiguity about the distribution of valuations. Ambiguity is modeled using Gilboa and Schmeidler's (1989) Maxmin Expected Utility preferences. We exploit variation in the number of bidders to identify the essential primitives of the model. The identification result yields a closed form for the inverse bid function, which suggests a two-step estimation procedure. We study asymptotic and finite sample properties of the estimators. We find evidence of ambiguity in USFS timber auctions which leads to aggressive bidding for bidders with high valuations and has important implications for auction design.

Veconlab Classroom Clicker Games: The Wisdom of Crowds and the Winner's Curse

The authors present a classroom “clicker” exercise in which students are asked to guess the number of items in a clear container before bidding on a money prize worth a penny for each item. Even if the distribution of guesses is unbiased, the highest bidder is likely to have overestimated the true number and ended up with a loss. Because winning becomes an increasingly rare and informative event as the number of bidders increases, the exercise generates a dramatic “winner's curse” in large classes where clicker systems are commonly used. Initial guesses about the number of items tend to suffer from perception bias, and this partial failure of the “wisdom of the crowds” can make bids even less rational.

A new approach to identifying generalized competing risks models with application to second-price auctions

This paper proposes an approach to proving nonparametric identification for distributions of bidders' values in asymmetric second-price auctions. I consider the case when bidders have independent private values and the only available data pertain to the winner's identity and the transaction price. My proof of identification is constructive and is based on establishing the existence and uniqueness of a solution to the system of nonlinear differential equations that describes relationships between unknown distribution functions and observable functions. The proof is conducted in two logical steps. First, I prove the existence and uniqueness of a local solution. Then I describe a method that extends this local solution to the whole support. This paper delivers other interesting results. I demonstrate how this approach can be applied to obtain identification in auctions with a stochastic number of bidders. Furthermore, I show that my results can be extended to generalized competing risks models.

An auction design for local reserve energy markets

In this paper we develop an auction mechanism that is designed for a local energy market. It aims to enable regionally or virtually restricted trading of ancillary services, which enhances the position of the balance group responsible party beyond that of simple accounting. Furthermore, it makes local market participants somewhat more independent from the transmission grid operator, but at the same time provides incentives for investments in distributed generation technologies. A wider spread of these technologies can help to save CO2 emissions, while at the same time a part of them can also be used to counter the fluctuations of energy from volatile renewable sources, such as wind and solar power. Because of their relatively high margins and small share in total production, ancillary services are well-suited for a remuneration scheme. Participants in the auction are, thus, private households, which impose specific design characteristics on the auction. Most importantly, it needs to be transparent and easy to understand, as homeowners will typically not have the insights of a professional trader as well as lack a similar position and motivation. Also, the confinement to a single balance group, i.e. a local market, means that especially in the beginning of the trading only a small number of bidders can be expected. Therefore, competition will initially be limited, so that the auction design needs to be adapted accordingly. In order to test the performance of the proposed auction market design under varying information policies, a simple agent-based simulation program has been developed. We find that the theoretical predictions hold and that competition quickly leads to price convergence.

Effects of competition on environmental water buyback auctions

As water extractions from the world's rivers have grown, flows available for the environment have dwindled. In many parts of the world governments are now considering strategies to restore environmental flows. One strategy is for a government to buyback water from irrigators for the environment with annual lease arrangements. In this paper we have studied the role of market competition (in terms of environmental water demand and number of sellers) in determining the performance of multi-round environmental water buyback auctions using a stylized agent based simulation model. The results suggest that rent extraction lowers as the number of bidders increase and water demand decreases. However, we find significant differences in the way changes in demand and supply influence rent extraction. Reduction in water demand has much greater impact on rent extraction than increasing the number of bidders in the market. Further, in wet years (when supply is abundant relative to demand) bidders engage in more competitive bidding compared to cases in dry years. Results from the analysis indicate that government agencies benefit more from arranging buyback tenders (1) with a small target relative to tenders with a large bidder population and (2) with greater opportunities for the bidders to learn from the market in wet years compared to dry years.

Price Formation on Land Market Auctions in East Germany – An Empirical Analysis

Although determinants of agricultural land prices have received considerable attention in the literature, little is known about price formation on structured markets such as land auctions. This paper aims to empirically test theoretical predictions regarding price formation in land market auctions. The analysis is conducted for the case of Saxony-Anhalt, Germany, where state-owned land constitutes a significant share of the agricultural land market. The utilised data consists of public auction data provided by the Land-gesellschaft Sachsen-Anhalt (i.e. the rural development agency in Saxony-Anhalt), and covers approximately 700 calls for bids from 2003 to 2010, supplemented with regional and structural data. Spatial correlation of land prices is considered by applying a spatial econometrics approach. Our analysis shows that apart from land characteristics, the number of bidders and the share of non-agricultural investors have an impact on the land price.

Pay-to-bid auctions: To bid or not to bid

We propose an all-pay auction format with risk-loving bidders paying a constant fee each time they bid for an object whose monetary value is common knowledge among the bidders, and bidding fees are the only source of benefit for the seller. We characterize a unique symmetric sub-game perfect equilibrium, and further show that the expected revenue of the seller is independent of the number of bidders, decreasing in the sale price and bidding fee, and increasing in the value of the object.

Varying the number of bidders in the first-price sealed-bid auction: experimental evidence for the one-shot game

The paper reports experimental data on the behavior in the first-price sealed-bid auction for a varying number of bidders when values and bids are private information. This feedback-free design is proposed for the experimental test of the one-shot game situation. We consider both within-subjects and between-subjects variations. In line with the qualitative risk neutral Nash equilibrium prediction, the data show that bids increase in the number of bidders. However, in auctions involving a small number of bidders, average bids are above, and in auctions involving a larger number of bidders, average bids are below the risk neutral equilibrium prediction. The quartile analysis reveals that bidding behavior is not constant across the full value range for a given number of bidders. On the high value quartiles, however, the average bid–value ratio is not different from the risk neutral prediction. The behavior is different when the winning bid is revealed after each repetition.

The Duo-Item Bisection Auction

This paper proposes an iterative sealed-bid auction for selling multiple heterogeneous items to bidders interested in buying at most one item. It generalizes the single item bisection auction (Grigorieva et al. Econ Theory, 30:107---118, 2007) to the environment with multiple heterogeneous items. We focus on the case with two items for sale. We show that the auction elicits a minimal amount of information on preferences required to find the Vickrey---Clark---Groves outcome (Clarke, Public Choice, XI:17---33, 1971; Groves, Econometrica, 61:617---631, 1973; Vickrey, J Finance, 16:8---37, 1961), when there are two items for sale and an arbitrary number of bidders.

Approximately optimal auctions for correlated bidders

We consider the design of dominant strategy incentive compatible, revenue-maximizing auctions for an indivisible good, when bidders' values are drawn from a correlated distribution. For independent distributions, Myerson showed that the optimal auction for risk-neutral bidders remains incentive compatible regardless of bidders' risk attitudes. We show that, for correlated distributions, the same is true when only two bidders are involved, whereas for more bidders, randomization can generate strictly more revenue. However, for risk-neutral bidders, we show this gain is never more than a 53-factor.This is a consequence of two results of independent interest: (1) a polynomial-time derandomization of auctions for two bidders; (2) a polynomial-time computable deterministic auction that 53-approximates the optimal revenue extractable from risk-neutral bidders.Moreover, we give a polynomial-time algorithm to compute optimal auctions for a constant number of bidders, and for any number of bidders we give polynomial-time algorithms with approximation factors arbitrarily close to 32.

Arriving in Time: Estimation of English Auctions With a Stochastic Number of Bidders

We develop a new econometric approach for the estimation of second-price ascending-bid auctions with a stochastic number of bidders. Our empirical framework considers the arrival process of new bidders as well as the distribution of bidders’ valuations of objects being auctioned. By observing the timing of bidder arrival, the model is identified even when the number of potential bidders is stochastic and unknown. The relevance of our approach is illustrated with an empirical application using a unique dataset of art auctions on eBay. Our results suggest a higher impact of sellers’ reputation on bidders’ valuations than previously reported in cross-sectional studies but the impact of reputation on bidder arrival is largely insignificant. Interestingly, a seller’s reputation impacts not only the actions of the bidders but the actions of the seller as well. In particular, experience and a good reputation increase the probability of a seller posting items for sale on longer-lasting auctions, which we find increases the expected revenue for the seller. Supplementary materials for this article are available online.

Market Good Flexibility in Capacity Auctions

We consider the allocation of limited production capacity among several competing agents through auctions. Our focus is on the contribution of flexibility in market good design to effective capacity allocation. The application studied is a capacity allocation problem involving several agents, each with a job, and a facility owner. Each agent generates revenue by purchasing capacity and scheduling its job at the facility. Ascending auctions with various market good designs are compared. We introduce a new market good that provides greater flexibility than those previously considered in the literature. We allow ask prices to depend both on agents’ utility functions and on the number of bids at the previous round of the auction, in order to model and resolve resource conflicts. We develop both optimal and heuristic solution procedures for the winner determination problem. Our computational study shows that flexibility in market good design typically increases system value within auctions. A further increase is achieved if each agent is allowed to bid for multiple market goods at each round. On average, the multiple flexible market goods auction provides over 95% of the system value found by centralized planning.

Design of discrete Dutch auctions with an uncertain number of bidders

The focus of this paper is on Dutch auctions where the bidding prices are restricted to a finite set of values and the number of bidders follows a Poisson distribution. The goal is to determine what the discrete bid levels should be to maximize the auctioneer’s expected revenue, which is the same as the average selling price of the object under consideration. We take a new approach to the problem by formulating the descending-price competitive bidding process as a nonlinear program. The optimal solution indicates that the interval between two successive bids should be wider as the Dutch auction progresses. Moreover, the auctioneer’s maximum expected revenue increases with the number of bid levels to be set as well as the expected number of bidders. Numerical examples are provided to illustrate the key results from this study and their managerial implications are discussed.

Bidder optimal assignments for general utilities

We study the problem of matching bidders to items where each bidder i has general, strictly monotonic utility functions ui,j(pj) expressing his utility of being matched to item j at price pj. For this setting we prove that a bidder optimal outcome always exists, even when the utility functions are non-linear and non-continuous. We give sufficient conditions under which every mechanism that finds a bidder optimal outcome is incentive compatible. We also give a mechanism that finds a bidder optimal outcome if the conditions for incentive compatibility are satisfied. The running time of this mechanism is exponential in the number of items, but polynomial in the number of bidders.