Profit Maximizing in Auctions of Public Goods

A profit-maximizing auctioneer can provide a public good to a group of agents. Each group member has a private value for the good being provided to the group. We investigate an auction mechanism where the auctioneer provides the good to the group only if the sum of their bids exceeds a reserve price declared previously by the auctioneer. For the two-bidder case with private values drawn from a uniform distribution we characterize the continuously differentiable symmetric equilibrium bidding functions for the agents, and we find the optimal reserve price for the auctioneer when such functions are used by the bidders. We also examine another interesting family of equilibrium bidding functions for this case, with a discrete number of possible bids, and show the relation (in the limit) to the differentiable bidding functions.     

Procurement auctions with ex-ante endogenous bribery

Corruption is a prevalent phenomenon in various procurement auctions. This paper explores a pattern of bribery between an auctioneer and a favored bidder, and also investigates the regulation scheme of buyer. In the model, the favored bidder is allowed to submit two bids simultaneously with the advantageous one to be announced; auctioneer decides the share of the difference between two bids which is the bribe transfer. The analysis shows that, the favored bidder does not participate in the corruption if his cost exceeds a threshold; otherwise he submits two bids whose difference is decreasing in the share. The corruption benefits both the auctioneer and the favored bidder but harms other bidders. The bribery endogenously leads to allocation inefficiency with a probability decreasing in the bribe share. Specifically, with two uniformly distributed bidders, we examine how the auctioneer optimizes the bribe share and how the buyer regulates the corruption. We find that, by driving the auctioneer to charge a higher bribe share that is less attractive for the favored bidder, severer regulation tends to reduce the probability of corruption. A buyer who adopts extremely severe regulation can exclude the corruption and achieve maximum social welfare, while a buyer who aims to maximize his own profit should tolerate some degree of the corruption.     

When less is more: Rationing and rent dissipation in stochastic contests

This paper shows how to maximize revenue when a contest is noisy. We consider a case where two or more contestants bid for a prize in a stochastic contest where all bidders value the prize equally. We show that, whenever a Tullock contest yields under-dissipation, the auctioneer?s revenue can be increased by optimally fixing the number of tickets. In particular, in a stochastic contest with proportional probabilities, it is possible to obtain (almost) full rent dissipation. We test this hypothesis with a laboratory experiment. The results indicate that, as predicted, revenue is significantly higher in a lottery with rationing than in a standard lottery. On the other hand, an alternative rationing mechanism that does not limit total expenditures fails to increase revenue relative to a standard lottery.     

Communication,competition and social gift exchange in an auction for public good provision

Reverse auctions are an established policy instrument for allocating conservation contracts. While the auction mechanism has been the subject of a number of studies, less attention has been paid to the post-bidding contract phase. As contracts involving natural resource management are usually incomplete, trust becomes crucial for the effectiveness of the programme. We test the effect of communication between auctioneer and bidders on bidding behaviour and contract fulfilment using experimental economics. We combine a repeated reverse auction with an effort-level game and use a bilateral chatting tool as treatment variable. Without communication, auctioneers tended to select the lowest-priced bidders, who invested substantially less than the socially optimal level of effort when fulfilling their contract to provide the public good. Relational contracting proved important, with effort levels and profits tending to be higher when auctioneers and bidders entered into consecutive contract relationships. In the communication treatment there was no evidence of price competition, as auctioneers were more likely to accept high-priced bids. However, an overall higher price level did not lead to efficiency losses, since contractors realised higher effort levels in return, establishing a ‘social gift exchange’. Our results demonstrate the importance of trust-based relationships between the auctioneering institution and landholders.     

BUNDLING IN AUCTIONS WITH NON‐LINEAR VALUATIONS*

We examine when a revenue‐maximising auctioneer prefers to auction a homogenous product in one bundle (a single‐object auction) than to sell the item in two or more shares. When the items are super‐additive the auctioneer always prefers a single‐object auction. When the product valuations are sub‐additive, the auctioneer is more likely to choose a share auction when there are a large number of potential bidders. When there are a small number of bidders the auctioneer will tend to prefer a single‐object auction.     

Laboratory Testbeds and Non-Market Valuation: The Case of Bidding Behavior in a Second-Price Auction with an Outside Option

Researchers now use the lab to examine the behavioral underpinnings of valuation before the field application which some argue has less experimental control. But lab valuation work raises its own set of concerns when it uses private goods to explore non-market valuation behavior because private goods have substitutes often unaccounted for in the lab. Therefore, the lab as a tool to testbed field valuation work may be limited. Herein we design an induced valuation experiment to explore bidding behavior in a second-price auction with an outside option that is a perfect substitute for the auction commodity. Theory predicts that rational bidders will consider the prices of outside options when formulating bidding strategies, and will reduce their bids whenever their resale value exceeds the price of the outside option. Our results suggest that bidders account for outside options when formulating bids with behavior following comparative static predictions. In addition, we provide evidence concerning hypothetical versus actual behavior with induced values – the data suggesting a hypothetical bias in the level of bids but not in bid shaving.     

Do preferences for charitable giving help auctioneers?

Preferences for charitable giving in auctions can be modeled by assuming that bidders receive additional utility proportional to the revenue raised by an auctioneer. The theory of bidding in the presence of such preferences results in a very counterintuitive prediction which is that, in many cases, bidders having preferences for charitable giving does not lead to a substantial revenue advantage for an auctioneer. We test this theory and this prediction with a series of experiments. In one experiment we induce charitable preferences exactly as specified in the model to see if bidders respond to them as predicted. We find that they do. We then conduct a second experiment in which the revenue from the auctions is donated to actual charities to verify the robustness of the prediction when charitable preferences are generated by a more natural source and find again that the theoretical prediction holds: even strong charitable preferences do not result in substantial revenue increases to the auctioneer.     

Common Value Auctions with Default: An Experimental Approach

This paper examines a common value auction in which bidder default is explicitly allowed. The lack of contractual enforcement has implications for the formation of bids as well as the revenue properties of the auction. Using a common value procurement auction, we explore these implications in an experimental setting. Our results show that bidders are more aggressive when default is allowed. A theoretical result shows that allowing default can actually be in the best interest of the auctioneer. Experimental evidence, however, indicates that this result does not hold true in practice. One possible reason for this discrepancy is that the data in our experiments is consistent with winner's curse behavior.     

Endogenous entry and self-selection in private value auctions: An experimental study

This paper presents the results of an experimental study of endogenous entry in first-price independent private value auctions. N potential bidders simultaneously decide whether to participate in an auction or receive a known outside option. In the second stage, entrants submit bids after learning their own private values and the number of entrants. An equilibrium model of heterogeneous risk averse bidders implies a self-selection effect, where bidding in the auction is lower with endogenous entry because only less risk averse bidders enter. This effect is confirmed by the experiment. We also observe excessive entry relative to the theoretical model.     

Auctions with endogenous participation and an uncertain number of bidders: experimental evidence

Attracting bidders to an auction is a key factor in determining revenue. We experimentally investigate entry and bidding behavior in first-price and English clock auctions to determine the revenue implications of entry. Potential bidders observe their value and then decide whether or not to incur a cost to enter. We also vary whether or not bidders are informed regarding the number of entrants prior to placing their bids. Revenue equivalence is predicted in all four environments. We find that, regardless of whether or not bidders are informed, first-price auctions generate more revenue than English clock auctions. Within a given auction format, the effect of informing bidders differs. In first-price auctions, revenue is higher when bidders are informed, while the opposite is true in English clock auctions. The optimal choice for an auction designer who wishes to maximize revenue is a first-price auction with uninformed bidders.     

eBay’s proxy bidding: A license to shill

We introduce a bidding strategy which allows the seller to extract the full surplus of the high bidder in eBay auctions. We call this a “Discover-and-Stop” bidding strategy and estimate that 1.39 percent of all bids in eBay auctions are placed by sellers (or accomplices) who execute this strategy. We argue that this kind of shill bidding is unnecessarily effective due to eBay’s proxy system and the predictability of other bidders’ bids. We also model eBay auctions with shill bidding and find that, in equilibrium, eBay’s profits are higher with shilling than without it. Finally, to determine whether bidders have an incentive to bid on their own items, we mimic the bidding behavior of shill bidders in actual eBay auctions and find some evidence of the strategy’s success.     

Multiple-unit English auctions

This paper examines the outcome of an ascending-price multiple-unit auction. Two bidders, facing continuous, downward-sloping demand functions, participate in the auction of some divisible objects. The auctioneer starts the process by announcing an initial price and asking both bidders to submit sealed-bids of desired quantities. The auctioneer increases the price until the total amount bid for is less than the total supply. We compute the outcome of this auction game under full information and suggest that this mechanism may not maximize expected revenue.     

Revealing information in auctions: the allocation effect

When there are two bidders, releasing independent information in an English auction with private values makes the seller worse off. However, this is no longer true with more bidders: when there is enough competition, revelation benefits the auctioneer. In three examples the dividing case is shown to be three bidders. This allocation effect applies to other standard auctions and parallels the bundling decision in a multi-unit auction. I would like to thank Jeremy Bulow, Willie Fuchs, Paul Klemperer, Rob McMillan, Phil Reny, Jeff Zwiebel and especially Andy Skrzypacz. I also grateful to two referees and an Associate Editor for a number of helpful comments.     

Unraveling in first-price auction

In a private values first-price auction with random number of bidders, the auctioneer has to decide whether to announce or not the actual number of bidders. If the auctioneer cannot commit to any particular announcement policy, then he would like to reveal when the number of bidders is high in order to increase bidding competition. By the same logic, the auctioneer should like to conceal if the number turns out to be small. When bidders' types are independent, full revelation by the auctioneer is shown to be a unique equilibrium with ‘skeptical belief’ as the unique equilibrium belief.     

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.     

Testing the continuity of individual bid density functions: Some further results

This brief paper analyzes the bidding behavior in OCS oil auctions of six individual bidders (using solo bids only) and of a consortium bidder over the period 1963–1979. Included are bidders that bid over the entire period, one that bids for only a short time at the beginning, and one that first makes such bids in 1970. Our findings strongly support those reported in an earlier paper for five bidders and a brief, three-auction sample period: bidders commonly utilize multiple bids of single dollar values within a given auction. The strength of the present results – for three of the seven bidders, over 30% of the bids made fell into this category – further buttresses our conjecture that the use of continuous bid functions is inappropriate for modelling offshore oil lease auctions.     

Optimistic irrationality and overbidding in private value auctions

Bidding one’s value in a second-price, private-value auction is a weakly dominant solution (Vickrey in J Finance 16(1):8–37, 1961), but repeated experimental studies find more overbidding than underbidding. We propose a model of optimistically irrational bidders who understand that there are possible gains and losses associated with higher bids but who may overestimate the additional probability of winning and/or underestimate the potential losses when bidding above value. These bidders may fail to discover the dominant strategy—despite the fact that the dominant strategy only requires rationality from bidders—but respond in a common sense way to out-of-equilibrium outcomes. By varying the monetary consequences of losing money in experimental auctions we observe more overbidding when the cost to losing money is low, and less overbidding when the cost is high. Our findings lend themselves to models in which less than fully rational bidders respond systematically to out-of-equilibrium incentives, and we find that our model better fits the effects of our manipulations than most of the existing models we consider.     

All equilibria of the multi-unit Vickrey auction

This paper completely characterizes the set of equilibria of the Vickrey auction for multiple identical units when buyers have non-increasing marginal valuations and there are at least three potential buyers. There are two types of equilibria: In the first class of equilibria there are positive bids below the maximum valuation. In this class, above a threshold value all bidders bid truthfully on all units. One of the bidders bids at the threshold for any unit for which his valuation is below the threshold; the other bidders bid zero in this range. In the second class of equilibria there are as many bids at or above the maximum valuation as there are units. The allocation of these bids is arbitrary across bidders. All the remaining bids equal zero. With any positive reserve price equilibrium becomes unique: Bidders bid truthfully on all units for which their valuation exceeds the reserve price.     

Bid Functions in Auctions and Fair Division Games: Experimental Evidence

In auctions a seller offers a commodity for sale and collects the revenue. In fair division games the object is collectively owned by the group of bidders who equally share the revenue. We run an experiment in which the participants face four types of allocation games (auctions and fair division game under two price rules, first– versus second–price rule). We collect entire bid functions rather than bids for single values and investigate price and efficiency of the different trading institutions. We find that the first–price auction is more efficient than the second–price auction, whereas economic rationality assuming heterogeneous bidders suggests the opposite. Furthermore, we study the structure of individual bid functions.     

An experimental study of precautionary bidding

Auctions often involve goods exhibiting a common-knowledge ex-post risk. In such auctions, precautionary bidding predicts that under expected utility, DARA bidders reduce their bids by more than the appropriate risk premium. Because the degree of riskiness of an auctioned good and bidders׳ levels of risk aversion are difficult to observe in field settings, we conduct experimental auctions that allow us to identify the precautionary premium directly. We find strong evidence for precautionary bidding. The effect is robust to changes in experimental design features. Our experiment provides the first empirical demonstration of precautionary motives in a strategic setting.