1. Kagel & Levin: The Winner’s Curse and Public Information in Common Value Auctions Economics 328 Spring 2004

2. What is the Winner’s Curse? Roughly, auctions can be divided into three classes. In a private value auction, individuals values for the object being auctioned are determined independently of each other. Thus, knowing my own value tells me nothing about the value of the object for other bidders. In a common value auction, the object has an identical value for all bidders. As such, variance in bids can only arise from differences of opinion about what the common value of the object actually is. An affiliated value auction is an intermediate case. Like a private value auction, the value of the item being auctioned is different for each bidder. Unlike a private value auction, these values are positively correlated among bidders. Thus, knowing my value for the item tells me something about the value of the item for other bidders. In reality, most auctions are affiliated value auctions. For common and affiliated value auctions, we often assume that bidders are imperfectly informed about the item’s value. Rather than knowing the value, each bidder has a noisy estimate of its value. While the value is the same for all bidders, the estimates are all different.

3. What is the Winner’s Curse? The “winner’s curse” is a phenomenon that affects both common value auctions and affiliated value auctions. In such auctions, it has been frequently observed that winner bidders tend to overbid. This substantially reduces their winnings below the levels predicted by theory, often leading to losses rather than profits. In the words of Kagel and Levin, “You win, you lose money, and you curse.” The occurrence of the winner’s curse was first noted for OCS (off-shore oil) auctions. It has been claimed that the winner’s curse occurs in a number of other markets as well – book publication rights, free-agency for professional baseball, corporate takeovers, IPOs, and real estate.

4. What is the Winner’s Curse? The winner’s curse derives from a judgement error. Suppose that each person’s estimate of the value of the object being auctioned off is the true value plus a random number with an expected value of zero. As in Kagel and Levin, assume values are uniformly distributed and signals are uniformly distributed around the values. As in Kagel and Levin, let ε be the maximum distance of the signal from the value. Given your estimate x i, what should you be able to infer about the object’s true value x? If you have no additional information about the object, you should believe that the expected value of the object is equal to your signal (assuming you are not up against an endpoint of the distribution of values). E(x|x i ) = x i (eq. 1) However, you know something more than just your signal. Let a player’s bid function give the amount she bids as a function of her signal. Assume all individuals use the same bid function. Any reasonable bid function must be strictly increasing in the signal. It follows that the winning bidder will be the person who has the highest estimate of the object’s value. In calculating your expected profits from winning an auction, you should understand that winning the auction indicates that your signal overestimates the objects value. The correct formula for the object’s expected value is as follows: E(x|x i = x 1 ) = x i – ε(N – 1)/(N + 1) (eq. 2)

5. What is the Winner’s Curse Comparing (eq. 1) with (eq. 2), we see that an individual who fails to correct their bid for the information revealed by winning the auction will systematically overestimate the value of the object. The formula given in (eq. 2) gives an upper bound on what any rational (risk neutral or risk adverse) individual should ever bid. Any individual who is bidding above the value given by (eq. 2) will (on average) earn negative profits. A rational (risk neutral or risk adverse) bidder in a first price auction should in fact bid less than the value given by (eq. 2) for strategic reasons. If you win by bidding exactly the value given by (eq. 2), you will on average earn no profit. By cutting your bid you decrease your chance of winning the auction, but you actually earn something when you win. The Winner’s Curse is fundamentally a disequilibrium phenomenon. Rational individuals should never fall for the Winner’s Curse, and game theory almost always assumes that individuals will be rational.

6. What Can Experiments Teach Us About the Winner’s Curse? The possibility of the winner’s curse was originally noted not by economists, but rather by petroleum engineers studying OCS auctions (Capen, Clapp, & Campbell, 1971). While winner’s curses have been claimed for other settings, economists have often been skeptical about these claims for several reasons. The winner’s curse represents a fundamental violation of rationality. Theorists simply refused to accept that this was possible. This was particularly true in settings (like OCS auctions) where the stakes were high and the bidders were experienced. Field data tends to be inherently unreliable, making it difficult to confirm whether the winner’s curse actually took place. It is also very difficult using field data to dismiss alternative explanations for apparent overbidding. It has been argued that the claims of a winner’s curse in the oil industry were actually a mechanism for colluding at lower prices. The winner’s curse tends to be more prevalent in auctions with larger numbers of participants. However, this may reflect bidders being surprised by the number of bidders and therefore undercorrecting for the winner’s curse. Controlled experiments can allow us to definitively establish the existence of overbidding, eliminate alternative explanations for over bidding, and explore why individuals might make seemingly irrational bids.

7. Some Initial Experimental Evidence Bazerman and Samuelson (1983) performed the first experiments demonstrating the winner’s curse. They had subjects bid on a variety of objects (jars of pennies, jars of nickels, jars of large paper clips worth 4¢ a clip, etc.) all of which, unbeknownst to subjects, were worth $8. They also elicited estimates on the items’ values. The average value estimated by subjects was $5.13, but the average winning bid was $10.01. In other words, the average winner actually lost slightly more than two dollars. B&S note that their results rely in large part on a small number of subjects who repeatedly overbid. This suggests that the winner’s curse might be must smaller with more experienced subjects due to both learning and bankruptcy. The degree of uncertainty associated with the objects being auctioned was an uncontolled element in the B&S setup. This makes is hard to precisely define irrational behavior or equilibrium behavior.

8. Some Initial Experimental Evidence Kagel, Levin, Battalio, and Meyer (1989) studied the winner’s curse in auction with inexperienced subjects. These auctions carefully control the uncertainty associated with the value of the item being auctioned. Over the first nine periods of these auctions, average profits were - $2.57 as compared to average risk-neutral Nash equilibrium (RNNE) payoffs of $1.90. For only 17.2% of auctions did the winner earn positive profits. Unlike Bazerman and Samuelson, these results cannot be attributed to a small number of irrational subjects. Almost half of all subjects go bankrupt (41.1%) and 59.4% of all bids are above the maximum predicted by (eq. 2). The results of Kagel et al are quite robust and have been replicated in a number of different studies using a variety of treatments and subject pools (e.g. Lind and Plott, 1991; Goeree and Offerman, 2000).

9. Why Might the Early Results Not Be Useful for Understanding Field Data? There are several issues about the experiments reported above that might limit their usefulness in understanding field settings: The experiments reported above use inexperienced subjects. In reality, many auction participants are quite seasoned. As such, the winner’s curse observed in the lab might be an artifact of using naïve individuals who haven’t learned to stop making a stupid mistake. The observation that many subjects go bankrupt raises several difficult issues. First, it accentuates the concerns about experience. If most of the people who fall for the winner’s curse go broke quickly, they may not matter much in reality. Second, limited liability changes the game being played, giving subjects an incentive to overbid. The subject pool for most experiments consists of students (either undergraduates, MBA students, or (rarely) PhD students). This subject pool may not be very representative of the types of people participating in real world auctions.

10. Kagel & Levin: The Winner’s Curse and Public Information in Common Value Auctions Research Questions: This paper addresses three important issues: Does experience with first price common value auctions reduce (or even possibly eliminate) occurrence of the winner’s curse? If experience does reduce overbidding, can we say something about what subjects are learning? In particular, are they merely learning an action or is “theory absorption” taking place? The theory suggests that a larger correction for the winner’s curse is needed in settings where the number of bidders is large. Kagel and Levin explore the effects of varying the number of bidders. Auction research is largely driven by practical concerns. People either buying or selling items through auctions want to know how to make more money. One strong prediction of game theory for common value auctions is that giving subjects additional information about the object’s value will yield higher bids (and hence higher revenue for sellers). This is an equilibrium prediction – in equilibrium, no winner’s curse should occur. What is the effect on seller’s revenue of giving buyers additional information in settings where there may be a substantial winner’s curse?

11. Kagel & Levin: The Winner’s Curse and Public Information in Common Value Auctions For all of the auctions in this paper, the value x was distributed uniformly over a range [x -,x + ] that was common knowledge. (Note that I had to change their notation.) After x is drawn, each subject then receives a signal about the value that is distributed uniformly over the interval [x – ε,x+ε]. Once again, the value of ε is common knowledge. As a theoretical benchmark, Kagel and Levin use the RNNE. For the range of estimates that aren’t against the ends of the distribution, the RNNE bid function is given below. The final term goes to zero rapidly as we depart the lower end of the distribution, so normally a bidder should bid only slightly above the minimum possible value the object could have given their signal. As N gets large, the expected winning bid becomes very close to the object’s true value and the expected profits of the winner become very close to zero. The RNNE is making a very strong assumption that all individuals are risk neutral. With risk adverse (or risk loving) individuals it becomes very difficult to pin down precisely what equilibrium predicts. However, as long as individuals aren’t risk loving, we should never see bids in equilibrium above the benchmark given by (eq. 2).

12. Kagel & Levin: The Winner’s Curse and Public Information in Common Value Auctions For a number of the auctions subjects are given a piece of public information about the value of the object. Most frequently, this piece of information is the lowest estimate that has been drawn. In the RNNE, provision with this information (or most any public information) has the effect of increasing bids and decreasing earnings (on average) of the winning bidder. More interestingly, with public information the expected value of the item subject to knowing you have the highest bid is identical to the expected value without conditioning on whether you win the auction. In other words, falling for the winner’s curse will no longer have any impact on the bid function!

13. Experimental Design All subjects had previously experienced a full session with an auction where the winner’s curse had occurred. These previous experiences differed both in terms of how institutions (first vs. second) price and in the number of bidders. They tried to avoid subjects who had gone bankrupt, although some subjects who had gone bankrupt slowly were included. The number of subjects in each auction was varied across session. Some of this variation was accidental (due to bankruptcies) but eventually they came up with methods to hold the number of bidders fixed. For some sessions, the number of bidders was systematically increased from a small number (4 bidders) to a larger number (6 or 7) bidders. The ranges of possible values and the preciseness of signals were varied across sessions.

14. Kagel & Levin: The Winner’s Curse and Public Information in Common Value Auctions Kagel and Levin list a number of initial hypotheses that they plan to test. Many of these can be viewed as “null” hypotheses – straw men that they expected to be knocked down. Behavior in auctions with only private information will be consistent with the RNNE. The bidder with the highest estimate will usually win the auction, but will not suffer from the winner’s curse. Public information (announcing the low estimate) will raise the seller’s revenue, preferably by the amount predicted by RNNE. The number of bidder participating in an auction will not affect the ability of high bidders to avoid the winner’s curse and will not eliminate the positive effects of public information on seller’s revenues. Overbidding might be due to the judgement error described above or might be due to subjects failing to recognize the strategic implications of the auction. In settings where judgement errors should play little role in bidding, RNNE should do a good job of predicting subject’s behavior (suggesting that the judgement error is responsible for the observed overbidding).

15. Results Under private information, there was pervasive occurrence of overbidding by experienced subjects (albeit with lower frequency than in the inexperienced bidder sessions). The magnitude of the overbidding was consistently higher with a large number of subjects. This was true even in the sessions where subjects first played an auction with only 4 bidders. While average profits were positive for sessions with small numbers of bidders, profits are almost always significantly smaller than the RNNE prediction. Previous experience with auctions with small numbers of bidders did not help subjects avoid overbidding in auctions with large numbers of subjects. The proportion of overbidding increased from 21.3% to 52.4% (session averages), not much different from the 55.8% proportion of ovebidding observed in sessions where subjects played with large numbers of subjects throughout. This suggests that changes in behavior for experienced subjects do not reflect theory absorption.

16. Results Public information consistently led to smaller gains in revenue than predicted by RNNE. Strikingly, the revenue effect was typically negative for settings in which the winner’s curse was present most strongly (without public information). These results suggest that the cause of the winner’s curse is a failure to correctly account for the information revealed by winning the auction, not a failure to grasp the strategic aspects of the game. From a practical point of view, these results suggest that releasing public information about an item’s value will not benefit the seller in settings where bidders are inexperienced or there are a large number of bidders (e.g. settings where the winner’s curse is particularly likely).

17. Comparisons with the OCS Auctions A critical question in thinking about the experimental results is what (if any) resemblance they bear to results in the field. Examining the results of OCS auctions, we find that the results of the “real” auctions are consistent with what we would expect given the experimental results. A critical distinction is made between “wildcat” leases where no drilling data exists that would indicate potential profitability and “drainage” leases where drilling data from adjacent tracts suggests the presence of oil. It is public information that drainage tracts are more likely have oil, although precisely how much more is private information. According to Nash equilibrium, the rate of return for non-neighbors (e.g. those without private information) should be lower for drainage tracts than for wildcat tracts. In fact, rates of returns are higher for both neighbors (88.6%) and non-neighbors (56.2%). This result is consistent with the experimental results – the public information reduces the winner’s curse enough to increase the non-neighbor’s profits, even though they are at an informational disadvantage compared to the neighbors. Alternative explanations for why non-neighbors might earn greater returns on drainage tracts are not consistent with the data.

18. Some Further Research Lind and Plott (1991) and Cox, Dinkin, and Smith (1998) have studied whether the winner’s curse results observed in the laboratory can be attributed to limited liability. Kagel and Levin (1991) also reanalyzed their earlier data to examine the effects of limited liability. The studies all agree that limited liability effects are not at cause for the winner’s curse. Dyer, Kagel, and Levin (1989) studied an experiment where subjects bid on construction contracts. The compare the behavior of undergraduates with the behavior of construction company executives. They find that construction executives are no better than students at avoiding the winners curse. Dyer and Kagel (1996) then did a detailed study of bidding on real world projects by construction companies to see how these companies could possibly survive if they were falling for the winner’s curse. Two explanations emerge: (1) There are important institutional differences between the real world and the laboratory that mitigate the winner’s curse. In particular, in the real world it is usually possible to adjust a low bid upwards after the fact. It is in nobody’s best interest for the contractor to make such a bad bid that they either go bankrupt or walk away from the project. (2) There is a great deal of situation-specific learning. Contractors have developed a number of rules of thumb for bidding that have the unintended effect of mitigating the winner’s curse.