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First-price common value auctions: bidder behavior and the "winner's curse."


Experimental auction markets are characterized by a strong

winner's curse in early auction periods as high bidders consistently

lose money, failing to account for the adverse selection problem

inherent in winning the auction. With experience and bankruptcy

on the part of the worst offenders, subjects earn positive average

profits, but these are far below Nash equilibrium predictions as a

sizable minority of bids exceed the expected value of the item

conditional on having the highest estimate of value. Individual bidding

behavior is explored to identify the mechanism whereby market

outcomes no longer display the worst effects of the winner's curse.


Numerous occurrences of the winner's curse have been reported in bidding for items of uncertain value, resulting in below normal or even negative average profits for bidders. The winner's curse results from bidders' failure to account for the adverse selection problem inherent in winning auctions for items of uncertain value. Capen, Clapp, and Campbell [1971] claim that the winner's curse resulted in low profits for oil companies in the 1960s in bidding on offshore oil and gas leases. Regarding corporate takeovers and mergers, Roll [1986] proposes a hubris hypothesis: acquiring firms generally fall prey to the winner's curse, paying too much on average for their targets. He claims that from the samples he has observed, the hubris hypothesis explains merger data as well as tax factors, synergy, or inefficient target management. Cassing and Douglas [1980] find that many baseball players in the free agency market have been overpaid on account of the winner's curse, and Dessauer [1981] reports a similar finding of overbidding in auctions for the book publishing rights. Based on these occurrences, it appears that many agents are not fully cognizant of the intricacies involved with bidding on alternatives that have uncertain worth.

The winner's curse results from the fact that although bidders may hold unbiased estimates of the auctioned item's value, this estimate can be overly optimistic given that participants' bids are influenced by their estimates of value. In other words, the winner's curse results from an adverse selection problem that bidders fail to account for fully in submitting their bids. The existence of a winner's curse implies a breakdown of rational expectations on the bidder's part (as discussed by Milgrom [1981]) and identifies a market that is out of equilibrium.

A winner's curse need not result from bidding on items with uncertain value provided proper adjustments are made. One adjustment to the adverse selection problem is to deflate the expected value of the item (and hence the bid) before any action is taken. For example, Cox and Isaac [1984] show that agents who maximize expected utility will revise their expectations downward and submit bids that are strictly less than the expected value conditional on the event of winning. When agents behave in this fashion, a winner's curse does not result in the sense of bidders paying more on average than the items are worth.

This paper focuses on sealed-bid auctions for objects of uncertain value, a market institution for which theoretical predictions and empirical evidence concerning a winner's curse are mixed. Current theoretical development excludes the possibility of bidders paying more on average than the items are worth; yet some empirical evidence in the sale of oil tracts, as seen in Capen, Clapp, and Campbell [1971], Lohrenz and Dougherty [1983], and Mead, Moseidjord, and Sorenson [1983], suggests that the winner's curse may be present. A series of experiments is designed and conducted in order to answer the following empirical research questions: Does the winner's curse exist in this auction framework; and if it does, what is its duration, its relation to agent experience in the market, and its breadth of impact across agents?

The paper is organized in the following manner. The structure of the auctions is given in section II. Section III contains a definition of the winner's curse and defines the risk-neutral Nash equilibrium for the auction market. Experimental results are presented in section IV and a summary and conclusions are given in section V.


Each experiment consisted of a series of auction periods in which a single unit of a commodity was awarded to the high bidder using a first-price sealed-bid procedure. The high bidder earned a profit equal to the value of the item less his bid; all other bidders earned zero profits. The value of the item, V, was not known at the time bids were placed.

V was drawn randomly from a uniform distribution on (VL, VH). Each bidder received a private information signal, si, randomly drawn from a uniform distribution on (V-Epsilom, V+Epsilom). VL, VH, Epsilom, and the underlying distributions were common knowledge. Given si, Epsilom, VL, and VH, the maximum and minimum possible values for the item were min (si + E, VH) and max (si - Epsilom, VL) respectively. In experiments 4 to 11 these bounds were computed for each subject and reported along with si.

Examples of the signal values relative to a given V were provided and discussed. Subjects were told that "over a sufficiently long series of auctions, the difference between your private information signal and the value of the commodity will average out to zero (or very close to it); but for a given auction, your private information signal can be above or below the value of the item. That's the nature of the random selection process generating the signals."

After all bids were tendered, V was announced, subjects' profits were calculated, and balances were updated. In experiments 1 and 4 to 9, the top three bids were posted. All bids were posted in experiments 2, 3, 10, and 11, with the private information signals posted, together with the bids in 10 and 11.

To cover the possibility of losses, subjects were given starting balances of $8.00 in experiments 1 to 9 and $10.00 in 10 and 11. Positive profits were added to this balance, and losses subtracted from it. If a balance dropped to zero or less, a subject was no longer permitted to bid, was paid his $4.00 participation fee, and was free to leave the experiment. (At the start of each auction period subjects were notified of the number of bidders remaining in the market.) Auction survivors were paid their end-of-experiment balance plus their participation fee in cash.

Since elements of the winner's curse were anticipated, starting balances were set so that (i) a subject could commit at least one gross overbid,(1) learn from his mistake, and still have a large enough balance to continue safely in the auction; and (ii) a conservative bidder who was shut out from winning by overly aggressive counterparts would earn a reasonable rate of return for participating in the experiment. The balance levels employed were successful on both counts, as losses averaged less than $3.00 in the early auction periods, and the majority of subjects were eager to participate in additional auctions.

Each of the experiments started with either two or three dry runs in which outcomes did not count toward players' final earnings. The analysis of the data begins with the first market period involving cash payoffs.(2) Table I summarizes the experimental treatment conditions.


The equilibrium bidding concept of choice in much of the recent literature is that of a symmetric risk-neutral Nash equilibrium (hereafter SRNNE), as found in Wilson [1977] and Milgrom and Weber [1982]. Restricting the analysis to signal values in the interval VL + Epsilom is less than or minus Si less than or minus VH - Epsilom yields the SRNNE bid function


Experimental Conditions
 Subject Population
 (Number Starting Market
Experiment Experiment) Period E VL VH
 1 U. of Houston 1-5 $ 5 $10 $30
 Undergraduates 6-13 $10 $20 $60
 2 U. of Houston 1-5 $ 5 $10 $30
 MBA students 6-10 $10 $20 $60
 (6) 11-18 $15 $20 $80
 3 U. of Houston 1-3 $ 5 $10 $30
 MBA Students 4-8, 15-20 $10 $20 $60
 (8) 9-14 $15 $20 $80
 4&5 Texas A&M 1-6 $ 5 $15 $100
 Undergraduates 7-18 $12 $15 $100
 6&7 Texas A&M 1-6 $ 5 $15 $100
 Undergraduates 7-20 $12 $15 $100
 8&9 Texas A&M 1-6 $ 5 $15 $100
 Undergraduates 7-16 $12 $15 $100
 10 U. of Houston 1-6 $ 6 $25 $225
 Law Students 7-16, 23-25 $12 $25 $225
 (5) 17-22 $18 $25 $225
 11 U. of Houston 1-6 $ 6 $25 $225
 Undergraduates 7-16 $12 $25 $225
 (8)(a) 17-26 $24 $25 $225

(a)This experiment employed six bidders with two "substitutes" to replace bankruptcies. All subjects had participated in a first-price private value auction.

b(si) = si - Epsilon + Y

(1) where Y=(2Epsilon/N + 1) exp {-(N/2Epsilon)[si-(VL+Epsilon)]} and N equals the number of bidders. Y contains a negative exponential which rapidly becomes negligible as si increases beyond VL + Epsilon.(3) Ignoring the exponential term in the bid function expected profit for the high bidder is positive and equal to 2Epsilon/N + 1.

In a symmetric Nash equilibrium, bidders properly account for the adverse selection involved in winning the auction and discount their bids accordingly. A proper response requires agents to deflate E(V~si), the expected value of the item conditional on the player's private information signal. This naive expectation does not adjust for the adverse selection problem. Instead, agents must focus on E(V~Si=s1), the expected value of the item conditional on having the highest signal value among all other signals. As noted by Cox and Isaac [1984], agents can avoid the winner's curse by entering bids that are strictly less than the posterior expected value, E(V~Si=s1).(4)

One can find a number of alternative definitions of the winner's curse in the literature, as illustrated by Cox and Isaac [1984]. This paper uses the following: An auction market exhibits a winner's curse wherever (i) there is a strong positive rank-order correlation between bids (bi) and private information signals (si), and (ii) individual bids exceed E(V~Si=s1). This definition is designed to characterize the mechanism underlying the market outcomes; namely, that the winner's curse results from an adverse selection problem in that (i) bidders generally win the auction when they hold the highest, or one of the highest, signals, and (ii) they fail to account for this fact in formulating their bids.

Condition (i) of this definition will hold for the Nash equilibrium bidding model as well as for the winner's curse, and simply guarantees the existence of an adverse selection. Bidding in excess of E(V~Si=s1) provides a readily measurable indication of subjects' failure to deflate the item's expected value accurately. A perfect rank-order correlation coefficient between bids and signals, in conjunction with only the high bidder bidding in excess of E(V/Si=s1), is sufficient to insure negative profits. Further, even with zero correlation between bids and signals, all subjects bidding in excess of E(V~Si=s1) is sufficient to insure negative average profits. As such, a reasonably high positive rank-order correlation between bids and signals, together with a reasonably large number of agents bidding in excess of E(V~Si=s1), is likely to generate ex ante negative expected profits for the high bidder in the auction.

It has been argued that since losses were limited to cash balances, rational agents would bid more aggressively than the SRNNE bid function. Although there are cases where limited liability can induce rational agents to accept gambles they would otherwise reject, for this particular experimental design limited liability for losses should have a negligible effect on rational bidders. A bid of si-E is close to the SRNNE and insures bidders against any possibility of losses. Consequently, a bidder deciding whether or not to bid Delta more than the SRNNE is fully liable for losses provided Delta is less than or equal to his cash value.(5) If a rational response to rival behavior is defined as a bid somewhere between the SRNNE bid (equation (1)) and E(V~Si=s1), then starting cash balances were over five times larger than the maximum expected loss associated with such a bid.(6)

With time and losses, cash balances can diminish to the point where limited liability may impact on rational bidding.(7) However, with bankruptcy bidders must exit the auction, losing potential profit opportunities in later auction periods. This may promote lower bidding with low cash balances. We test for the net impact of these two opposing forces in reporting the experimental results.


Market Outcomes

Data from experiments 2, 4, 5, and 10 provide representative time series of market outcomes. Each of the four figures shows the actual profits earned for each market period (cross marks) along with the profits that would have been earned if everyone had bid according to the SRNNE model (closed circles). At the top of each figure the rank-order correlation coefficient is shown between the bids and signals by market period.

With the sole exception of experiment 9, high bidders earn negative average profits in the early auction periods. The full extent of these losses is captured in Table II where profits earned in the first nine auction periods are reported (the experiments lasted an average of seventeen to eighteen periods, not including trial runs). Negative profits were earned in approximately 80 percent of these periods, with losses averaging $2.57 per period, compared to positive expected profits of $1.90 per period that would have been earned under the SRNNE model.(8) The t-statistics shown in Table II indicate that the hypothesis of nonnegative profits can be rejected at the 5 percent significance level in seven of the eleven experiments. Treating the eleven experiments as independent repeated trials and combining the t-test outcomes as discussed in Maddala [1977, 47-48], the hypothesis of zero or positive profits is soundly rejected (X raised to 2 = 83.9, 22d.f., p<.001).

Examining rank-order correlation coefficients between bids and signals for these periods shows that the correlation coefficient exceeded .5 in about 80 percent of all auction periods. Further, approximately 60 percent of all bids exceeded E(V~Si=s1). These two statistics indicate that the losses observed are rooted in an adverse selection process resulting in bidder failure to discount bids sufficiently. Similar conclusions are reached on the basis of the frequency with which the high signal holder won the auction, approximately 60 percent of all cases, in conjunction with the frequency with which the high bidder's bid exceeded E(V~Si=s1), almost 82 percent of all auction periods! Note finally that the more complete information conditions of experiments 10 and 11, where individual bids were posted together with signal values in all periods, did nothing to attenuate the overly aggressive bidding. Thus the results cannot be attributed to bidder ignorance of rivals' strategies relative to their signal values. The winner's curse seems to be alive and well and present in our early auction market periods!(9)


Profits and Bidding in First Nine Auction Periods
 Percent of
 Percentage Average Predicted
 Auctions Won
 of Auctions Actual Profits Percentage
 by High
 with Positive Profits Under SRNNE of All Bids
Experiment Profits (t-statistic) (Sm)(a) bi> E(V\ Si=s1)
1 0.0 -4.83 .72 63.4
 (-3.62)(**) (.21)
2 33.3 -2.19 2.18 51.9
 (-1.66) (1.02)
3 11.1 -6.57 1.12 74.6
 (-2.80)(*) (1.19)
4 11.1 -2.26 .85 41.8
 (-3.04)(**) (.43)
5 33.3 -.84 3.60 48.1
 (-1.00) (1.29)
6 22.2 -2.65 2.55 67.3
 (-1.53) (1.17)
7 11.1 -2.04 .57 58.5
 (-2.75)(*) (.25)
8 11.1 -1.40 1.59 51.9
 (-2.43)(*) (.34)
9 44.4 .32 2.37 35.2
 (.30) (.76)
10 0.0 -2.78 3.53 77.2
 (-3.65)(**) (.74)
11 11.1 -3.05 1.82 81.5
 (-3.53)(**) (.29)
Average(c) 17.2 -2.57 1.90 59.4
 Percent of
Percentage of Subjects
High Bids Going
b1>E(V~Si=s1) Bankrupt(b)
100.0 50.0
 88.9 16.7
 88.9 62.5
 55.6 16.7
 88.9 50.0
100.0 33.3
 66.7 50.0
 55.6 16.7
 66.7 16.7
100.0 20.0
 88.9 37.5
 81.8 41.1

(a)SM = standard error of mean. (b)percentage over all market periods in experiment. (c)weighted by number of auctions in each experiment. (*)statistically significant at the 5 percent level, two-tailed test. (**)statistically significant at the 1 percent level, two-tailed test.

To capture the effects of experience on market outcomes, Table III brings together data for the last five auction periods for the experiments. Player earnings clearly improved with experience, as positive profits were earned in 57.4 percent of the last five auction periods (compared to 17.2 percent in the first nine auction periods). Positive average profits were earned in eight of eleven experiments, averaging $0.49 per auction period across experiments. Thus, the null hypothesis of zero or nonnegative profits can no longer be rejected.

While the profit data indicate that the worst effects of the winner's curse had been eliminated, strong traces still remained as 74.1 percent of all auctions were won by the highest signal holder, indicating strong adverse selection forces at work; while in 35.2 percent of all auctions the high bid exceeded E(V~Si = s1), indicating a failure to account for the adverse selection problem. While this represents a sharp reduction in the frequency with which the highest bid exceeded E(V~Si = s1), (compared to the first nine auction periods), it is still a sizable percentage. Although average profits were positive, they were only 10.2 percent of profits predicted under the SRNNE. Further, in only two of eleven experiments profits amounted to 50 percent or more of the profit opportunities as measured by the SRNNE standard. This poor profit performance relative to the SRNNE standard is directly attributable to the winner's curse, given the relative frequency with which the winning bid exceeded E(V~Si = s1).(10)

Individual Bidding Behavior Over Time Learning. Tables II and III indicate quite clearly that learning takes place at the market level as average profits turn from negative to positive and there is a sharp reduction in the frequency with which the high bid exceeds E(V~Si = s1). Given the closed entry conditions of the experiments, a number of different scenarios could underlie this result. First, the survivors, those players who remained solvent and were bidding in the last five market periods, began bidding just like those who went bankrupt. Only they were lucky in the sense that they received relatively low signal values and did


Profits and Bidding in Last Five Auction Periods
 Percentage Average Average
 of Auctions Actual Predicted Profits
 Percentage of
 With Positive Profits Profits under a Percentage
 All Bids
Experiment Profits (t-statistic) SRNNE (SM)(a) of the SRNNE
 bi>E(V\Si = s1)
 1 0.0 -1.82 5.15 -35.3
 (-2.54) (1.11)
 2 60.0 1.51 6.59 22.9
 (1.16) (2.04)
 3 60.0 1.74 3.16 55.1
 (1.02) (2.75)
 4 100.0 3.08 4.94 62.3
 (3.55) (1.77)
 5 60.0 .77 2.79 27.6
 (.45) (1.46)
 6 40.0 .22 3.39 6.5
 (.08) (1.86)
 7 80.0 1.29 3.15 41.0
 (1.01) (1.15)
 8 40.0 -4.12 1.87 -220.3
 (-1.42) (1.32)
 9 40.0 -1.52 3.45 -44.1
 (-.47) (2.19)
 10 80.0 2.62 11.64 22.5
 (1.38) (3.99)
 11 60.0 1.17 6.99 16.7
 (.64) (.76)
Average(b) 57.4 .49 4.82 10.2

Percentage of Auctions Won
 by High Percentage of
 Signal High Bids
 Holder b1>E(V\Si=s1)
 75.0 100.0
 80.0 40.0
 80.0 20.0
 80.0 40.0
 60.0 20.0
 80.0 20.0
 60.0 20.0
 60.0 60.0
 80.0 60.0
 100.0 60.0
 60.0 40.0
 74.1 35.2

(a)SM = standard error of mean. (b)weighted by number of auctions in each experiment. not win very often. With time, these players learned to bid more conservatively and/or simply profited from the reduced competition resulting from bankruptcies of others. Alternatively, the survivors may have simply bid more conservatively to start with relative to their signal values. In this polar case improved market performance results strictly from those bidding in excess of E(V~Si = s1) suffering losses and eventually dropping out of the market. As a consequence, those who began bidding below E(V~Si = s1) come to dominate market outcomes. Actual market outcomes may, of course, result from a combination of these forces.

Table IV provides data relevant to evaluating these alternatives. The first two columns compare survivor bidding behavior over the first three auction periods with their bidding behavior in the last five market periods. The last column of Table IV shows bidding behavior of bankruptcies over the first three market periods. The number of bidders remained approximately constant over the first three periods as the losses that occurred then were generally not large enough to cause a significant number of bankruptcies.

Table IV shows that on average survivors began bidding in excess of E(V~Si = s1), as 63.5 percent of all survivor bids exceeded this value in the first three market periods. The implication is that a majority of survivor bids in the first three periods would have resulted in negative profits had they been unlucky enough to receive relatively high signal values! In this respect, the winner's curse is present in early auction periods even for survivors.

There appears to be considerable individual learning over time, however, as by the last five auction periods only 23.5 percent of the survivor bids exceeded E(V~Si = s1). It is possible, of course, that survivor learning is exaggerated to the extent that the number of bidders was reduced from bankruptcies (recall from footnote 9 that E(V~Si = s1) is decreasing in N). Experiment 11 affords some limited evidence on this point as the number of bidders was held constant at six for seventeen auction periods via the use of substitute bidders replacing bankruptcies. Looking at the bids of the four survivors who started bidding in period one, 83 percent of all bids exceed E(V~Si = s1) in the first three auction periods and only 10 percent of all bids exceed E(V~Si = s1) in periods thirteen to seventeen, not unlike the general learning effects reported in Table IV. The less aggressive bidding behavior on the part of survivors in terms of the E(V~Si = s1) benchmark cannot, in this case be attributed to a reduction in the number of bidders.

Comparing bankruptcies with survivors shows that while only 11.7 percent of survivors bid in excess of the naive expectation E(V~Si = s1) in the first three market periods, some 35.6 percent of nonsurvivor bids exceeded this expectation. Pooling the first two bid categories, 75.3 percent of the nonsurvivor bids exceeded E(V~Si = s1), compared to only 63.5 percent for the survivor bids. Thus, subjects going bankrupt tended to set themselves up for


Bidding Relative to Signal Values Survivors with and without

Experience and Survivors versus Bankruptcies
 Percentage of Bids
 Bidding by Bidding by
 Survivors Bankruptcies
 Periods Last Five Periods
Bid Relative to Signal Values one to three Periods one to three
b(si) > E(V~si) 11.7 4.4 35.6
E(V~Si = s1) < b(si) < E(V~si) 51.8 19.1 39.7
RNNE Bid < b(si) < E(V~Si = s1) 18.3 43.1 9.6
b(si) < RNNE Bid 18.2 33.4 15.1

losses more frequently than survivors, and the losses for the subjects going bankrupt were generally larger. Cash Balance Effect. With time and losses, cash balances diminish to the point where limited liability for losses may induce overly aggressive bidding. Alternatively, low cash balances may induce less aggressive bidding, since with bankruptcy bidders must exit the auction, losing potential profit opportunities in later auction periods. To determine the net effects of these two forces, individual subject bid functions were estimated for all signal values in the interval (VL + Epsilom, VH - Epsilom) using the following specification:

bit = alpha 0 + (alpha 1)(sit) + (alpha 2)(Epsilom t) + (alpha 3)(Nt) + (alpha 4)(balance it) (2) where sit and balanceit are bidder i's private information signal and cash balance at the beginning of period t, and Epsilom t and Nt are the value of Epsilom and the number of bidders in period t. Bid functions were estimated separately for each experiment using a fixed-effects regression model, and for each individual subject. Estimated coefficient values for the cash balance variable from each experiment are shown in Table V, along with the number of subject having positive or negative cash balance coefficients.

A positive coefficient value indicates that subjects were bidding less aggressively (lower) with smaller cash balances, while a negative coefficient


Effects of Cash Balances on Bidding: Coefficient Value for Cash Balance

Variable in Bid Function
 Individual Subject Regressions(a)
 Sign of Coefficient
 Fixed Effects (Number of Bidders
 Model Estimated Significantly Different from
 Coefficient Value zero at 10 percent Level)
Experiment (Standard Error) Negative Positive
 1 -.10 1 3
 (.50) (2)
 2 .64(**) 1 4
 3 .01 1 1
 4 .09 2 4
 (.13) (1)
 5 .26 3 2
 (.27) (1) (1)
 6 -.02 1 4
 (.08) (1) (1)
 7 .32(*) 1 4
 (.17) (2)
 8 1.38(**) 2 3
 (.47) (1) (2)
 9 .37(**) 2 4
 (.10) (1) (2)
 10 .06 2 3
 (.07) (1) (2)
 11 -.04 3 4
 (.05) (2)

(*)Significantly different from zero at 10% level. (**)Significantly different from zero at 5% level. (a)Coefficient estimates could not be obtained for all subjects. indicates more aggressive (higher) bids with smaller balances. The fixed-effects regression coefficients are positive in eight of eleven experiments and are significantly different from zero in four of these eight cases. Of the three experiments generating negative coefficient estimates, none are different from zero at conventional significance levels.

This general pattern of less aggressive bidding with lower cash balances is found in the individual subject regressions as well. Close to two-thirds of the fifty-five subjects have positive coefficients, indicating that they bid less aggressively with lower cash balances. In fifteen out of these thirty-six cases, bidding was significantly lower with lower cash balances. In contrast, only five subjects had negative coefficient estimates that were different from zero at the 10 percent significance level or better.(11)

Although the results of the regressions indicate that lower cash balances generally resulted in lower bids, it is not clear that this reflects a cash balance effect. It could be that it took real losses (hence lower cash balances) for bidders to perceive that they had to bid less aggressively relative to signal values to earn positive profits.(12)

This alternative interpretation is supported by two facts. First, ten of the fifteen subjects whose cash balance coefficients were significantly positive never had their balances drop below the $4.00 level, so that they were always in a relatively secure operating position. Second, Dyer [1987] conducted a series of common-value offer auctions with inexperienced bidders using procedures similar to ours. In two experiments bidders had starting cash balances of $10.00, while in a third experiment, with virtually identical procedures, they had starting balances of $20.00. He reports no significant differences in individual subject bid functions across experiments. Definitive sorting out of cash balance effects from learning effects will require more experiments with exogenous variation in cash balances.


This study shows a strong initial winner's curse as subjects earned negative profits and consistently bid in excess of E(V~Si = s1). Both survivor (in 63.5 percent of the auctions) and bankruptcies (in 75.3 percent of the auctions) bid in excess of E(V~Si = s1) in the first three auction periods. As such, survivorship, is at least in part dependent on being lucky enough not to receive high valuation signals in the early rounds, and it is clear that the market outcomes are not dependent on the aberrant behavior of a few individuals. Further, the winner's curse is unaffected by the posting of subjects' signal values along with their bids.

With experience the winner's curse is attenuated as bidders earned modest positive profits, and the majority of bids were less than E(V~Si = s1) over the last five auction periods. Performance is relatively stable in the sense that few bankruptcies occurred as well. These adjustments in market outcomes are in part attributable to bankruptcy of the most aggressive bidders, and in part a result of survivors learning to bid less aggressively. Nevertheless there are still strong traces of the winner's curse as profits realized are only 10 percent of the profit opportunities as defined by the SRNNE, and a sizable minority of bids still exceeded E(V~Si = s1).

Kagel and Levin [1986] report results from a series of first-price common value auction experiments in which all subjects were experienced in that they had previously participated in one or more common value auction experiments. These results indicate that with small numbers of competitors (three or four) bidder performance improved to the point where subjects consistently earned profits closer to the SRNNE level than to the zero or negative profit levels associated with the winner's curse. Previous participation in a common value auction environment clearly reduces the impact of the winner's curse in this case. Nevertheless, increases in the number of bidders (to six or seven) resulted in reemergence of the winner's curse with bidders earning negative average profits and consistently bidding in excess of E(V~Si = s1). The continued dominance of strategic forces promoting increased bidding in the presence of increased numbers of rivals for these experienced bidders is indicative of the strength of the forces underlying the winner's curse. Further, a comparison of responses of these experienced bidders with bidders in early Outer Continental Shelf (OCS) lease sales shows bidding patterns in response to the release of public information which are similar and interpretable well only in the context of a winner's curse.

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(*) University of Houston and University of Pittsburgh, University of Houston, Texas A&M University, and Louisiana Tech University, respectively. This research was partially supported by grants from the Energy Laboratory and the Center for Public Policy at the University of Houston, the Technology and Society Research Division of the Texas Engineering Experiment Station, the Information Science and Economics Divisions of the National Science Foundation, and the Sloan Foundation program in behavioral economics. Tom Saal, Doug Dyer, and Susan Saroai provided able research assistance. Paul Milgrom and Ron Harstad provided helpful comments on an earlier draft, as did our referees.

(1)Bid were restricted to be nonnegative and less than or equal to Si + E. The latter restriction was explained on the grounds that bidding in excess of Si + E would insure losses. The full set of instructions are available from the authors.

(2)In the second half of experiments 1 to 9 subjects bid simultaneously in two independent common value auctions. Analysis of behavior in this second set of auctions is reported in the working paper by Kagel, Levin, Battalio, and Meyer [1984].

(3)This bid function and the corresponding bid function outside the interval (VL + E, VH-E) are explicitly derived in our working paper, available upon request. Also see Kagel and Levin [1986], footnote 8.

(4)This is provided that rivals are bidding their signal values or less.

(5)The exponential term Y on the right hand-side of (1) is ignored, as it quickly goes to zero.

(6)For example, is the A&M experiments with N = 6 and E = $5.00, the difference between (1) and E(V1Si = S1) is $1.43 (since E(V1Si = S1) = Si - (N -1)E/(N +1), which is substantially less than the beginning cash balance of $8.00.

(7)By definition of a Nash equilibrium, increasing bids above the equilibrium bid function reduces expected profit. Consequently, for those signal values for which the SRNNE bid function is effectively Si-E, even in cases where subjects have zero cash balances, it is "irrational" for risk-neutral bidders to deviate from the Nash norm. The intuition here is straightforward. There are positive expected profits for all bidders at the Nash equilibrium. For one bidder to bid higher than Nash involves the following: (1) it improves the chance of winning, while any possible losses map to zero due to limited liability and zero cash balances; but (2) deviations from the best response implies a reduction in ex ante expected profits. This second force is simply stronger than the first when the Nash bid is Si-E.

(8)Bankruptcies occured after the first nine auction periods in experiments 5, 7, 8, 9, 10, and 11 so that all losses reported here are real. If "paper" losses are omitted (i.e., losses in excess of cash balances) in those experiments with bankruptcies in the first periods, average losses were $4.20 (1), $1.78 (2), $4.02 (3), $1.91 (4), and $1.93 (6), where the number after the loss figure corresponds to the experiment in question. Average real losses across all experiments were $2.15 per auction period. Collectively, bidders turned back $212.57 of the starting balances we had given them.

Under the rules of the game, high bidders could have done much worse than the losses reported in Table II, generating average losses of over $12.00 per period if they had consistently bid min(Si + E, VH). Thus, we can reject the hypothesis that the high bidders had simply adopted a win-at-any-cost-strategy, or had simply decided to settle for their participation fee and were trying to minimize the time cost of obtaining it.

(9)This is a particularly strong finding given that bidding maxSi-E, VL insured them against losses and yields positive average profits as long as others bid b(Si) less than or minus Sj, a bidding profile that was commonly satisfied.

(10)First-price private value auction experiments such as those reported by Cox, Roberson and Smith [1982] typically report profits well below the risk-neutral Nash equilibrium prediction, a result which can be attributed to risk aversion on the bidder's part. There are several reasons that the low profit levels here are not attributed to similar forces. First, realized profits are a much smaller percentage of risk-neutral predicted profits than in private value auctions. Second, theoritically, comparable degrees of risk aversion are likely to promote bidding much closer to the risk-neutral model's predictions here than in private value auctions. This is because risk aversion in relationship to item valuation considerations imposes a downward pressure on bids that is completely absent in private value auction, where individual bidders know the value of the item (to themselves) with certainty. In fact, if the latter force is sufficiently strong, bidders will never bid above min (VL, Si-E) here, which would result in larger profits than predicted under the SRNNE.

(11)An alternative specification including a time trend variable on the right-hand side of (2) yields virtually the same results as those reported.

(12)Negative coefficient values cannot be interpreted unambiguously either. Suppose a bidder starts out bidding aggressively but is lucky enough to receive low signal values, so that he does not suffer losses. Observing the fate of others suffering losses and bankruptcies, he determines that he must bid lower. Lower bidding coincides with more favorable signal values, so that he wins and his cash balance increases. Something of this sort may well have actually occurred since of the five subjects with significant negative coefficients, minimum cash balances dropped $2.76, $6.06, $7.99 and $8.00 (for two bidders). In only one of these cases had balances dropped to the point where limited liability for losses could plausibly account for the more aggressive bidding.
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Author:Kagel, John Henry; Levin, Dan; Battalio, Raymond C.; Meyer, Donald J.
Publication:Economic Inquiry
Date:Apr 1, 1989
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