Excessive Optimism in First-Price Auctions Peter Fishman Department of Economics University of California, Berkeley

Barbara A. Mellers Haas School of Business University of California, Berkeley

June 2007 (Preliminary, please do not cite without authors’ permission)

Abstract

Economic experiments on first-price sealed bid auctions have consistently demonstrated overbidding relative to ascending auction formats and the risk-neutral Nash equilibrium. Lucking-Reiley (1999), however, finds that in online auctions for Magic cards, first-price auctions violate revenue equivalence by underperforming other auction formats. Further, the prevalence of ascending formats used by online auction sites, given revenue-maximizing sellers, is difficult to reconcile with the laboratory findings on auctions. Laboratory experiments typically assign subjects a private value for an imaginary good. We explore the role of these assigned values in our understanding of behavior in first-price sealed bid auctions. We conduct an experiment in which participants bid for a real object based on internally-generated private values and solicit subjects’ pleasures at various prices for the object. When bidding for an Amazon.com gift certificate, we find that subjects underbid in a first-price auction format. The results are consistent with field studies of online auctions as well as psychological studies of excessive optimism and loss aversion.

*We thank Elena Katok, Matthew Rabin, Jose Silva, and Paul Tetlock for helpful comments.

Introduction In a typical economic experiment of first-price sealed bid auctions, participants are told to imagine they are bidding for an object. The experimenter assigns to each bidder a number that is unknown to all other bidders and represents the participant’s private value--the perceived monetary worth of the object for that bidder. Participants presumably bid an amount that reflects a tradeoff between their desire to be the highest bidder and their desire to earn a profit from the exchange. Profit is defined as the difference between the bidder’s private value and the winning bid. This paradigm for studying first-price, sealed bid auctions may seem artificial, but to many researchers, the benefits are well worth the costs. The assignment of private values to bidders provides the control necessary to test the agreement between actual bids and the risk-neutral Nash equilibrium strategy. Results from several experiments have shown that people bid more than they should relative to the Nash equilibrium (see Cox, Roberson, and Smith, 1982, and for a review of studies Kagel, 1995). Less controlled field studies have provided additional insights about bidding behavior. The revenue equivalence theorem (see Vickrey, 1961) predicts that, under simple Nash equilibrium assumptions, first-price, second-price, Dutch, and English auctions should yield equivalent selling prices. But studies show that revenue equivalence does not hold. Lucking-Reily (1999) revenues are an average of 30% lower with firstprice auctions than with other formats. To summarize, laboratory studies of first-price auctions reveal overbidding, yet a field study of Internet auctions shows that first-price auctions result in lower revenues than other auction formats. Do these results imply that participants in second price,

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Dutch, or English auctions would engage in even more laboratory overbidding than participants in first-price auctions? The evidence suggests otherwise; second-price auctions and English clock auctions are typically consistent with Nash equilibrium bidding. Deviations are small and nonsystematic (see Kagel & Levin, 1993 and Kagel, 1995). What explains these seemingly contradictory results? Chakravarti et al.(2002) proposed two hypotheses. Lower revenues of real-world, first-price auctions may be attributable to the number of bidders who participate in different auction formats. In the laboratory, the number of bidders is fixed, while in the field, the number of bidders could be determined by the auction format. Even if subjects overbid in first-price auctions (and not second-price auctions), the second-price auction may raise more seller revenue given more bidders participate. Namely, the maximum willingness-to-pay is increasing in the number of bidders, which could dominate overbidding. Empirical work on endogenous entry of bidders lends support to this notion (Ivanova-Stenzel & Salmon, 2006). Alternatively, private values for real-world goods may be substantially different from private values for fictitious commodities used in laboratory studies. In this paper, we take a closer look at Chakravarti et al.’s second hypothesis. In the standard experimental paradigm for first-price, sealed bid auctions, participants are instructed to bid for a hypothetical object based on a psychologically meaningless number. Without the excitement created by a real good, participants might simply focused on the joy of being a winner. A large bid could be a natural human response to an auction with no sense of real loss due to the absence of a real good.

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Outside the laboratory, bidders in auctions participate because they want objects, events, or experiences with easily imaginable consequences. As noted by Heyman, Orhun, and Ariely (2003), bidders in auctions develop a sense of ownership (or quasiendowment) during the process, and those feelings boost their competitive urges if they are outbid. Bidders also may try to minimize regret (Greenleaf, 2004). In short, bids depend on the extent to which the object fulfills a bidder’s needs, wants, or desires, as well as the social interplay that occurs during the auction itself. Both personal and the social components of auctions are missing from the standard paradigm for first-price auctions. It seems unlikely that these psychological processes will emerge from the assignment of abstract numbers to represent private values and subsequent bids for a fictitious object. We offer a new paradigm for exploring bidding behavior in first-price, sealed bid auctions. First, participants bid for a known object which, in our study, was a $10 Gift Certificate at Amazon. Bidders form their own private values based on their desires and needs. Second, we measure each bidder’s beliefs about the likelihood of winning at a set of fixed bids. Third, we measure the pleasure that bidders imagine about winning at the same set of fixed bids and use that information to estimate private values. With this procedure, we can compare actual chances of winning against bidders’ beliefs and evaluate the extent to which bidders are accurately calibrated. Furthermore, using affective forecasts about possible consequences of the auction, we can infer a bidder’s private value. We make the assumption anticipated feelings or pleasure reflect experienced utility. Furthermore, we assume that a bidder's private value is the bid that he or she associates with affective neutrality. That bid is the amount of money for which the

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bidder is indifferent between losing the money and winning the auction, Finally, using our estimates of private values, we can assess the accuracy of bids relative to the Nash equilibrium and explore descriptive models of behavior. We compare the results of this procedure with those based on the traditional paradigm and field studies. Previous studies of first-price auctions have not measured the beliefs of bidders, so we do not know the assumptions that bidders make about the actions of other bidders nor whether those assumptions are accurate. If bidders were overly optimistic and believed that others would make bids that were lower than reality suggests, bidders would likely underbid relative to the Nash equilibrium. If bidders were overly pessimistic and believed that others would make higher bids than they actually did, bidders would presumably overbid. Past research showing that people overbid suggests that bidders are overly pessimistic, a highly unusual finding in light of past research on unjustified optimism. Weinstein (1980) demonstrates the tendency to believe that one is more likely to experience good outcomes and less likely to experience bad outcomes than people in similar circumstances. Excessive optimism has also been demonstrated in business planning, corporate acquisition, and corporate finance (Heaton, 1997; Boehmer & Netter, 1997; Lovallo & Kahneman, 2003). In addition, a large literature in psychology has shown that people are overconfident in their abilities. Overconfidence occurs when average ratings of confidence in one's knowledge exceed accuracy rates (Baron, 1994, Hazard & Peterson, 1973; Lichtenstein, Fischhoff, & Phillips, 1982; Phillips & Wright, 1977; Yates, 1990). Given these well-documented effects, undue optimism--not undue

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pessimism--among bidders would seem likely. We now investigate the beliefs and bids of participants in an experimental study of first-price auctions. Method Undergraduate students were told that they could participate in auctions with 4 other bidders. In each auction, the prize was a $10 Amazon Gift Certificate. Each bidder filled out a questionnaire with a variety of questions including his or her highest bid. After the experiment, bidders were assigned at random to a group of five, and the highest bidder in each group won a gift certificate. Winners were contacted one or two weeks later. All students chose to participate. They stated their highest bid for the gift certificate. Bids could only be made in $1 units, so 11 bids ranging from $0 to $10 were possible. Participants also reported how they would feel if they won the gift certificate having made each of the 11 bids. Pleasure was measured on a scale from -8 to 8, where -8 = "Extremely Unhappy" and 8 = "Extremely Happy". Finally, participants indicated their beliefs that each possible bid would be the highest bid among the four others’ bids on a scale from 0% to 100%. Beliefs summed to 100%.2 Approximately 1 to 2 weeks later, winners were contacted. After paying the amount bid, they were given the gift certificate.3 Participants were 221 undergraduates at the University of California, Berkeley. The experiment took approximately 10 minutes to complete, and all of the students received course credit in an undergraduate business courses for their participation.

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Results Bids and Beliefs Figure 1 shows the relative frequencies of observed bids, ranging from $0 to $10. Ten percent of bidders bid nothing for the gift certificate, while 2% were willing to pay the full amount. The modal bid was $5, and the mean bid was $4.80. One might wonder why the modal bid was not closer to $10. The delay between the experiment and the receipt of the gift certificate may have reduced the size of the bids. If winners had been awarded with gift certificates immediately after the auction, bids might have been higher. --------------------------------------Insert Figures 1 and 2 about here ---------------------------------------Figure 2 shows perceived and actual probabilities that each bid would be the highest bid among all competing bidders. Perceived cumulative beliefs appear with a 95% confidence interval. True probabilities were obtained from a Monte Carlo simulation by taking the distribution of one million highest bids obtained from random draws of sets of four bids taken from the distribution of participants’ actual bids. In the context of a first-price auction, excessive optimists are bidders who believe that the highest competing bid is too low. A comparison of the two lines shows that participants were excessively optimistic about winning. Beliefs and actual probabilities of winning at $5 illustrate this finding. On average, bidders thought the chance of winning the auction with a $5 bid was 47%, while in fact the chance was only 11%. To investigate whether beliefs were systematically related to bids, we computed the cumulative beliefs of participant groups, conditional on bids. We formed five groups consisting of those who made very low bids ($0 and $1), low bids ($2 and $3), medium

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bids ($4, $5, and $6), high bids ($7 and $8) and very high bids ($9 and $10). Cumulative beliefs for these groups appear in Figure 3. We find heterogeneity in subjects’ optimism. Those with very low bids were most optimistic (most left-biased beliefs), and those with very high bids were the least optimistic (and also best calibrated). The relationship between bids and beliefs suggests that participants assumed that opponents would make bids similar to their own. Low bidders thought others would tend to bid low, and high bidders thought others would tend to bid high. Results are consistent with false consensus bias (Ross, Greene, & House, 1977, Mullen et al., 1985), which in this setting inclines bidders to believe other subjects value the good similarly. ------------------------------Insert Figure 3 about here ------------------------------Affective Indifference Points Bids are systematically related to anticipated pleasure as well as judged beliefs. Figure 4 shows average feelings of pleasure with winning at each bid for the same five groups that appear in Figure 3. All of the groups anticipate significant pleasure from winning with a bid of $0. As bids increase, individual differences begin to appear. Low bidders predict less pleasure than high bidders at winning with all other bids. Low bidders are harder to please. Figure 3 demonstrates a connection between beliefs and bids, and Figure 4 shows a connection between bids and pleasure. Decision affect theory (Mellers et al. 1997, 1999), predicts a relationship between beliefs and pleasure. Surprise amplifies the emotional impact of an outcome such that surprising gains are more pleasurable than expected gains, and surprising losses are more painful than expected losses. Low bidders

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should be more surprised than high bidders about winning with a $9 bid. Furthermore, low bidders should be less pleased than high bidders about winning with a $9 bid. Conversely, high bidders should be more surprised than low bidders about winning with a $4 bid. The same high bidders should be happier than low bidders about winning with a $4 bid. This pattern is consistent with decision affect theory. As mentioned earlier, we defined a bidder’s private value for the gift certificate as the amount of money for which a bidder would feel indifferent between paying the sum and winning the auction. Indifference points for the five groups are shown in Figure 4 with the dashed lines. Points are the vertical projections on the x-axis when each curve intersected with the dashed line. Private values are about $7.00, $6.50, $8.00, $9.00 and $10.00 for Very Low bidders to Very High bidders, respectively. Actual bids were $.50, $2.50, $5.00, $7.50, and $9.50, respectively. For each group, bids are less than private values, a result that must occur if indifferent points are a reasonable proxy for private values. Figure 5 shows the distribution of private values for all bidders. The average private value is $8.10, much higher than the average bid of $4.80.5 ----------------------------Insert Figures 4 and 5 about here -----------------------------Describing the Bidding Process If bidders’ beliefs had been perfectly calibrated, the mean profit maximizing bid would have been $6.62, significantly higher the mean observed bid of $4.80 (t(220) = 10.06). On average, bidders underbid, not overbid, relative to the profit maximizing strategy. Furthermore, the majority of individuals (65%) underbid, and only 21% bid overbid.

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What might describe bidders’ actual strategy? Suppose bidders assigned bids that maximized subjective rather than objective expected profits. The subjective expected profit from each bid is the difference between the private value and that bid, multiplied by cumulative probability of winning with that amount. The mean profit-maximizing bid if participants based their bids on their own beliefs was $5.09. This mean does not differ significantly from the actual mean of $4.80. Furthermore, the correlation between observed bids and predicted bids is 0.60, significantly different from zero (t(220) = 11.0).6 Though bidders were overly optimistic in their beliefs about the highest competitive bids, their bids were generally consistent with a rule of maximizing subjective expected profits. Figure 6 presents a 3 dimensional histogram of actual bids and predicted bids with the height of the curves representing the number of bidders with an actual bid and predicted bid combination. The axes on the histogram floor are actual bids (left side) and predicted bids (right side). The highest corner of the histogram floor represents an actual and predicted bid of $0, and the lowest corner is an actual and predicted bid of $10. If predictions were perfectly correlated with actual bids, all of the observations would fall along on a straight line from the top to the bottom of the histogram. Although some deviations occur, most points fall near the center and those that differ do not appear to be systemic. ----------------------------Insert Figure 6 about here -----------------------------Another bidding strategy that we can examine is the maximization of subjective expected pleasure (Mellers et al., 1999). By this account, participants would select the bid

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that provided the greatest pleasure on average. To generate predictions, we computed the subjective expected pleasure of each bid for each participant (i.e., the judged pleasure of winning at that bid instead of the profit at that bid, multiplied by the cumulative belief that the bid would be the highest competitive bid, plus the displeasure of losing, multiplied by the belief that bid would not be highest competitive bid). The bid with the highest expected pleasure was the predicted bid. For this strategy, the predicted mean bid was $5.71, significantly greater than $4.80 (t test). Profit maximization was a better descriptor than pleasure maximization of the bidding process. Conclusion We conducted first-price sealed-bid auctions based on $10 Gift Certificates from Amazon. Participants made bids, rated their anticipated pleasure of winning at each even dollar bid, and stated their beliefs that each even-dollar bid would be the highest competitive bid. The average bid was $4.80. On average, bidders were excessively optimistic about winning with lower bids. Salo and Weber (1995) proposed that, when the distribution of private values was unknown, bidders would be excessively pessimistic due to ambiguity aversion. Our findings suggest the opposite; even when bidders do not know the private values of others, they are excessively optimistic. To assess the agreement of observed bids with predictions of the Nash equilibrium, we assumed that a bidder’s private value was the amount associated with affective neutrality. With that bid, the participant predicted that he or she would be neither pleased nor displeased with winning. Using this definition of private value, we found that the mean predicted bid was $6.62, significantly higher than $4.80. Participants appeared to underbid, not overbid, as found with the standard paradigm. Underbidding

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presumably occurred due to participants’ inaccurate beliefs about the likelihood of winning with smaller offers. Finally, bids were consistent with the maximization of expected profits based on participants’ subjective beliefs. With that strategy, the predicted mean bid of $5.09 was statistically indistinguishable from the observed mean bid of $4.80, and the correlation between observed and predicted bids was .60. Theories of Bidding Behavior Theoretical work on first-price sealed bid auctions has been exclusively directed toward explanations of overbidding, and several accounts have been proposed. The initial explanation was risk aversion, then constant relative risk aversion (Cox, Smith, and Walker, 1988). To account for problems pointed out by Harrison (1989), Friedman (1992) proposed instead that bidders had asymmetric loss functions. Further explanations included the quantal response equilibrium (Goeree, Holt, & Palfrey, 2002), regret (Engelbrecht-Wiggans, 1989), spiteful bidding (Morgan, Steiglitz, & Reis, 2003), and ambiguity aversion (Fox & Tversky, 1995). If the data used to construct these theories are invalid, the theories have little to do with actual bidding behavior. We argue that the standard paradigm yields questionable results. Our paradigm, however, not only produces reliable and replicable results, those results, in conjunction with economic field research and psychological work on subjective beliefs, provide a coherent picture of bidding behavior. Underbidding makes sense in light of field studies showing lower revenues from first-price, sealed bid auctions. It also explains the real-world empirical paucity of sealed-bid auctions relative to ascending-bid auctions.

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Underbidding does not always occur. In more “emotional” auction settings with real time markets, opportunities to submit multiple bids, and skilled auctioneers who know how to stir up crowds, the results of our paradigm may show overbidding and excessive pessimism. These are factors that should be explored in the laboratory and in field research. An even richer description of bidding behavior should emerge.

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Heyman, J., Orhun, Y., and Ariely, D. (2004). “Auction fever: The effect of opponents and quasi-endowment on product valuations.” Journal of Interactive Marketing. Volume 18, 7-21. Ho, T. H. (2001) An Experimental Study of Several Internet Pricing Mechanisms. University of Pennsylvania Seminar. Kagel, J.H., 1995. Auctions. In: Kagel, J.H., Roth, A.E. (Eds.), The Handbook of Experimental Economics. Princeton University Press. Kahneman, D., & Lovallo, D. (1993). “Timid choices and bold forecasts: A cognitive perspective on risk-taking.” Management Science, 39, 17-31. Lazear, E., Malmendier, U., Weber, R. (2006). “Sorting in Experiments with Application to Social Preferences.” Working paper. Lovallo, D. & Kahneman, D. (1993). “Delusions of Success: How Optimism Undermines Executives” Harvard Business Review, 2003. McGraw, A.P., Mellers, B.A., & Ritov, I. (2004). “The affective costs of overconfidence.” Journal of Behavioral Decision Making, 17, 281-286. McKelvey, R.D. & Palfrey, T.R. (1995). “Quantal Response Equilibria in Normal Form Games.” Games and Economic Behavior. 7, 6-38. Mellers, B. A., Schwartz, A., Ho, K., & Ritov, I. (1997). “Decision affect theory: Emotional reactions to the outcomes of risky options.” Psychological Science, 8, 423429. Mellers, B. A., Schwartz, A., & Ritov, I. (1999). “Emotion-based choice.” Journal of Experimental Psychology: General, 128, 332-345. Neale, M. A., & Bazerman, M. H. (1985). “Perspectives for understanding negotiation: Viewing negotiation as a judgmental process.” Journal of Conflict Resolution, 29, 33-55. Pezanis-Christou, P., & Sadrieh A. (2003). “Elicited bid functions in (a)symmetric firstprice auctions.” Working paper. Salo, A.A., & Weber, M. (1995). “Ambiguity aversion in first-price sealed-bid auctions.” Journal of Risk and Uncertainty, 11, 123-137. Weinstein, N. D. (1980). “Unrealistic optimism about future life events.” Journal of Personality and Social Psychology, 39, 806-820. Yates, J. F. (1990). “Judgment and decision making.” Englewood Cliffs, NJ: PrenticeHall.

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Footnotes

This work was supported by an NSF grant (SES-00111944) and a visiting scholar fellowship to the second author at the Russell Sage Foundation. The authors thank Paul Tetlock for many insightful comments. Email correspondence can be addressed to either author at [email protected] or [email protected]. 1

Carpenter et al. (2004) characterize this type of experiment as a lab experiment

with a physical good. 2

In 6% of cases the sum of the probabilities of all outcomes was not equal to 100.

In these cases, we scaled each percentage by the 100 divided by the sum. 3

We used standard 1st price auction rules, but ties resulted in no winners.

4

When ties occurred, we selected the midpoint as the prediction for this strategy

and all others. 5

Fewer than 3% of bidders had affective indifference points that exceeded their

actual bids. 6

7

All significance tests were conducted with an alpha level of .05.

Ho (2001) finds the Priceline.com format to yield the lowest prices for price

takers versus posted price (Amazon.com) and second-price formats (Ebay.com). This result is consistent with underbidding in first-price auctions in less artificial settings.

Figure Captions

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Figure 1. Histogram of bids. Figure 2. Cumulative chances of winning at each bid plotted against bids with separate curves for average beliefs about winning (solid line) and actual probabilities of winning (dashed line). Figure 3. Individual differences in cumulative beliefs plotted against bids with separate curves for those who made very low bids ($0 to $1), low bids ($2 to $3), medium bids ($4 to $6), high bids ($7 to $8), and very high bids ($9 to $10). Figure 4. Individual differences in judged pleasure plotted against bids with separate curves for those who made very low bids ($0 to $1), low bids ($2 to $3), medium bids ($4 to $6), high bids ($7 to $8), and very high bids ($9 to $10). The dashed line represents affective neutrality. Figure 5. Relative frequencies of indifference points. Figure 6. Three dimensional histogram of actual bids, predicted bids and number of bidders with a particular bid-predicted bid combination.

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Figure 1.

First-Price Sealed Bids

Frequency

0.2 0.15 0.1 0.05 0 $0

$1

$2

$3

$4

$5

$6

$7

$8

$9 $10

Bid

Figure 2.

Cumulative Chances

1.0 0.8

Percieved

0.6 Actual

0.4 0.2 0.0

$0 $1 $2 $3 $4 $5 $6 $7 $8 $9 $10 Bid

Figure 3.

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100 90

Cumulative Belief

80 70 60 50

$7 - $8

$9 - $10

40 30 $0 - $1

$2 - $3

20 10 0 $0

$1

$2

$3

$4

$5

$6

$7

$8

$9

$10

Bid

Figure 4.

Judged Pleasure

8 6

$9-$10

4

$7-$8 $4-$6

2 0 -2

$0-$1

-4

$2-$3

-6 $0

$1

$2

$3

$4

$5

$6

$7

$8

$9

$10

Bid

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Relative Frequency

Figure 5.

0.5 0.4 0.3 0.2 0.1 0 $0

$1

$2

$3

$4

$5

$6

$7

$8

$9 $10

Indifference Point

Figure 6.

Bid

Predicted Bid

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