Personality Traits and Bidding Behavior in Competing Auctions∗ Robert G. Hammond†

Thayer Morrill‡

August 8, 2016

Abstract We study strategic behavior in an “alternating recognition” model of English auctions with competing sellers, which mimics a structure that is common in online marketplaces such as eBay. To relate decision making in our experimental setting to individual differences, we measure subjects’ personality with the Big-Five Trait Taxonomy. Our results suggest that personality has meaningful predictive power in explaining bidding behavior but only for female subjects. Further, females also earn more than males and the gender gap in earnings is large and significant. Finally, personality indirectly affects earnings through the choice of strategies but has no direct effect on earnings, controlling for strategies. This is an important result in that it demonstrates the mechanism through which personality matters in our setting. JEL classification: C91, D44, L81 Keywords: Competing sellers, Big Five personality traits, gender, auctions, online markets

∗ We thank an associate editor, two referees, David Dickinson, Todd McElroy, and participants at the 2012 North American Economic Science Association Conference (Tucson), the 2012 INFORMS Annual Meeting, and the University of Rennes for comments; the Faculty Research and Professional Development Grant fund for financial support; and Kelsey Hample for excellent research assistance. † Department of Economics, North Carolina State University. Contact: robert [email protected]. ‡ Department of Economics, North Carolina State University. Contact: thayer [email protected].

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Introduction We study bidding behavior in competing auctions using a simple but realistic model of dynamic

bidding in the “alternation recognition” bidding model of Harstad and Rothkopf (2000). The setting has multiple sellers simultaneously listing one unit of a homogeneous good for sale. In this framework, Peters and Severinov (2006) document a focal equilibrium in competing auctions where bidders engage in incremental bidding of the following sort. The first bidder submits the minimum permissible bid with the seller whose reserve price is the lowest, the second bidder submits the minimum permissible bid with the seller whose reserve price is now the lowest, etc. This process continues until the bidder with the k + 1st highest value is incrementally outbid, where k is the number of sellers/goods. While this focal equilibrium generates efficient allocations, other equilibria exist and theory provides little guidance when forming an expectation of which strategy bidders will follow in field data from online marketplaces. To guide our understanding, we use a laboratory experiment to study “alternation recognition” English auctions. A key goal is to incorporate psychological factors into an analysis of bidding behavior in a competitive environment. We start from the premise that individuals are different, then quantify an important set of these differences and map them into decision making in an interesting economic environment. A deeper understanding of how different types of individuals make decisions helps economists better design economic environments in fields such as market design. To this aim, we implement the Big-Five Trait Taxonomy (John et al., 2008), a personality measurement system, to quantify the degree to which our experimental subjects vary along the following personality dimensions: openness/closedness to experience, conscientiousness/lack of direction, extraversion/introversion, agreeableness/antagonism, and neuroticism/emotional stability. Our experimental setting allows us to gain a fuller understanding of bidding behavior in competitive environments such as eBay (Kagel and Levin, 2008). We find interesting gender differences in the effect of personality traits on strategic decision making in our auction setting. Conscientiousness and extraversion have an economically and statistically meaningful effect on how well bidders conform to theoretical models of bidding in competing auctions. However, these two traits have meaningful predictive power only for females, while none of the five traits have meaningful predictive power for male bidders.

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We interpret our results in the context of the large literature on gender differences in competitiveness (Niederle and Vesterlund, 2007; Eckel et al., 2008; Croson and Gneezy, 2009). In our competitive auction setting with incremental bidding, personality matters for females but not for males. However, it has been commonly found that males are more competitive than females. Jointly these two results could suggest that it is males’ competitiveness that explains why personality does not have any predictive power on bidding in our setting.1 Under this interpretation, personality has an association with males’ behavior in noncompetitive settings but their willingness to engage in competition attenuates the association of personality and behavior in competitive settings. There is evidence from the related literature that suggests the importance of conscientiousness and extraversion is broad and extends beyond our laboratory setting. Specifically, in related work on the effect of personality on decision making in the field, low conscientiousness and high extraversion has been found to work in conjunction to affect strategic thinking in other domains. See Eroglu and Croxton (2010) for evidence in the context of forecasting and Witt (2002) in the context of hiring decisions. Considering the existing work on personality traits, personality differences have been shown to explain strategic decision making for important economic outcomes, including savings behavior (Ballinger et al., 2011), cooperation (Boone et al., 1999), and bargaining (Swope et al., 2008). An analysis of strategic decision making in a competitive auction setting with incremental bidding is worthwhile because it presents a novel avenue for study of the behavioral determinants of market outcomes. We find that personality affects earnings in our setting only through its effect on strategic bidding behavior, which demonstrates the mechanism through which personality matters in market environments. Our findings are also related to other work from the lab, such as Grebitus et al. (2013), who find that extraversion is meaningfully correlated with behavior in auction environments. In work on exposure to the winner’s curse, Chlaß (2011) finds effects that are analogous to ours for both conscientiousness and extraversion. However, there is much less work exploring gender differences in the effect of personality on behavior. A particularly relevant exception is M¨ uller and Schwieren (2012), who document that personality affects performance in the competitive environment they study, the real-effort tournament task of Niederle and Vesterlund (2007). Further, the authors find 1

We thank a referee for suggesting this interpretation.

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that personality (specifically neuroticism) mediates gender differences in the willingness to compete. To explore this personality-competitiveness mediation hypothesis, we sought corroboration for the interactions we find of conscientiousness and extraversion with gender. First, in personal correspondence with the authors of Grebitus et al. (2013), it was noted that the relative predictive power of personality in Grebitus et al. (2013) differs for females and males, similar to our finding. Further, Grebitus et al. corresponded that these gender differences are found in a competitive setting (an auction) but not a noncompetitive setting (hypothetical choice), which is consistent with the arguments of M¨ uller and Schwieren (2012). Second, in personal correspondence with the author of Chlaß (2010, 2011), it was noted that personality traits have similar effects as in our study. However, in Chlaß (2011)’s noncompetitive setting (an auction with only one bidder), she does not find strong gender differences. We take our results, along with those of Chlaß (2011) and Grebitus et al. (2013), as evidence that there are gender differences in the effects of personality on behavior in competitive settings but not in noncompetitive settings; in competitive settings, personality can predict the behavior of females but not males.

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Theoretical Analysis of Bidding in Competing Auctions Harstad and Rothkopf (2000) introduce a natural generalization of the classic English auction.

In the standard English auction model, once a bidder stops bidding, she exits the auction. Moreover, this exit is public, so the other bidders may infer the value she places on the good. However, in practice, it is common to observe a bidder “pause.” That is to say, a bidder may be the highest bidder at a low price, stop actively bidding for a period of time, yet resume bidding once the auction nears its conclusion. In particular, Harstad and Rothkopf move away from the standard “button” auction, which relies on an assumption of public and irrevocable exits. Instead, they assume an exogenously determined order of moves, and they allow a bidder who declines to bid during one of her turns may choose to bid when her turn comes again.2 This “alternating recognition” model alternates between the first two bidders in the bidding order until both bidders consecutively pass, at which time the third bidder enters. These three bidders alternate turns in order until there are three consecutive passes and the process continues until all bidders have entered. The auction ends 2

We refer to declining to bid as passing, which follows the terminology from card games.

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when all bidders have entered and all consecutively pass. Peters and Severinov (2006) use a similar framework to model a marketplace such as eBay where there are many buyers and many sellers. Here, entry, exit, and re-entry is particularly important. An active bidder may choose to submit a small bid on an item, a large proxy bid on an item, or no bid at all. However, a bidder who chooses not to bid may yet wish to resume bidding later in the auction. Similarly, submitting a small bid on one item does not preclude a bidder from placing a larger bid with the same or different seller in the case where she is outbid. More formally, the mechanism in Peters and Severinov (2006) is an open, second-price auction with proxy bidding. They analyze a particular equilibrium in the alternating-recognition model. There are many buyers and sellers. Sellers, who each have a single unit of a homogeneous good, run a second-price auction with a reserve price. Each bidder wishes to acquire a single unit of the good and has a private value for the good.3 Buyers can submit as often as they like, and they are free to move between sellers. The bidders are also able to submit proxy bids. The proxy system displays the current standing bid, which is equal to the second-highest of all currently entered bids. The minimum permissible bid is one bid increment above the current standing bid. A bidder can bid this minimum permissible bid or any number higher. Before the start of the auction, sellers choose public reserve prices but sellers play no further role once the auction begins. Peters and Severinov (2006) characterize a perfect-Bayesian equilibrium for this market where each bidder bids with the seller whose standing bid is the lowest and submits a bid equal to the minimum permissible bid. While not unique, Peters and Severinov argue that this equilibrium could be focal due to its simplicity. Further, Peters and Severinov (2006) document that, in this equilibrium, all sellers set their reserve prices at their i.i.d. costs; given incremental bidding, it follows that this focal equilibrium generates efficient allocations. This efficiency result is interesting in the light of the competing auctioneers literature. To mention examples, Peters (1997) finds negative results for efficiency, while Peters and Severinov (1997) find that efficiency is obtained when bidders learn their valuations after selecting among auctions, as in Wolinsky (1988), but not when bidders know their valuations ex ante, as in McAfee (1993). 3

In particular, no bidder is exposed to the winner’s curse. This is in contrast to Harstad and Rothkopf (2000). There, the entry and exit is critical for information acquisition as each bidder has imperfect information regarding the value of the good and other bidders’ information is informative to her. In contrast, the entry and exit in Peters and Severinov (2006) is not relevant to the buyer’s payoff from acquiring a unit of the good.

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Our empirical application focuses on bidding behavior relative to that which is prescribed by the Peters and Severinov (2006) focal equilibrium, hereafter called the PS06 strategy: submit an incremental bid (i.e., the minimum permissible bid) with the seller whose standing bid is the lowest. We will describe behavior that is consistent with PS06 bidding behavior as “rational” and behavior that is inconsistent with PS06 bidding behavior as “irrational.” These terms are not meant in a pejorative sense but instead refer to bidding relative to what is predicted by fully rational auction models. Strategies other than the PS06 strategy include maximal bidding, where a bidder places a bid equal to her willingness-to-pay. Submitting a maximal bid early in the auction is known as squatting and can be harmful with proxy bidding because other bidders only see the current bid, which is lower than the proxy bid (for non-incremental proxy bids). At the opposite extreme, sniping involves a bidder who passes during all her early turns and then submits a maximal bid near the end of the auction. In an “alternating recognition” English auction, there is no obvious disadvantage to sniping as long as a bidder correctly perceives when passing is risky in that the auction could end before her next turn. Despite the noisiness of field data, there is related work that examines the choice among these strategies in naturally occurring marketplaces. Anwar et al. (2006) test the Peters and Severinov (2006) model using eBay data, documenting the existence of “cross-bidding” among sellers. Using the controlled experimental design that is explained next, we are able to more cleanly quantify the degree to which bidders’ strategic behavior conforms to theoretical models of English auction bidding.

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Experimental Design We recruited students from an email listserv at North Carolina State University to participate in

a laboratory experiment whose purpose was “to gain a better understanding of how markets work.” The instructions are in Appendix A. The experiment was run in the z-Tree experimental software (Fischbacher, 2007). We use this environment to ask how subjects bid in a competitive auction environment and how personality traits affect bidding strategies and market outcomes. Following the terminology on eBay, we take the example that we give to subjects in the instructions directly

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from their help page.4 All subjects played the role of bidders, while sellers were computerized (i.e., reserve prices were set by the computer). All treatments have three sellers, each with one unit of a homogeneous good. Bidders enter proxy bids similar to many internet auction markets, where a bidder reports her max bid and the computer raises the price following a second-price auction rule. In particular, each seller’s standing bid is a function of the bids received by that seller up to this point in the auction. The standing bid starts at the seller’s reserve price and becomes the second-highest of all bids received by the seller plus one bid increment. The proxy bidding system allows minimum permissible bids (1 ECU above the standing bid), maximal bidding (equal to the bidder’s value), or anything in between. Bidders are also allowed to bid above their value and it is not explained to them why doing so is a bad idea. At each turn, if the bidder is not a high bidder on any seller’s good, then she can bid with any seller in any amount above the seller’s standing bid. Alternatively, the bidder can choose to pass and wait for her next turn. If the bidder wants to pass for all remaining turns within a given auction, she can drop out of the auction. Finally, if the bidder is a high bidder, then she can raise her existing bid or pass. We use a two-by-two experimental design with variation across the number of bidders, four versus six, and the informational environment, low (Figure 1) versus high (Figure 2). In the highinformation treatments, subjects were told the total number of bidders in the auction, how many bidders have yet entered, and the bidder number (i.e., bidder identity) of the current high bidder for each seller’s good. In the low-information treatments, subjects were only told their own order of entry into the auction and whether a seller’s good had yet received a bid. The main data for the experiment were generated from four sessions: two sessions with the high-information treatment and two sessions with the low-information treatment. Four-bidder and six-bidder treatments were run within a session in order to balance the total number of subjects in groups of each size. Groups were anonymously and randomly formed at the start of the session, then fixed for the entire session. Several components of the theoretical model need to be parameterized. In what follows, values and prices are expressed in terms of experimental dollars (ECUs), which were converted into American dollars at the end of the experiment. First, bidders’ values and their order of entry iid

changed from auction to auction. Values were distributed as follows: v ∼ U [0, 100], where U [·] de4

See http://pages.ebay.com/help/buy/bidding-overview.html.

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notes the discrete uniform distribution (i.e., integers). Sellers’ reserve prices were randomly drawn according to U [0, 25] for four-bidder groups and U [0, 60] for six-bidder groups. This approach is consistent with a computerized-seller version of the Peters and Severinov (2006) model in which sellers have i.i.d. cost draws and the computer implements the pricing strategy prescribed by the efficient-pricing focal equilibrium. Finally, the minimum bid increment is 1 ECU. Of the 90 minutes that each session lasted, the first 15 minutes covered the instructions, including questions and answers. Then, subjects participated in the bidding experiment for 60 minutes, where we ended groups individually as the time limit of 60 minutes was approaching. Subjects were not told how long bidding itself would last, only that the entire experiment would last no more than 90 minutes. The final 15 minutes consisted of an unincentivized personality questionnaire within z-Tree, as will be explained in the next section. Subjects were given feedback following each auction on the following: which seller’s good they bought (if any), the price they paid (if any), and their earnings in experimental dollars (zero if not a high bidder). In addition, in the high-information treatments, subjects were told whether or not each good sold and, if so, at what price. Finally, at the end of the session, subjects were given feedback on their total experimental earnings, the exchange rate, and their take-home earnings to be paid in cash. Participants were paid in cash at the end of the experiment, with take-home earnings averaging $25 including a $5 show-up fee. For a 90 minute experiment, an average earnings of $25 is well above these students’ average hourly wages. The standard deviation in earnings is $10.75 and earnings range from a minimum of $5 and a maximum of $63 (where both numbers include the show-up fee). Subjects were told that the first auction in which they participated would only be for practice. Further, they were told that their total earnings would be the sum of their earnings in the remaining auctions, starting from the second auction. Pilot testing indicated that there would be substantial variation in the number of completed auctions within 60 minutes by group, stemming from differences between four and six-bidder groups and differences in bidding strategies across groups. As a result, we explained to subjects that experimental earnings in ECUs would be converted into American dollars with an exchange rate that made average earnings equal to $25. We emphasized that this dynamic exchange rate removed the incentive to move more quickly than they otherwise found optimal. That is, if we pre-committed to a fixed exchange rate, then subjects would want to complete as many auctions as possible. Our approach avoids biasing bidding 8

strategies in this way.

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Quantification of Personality Traits Our goal is to connect bidding behavior within this experimental auction setting to important

features of individuals that affect their decision making in a wide range of economic environments. The particular characteristics of interest are drawn from the study of personality within the field of human psychology. These traits are important because they have been shown to influence the way in which individuals process information and make decisions. While we do not discuss the vast psychological literature in detail, a number of overviews are available (e.g., Brody and Ehrlichman (1998)). Instead, we focus on the intersection of economics and the psychology of personality traits (Caplan, 2003; Borghans et al., 2008; Almlund et al., 2011). In particular, we consider the Big Five personality traits, which are the dominant approach in psychology to summarizing overarching personal characteristics in a comprehensive way (McCrae and John, 1992; John et al., 2008).

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Definitions of the Big Five

The Big Five personality dimensions are a taxonomy of specific domains of personality that broadly characterize a number of distinct traits into the following five factors: 1. Openness to Experience – degree to which a person needs intellectual stimulation, change, and variety: curious/inquisitive (high pole) vs. consistent/practical (low pole); 2. Conscientiousness – degree to which a person is willing to comply with conventional rules, norms, and standards: organized/thorough vs. lackadaisical/spontaneous; 3. Extraversion – degree to which a person needs attention and social interaction: outgoing/energetic vs. solitary/ reserved; 4. Agreeableness – degree to which a person needs pleasant and harmonious relations with others: compassionate/trusting vs. cold/cynical; and 5. Neuroticism – degree to which a person experiences the world as threatening and beyond his or her control; sensitive/nervous vs. secure/confident. 9

The acronym OCEAN is useful when referring to the five factors. The above definitions for each factor are drawn from Borghans et al. (2008) and the adjectives that are commonly used to describe individuals at the low and high pole, respectively, for each factor are drawn from Gough and Heilbrun (1983). We consider each factor in turn, followed by a discussion of what we expect to observe in terms of each factor’s correlation with bidding behavior in our auction environment. Openness to experience can be referred to as intellect or culture; particular facets include curiosity and imagination. This factor is thought of as an intrinsic interest in ideas but is more specifically associated with emotion, abstraction, and appreciation of artistic beauty. It is in contrast to a preference for familiar and straightforward things and a resistance to change. Conscientiousness refers to socially prescribed impulse control; particular facets include orderliness and self-discipline. This factor can be incorrectly thought of akin to the willingness to exert effort, but is really about the willingness to follow norms. For example, low conscientiousness individuals are more likely to submit work with spelling errors, not because they are less hard working, but because the social norms of grammar are less predominant in their decision-making process. Extraversion refers to an energetic approach to one’s outward life; particular facets include assertiveness and expressiveness. This factor can be broken into social dominance and social vitality, where the former refers to the assertive and forceful facets of extraversion and the latter refers to the outgoing and sociable facets. Individuals at the lower pole, introverts, need less external stimulation. Agreeableness refers to a prosocial disposition; particular facets include empathy and trust. This factor does not primarily refer to an individual who is amicable, but instead refers to an individual for whom amicable interpersonal interactions are important. While the two are related, the defining characteristic of high agreeableness individuals is that they need harmony among the persons with whom they interact for their own inner satisfaction. Neuroticism can be referred to by its lower pole, emotional stability; particular facets include anxiety and self-consciousness. Less emotionally stable individuals view the world around them negatively and are more likely to experience the negative emotions of nervousness, sadness, and tension. For these five factors, our hypotheses of interest center on the monotonous nature of the Peters and Severinov (2006) (PS06) focal strategy, in which the bidder simply bids on the lowest-priced 10

object and increases her bid by the smallest possible increment. If a person is easily bored, then we anticipate that they will be drawn to the variety of playing other, non-standard strategies. As a result, we hypothesize that low-openness bidders are more likely to play the focal strategy than high-openness bidders. In contrast however, openness has been used a proxy for intelligence and thus if one views PS06 bidding as an equilibrium strategy that requires intellect to deduce, then the opposite relationship should hold. Next, we predict that high-conscientious people are more likely to play the focal strategy because doing so requires the bidder to be meticulous and patient. To a lesser extent, we would expect low-agreeableness and more emotionally stable bidders to be more likely to play the focal strategy. Finally, we have no prior on how extraversion should interact with a bidder’s strategic behavior in our auction environment. While it is the leading approach toward the quantification of personality, the Big Five has also been criticized. For example, Block (2010) summarizes several concerns with the Big Five, including the critique that it lacks a theoretical foundation, omits important traits that do not fit within the five factors, and ignores trait development.

4.2

Measuring the Big Five

We measure the personality traits of our experimental subjects in order to relate personality differences to bidding behavior in a competitive auction and understand how different types of individuals make decisions in such an environment. In particular, we use the Big Five Inventory, which is a widely used Big Five questionnaire that is relatively short and well documented in terms of reliability (Costa and McCrae, 1992; John et al., 2008). The Big Five Inventory questionnaire consists of 44 short phrases that are described to subjects as “a number of characteristics that may or may not apply to you.” For each phrase, subjects are asked to “indicate the extent to which you agree or disagree with that statement.” Answers between one and five correspond to disagree strongly, disagree a little, neither agree nor disagree, agree a little, or agree strongly, respectively. The phrases are introduced with the statement “I am someone who . . .” and particular examples include the following (using the acronym OCEAN to refer to the five factors): “Is original, comes up with new ideas” (O), “Makes plans and follows through with them” (C), “Is talkative” (E), “Has a forgiving nature” (A), and “Worries a lot” (N). 11

The score for each factor ranges from one to five, averaging the answers on those phrases (out of 44 phrases) that correspond to each factor. Some phrases are mapped into factors using reserve scoring, where numerical answers are subtracted from six before calculating the average (e.g., “Can be somewhat careless” (C) and “Tends to find fault with others” (A)).5 Table 1 provides summary statistics for the scores on each factor among the 81 subjects in our sample, while Figure 3 provides the score distributions broken down by gender of the subject.6 These kernel density plots show unimodal distributions of all five factors for men and of openness, conscientiousness, and agreeableness for women. A pronounced bimodality exists in extraversion for women and a mild bimodality exists in neuroticism for women. Beyond these differences in peaks, the personality score distributions for men and women are quite similar. Confirming this, Table 2 summarizes the personality traits of the 20 female and 61 male subjects in our data. All gender differences in the average scores are small and statistically insignificant. Further, we compare personality scores for our subjects to a large-scale sample of individuals, 5,014 of whom were 22 years old (the average age of our subjects) (John and Srivastava, 1999). We find statistically meaningful differences between our subjects and the larger sample in terms of average scores for two of the five traits: our subjects are less open to experience and more emotionally stable. Finally, Table 3 provides the correlation among the Big Five for these 81 subjects. Only one correlation is larger than 0.30 in absolute value: extraversion and neuroticism have a correlation of -0.43, suggesting that extraverts are more emotionally stable. These correlations suggest that there is little duplication of personality facets. 5

The questionnaire is freely available for research purposes. See http://www.ocf.berkeley.edu/∼johnlab/bfi.htm to download the inventory and http://www.outofservice.com/bigfive for self administration. 6 One subject became ill and did not complete the bidding task or questionnaire. We exclude the subject from all analysis but retain the data from the remaining five members of this subject’s group. The monitor during the session dropped the subject out of all remaining auctions and announced this fact to all subjects in the session (the third session). Because subjects were not aware who was in their group and the experimental design did not provide information on drop outs, there is no reason to believe that the subjects knew whether they were in the affected group. As a result, we argue that the data from the remaining members of the group are still informative. However, all results with the affected group removed confirm the main results and are available from the authors upon request.

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5

Results from the Lab

5.1

Bidding Behavior

We briefly summarize the results that follow. This section shows that personality traits have a meaningful effect on a subject’s choice among bidding strategies, while Section 5.2 shows that bidding strategies have a meaningful effect on a subject’s earnings. Taken together, we find that personality traits affect strategies which in turn affect earnings but, once controlling for strategies, personality does not have a direct effect on earnings. These results are novel in that they demonstrate the mechanism through which personality matters in market environments. We analyze how personality traits affect subject’s choice among bidding strategies. The results are shown separately for females and males, along with the results from a t-test of a difference in the estimate by gender. In Tables 4-8, the first column labeled Mean provides the mean level of the strategy in question, while the next five columns labeled by the first letter of the personality traits provide the marginal effect of a one point increase in the trait on the propensity to use the strategy in question, separately by gender. The last two rows provide the difference in the estimates by gender, along with the standard error of the difference. For the results in Tables 4-8, the regression analysis uses a Probit model with standard errors clustered at the subject level. For the 81 subjects in our sample, the data contain 680 bidder-auction observations from 152 auctions. We observe 2,239 bids out of 2,554 bid opportunities, which implies that bidders chose to place a bid 87.7% of the time that it was their turn and they were not already a high bidder. The first three outcomes that we consider (Tables 4, 5, and 6) involve a bidder’s strategy choice using bid-level data. First, Table 4 considers a bidder’s propensity to bid on the seller whose standing bid is the lowest (within 1 ECU). Around two-thirds of bids are on the lowest-price seller. Second, Table 5 considers a bidder’s propensity to submit an incremental bid on the lowest-price seller, which is a subset of the strategy in the previous table where the strategy here additionally requires that the bidder submit a bid that is no greater than the second-lowest standing bid (within 1 ECU). Around 40% of bids are PS06 bids, suggesting that the focal equilibrium bidding strategy from Peters and Severinov (2006) is common in these data but does not describe the majority of bids. Third, Table 6 considers a bidder’s propensity to squat on a particular seller’s good, which we define as submitting a bid equal to the bidder’s value “early” within the course of an auction. 13

Early is defined as in the first 75% of the bidder’s bidding opportunities, which ignores bidding one’s value at the end of an auction when doing so is indistinguishable from incremental bidding. Bidders use this strategy for 3-5% of their bids. The fourth and fifth outcomes of interest are bidder/auction-level outcomes, which are useful for strategies that are primarily a function of the totality of bids that a bidder placed within an auction, rather than of an individual bid. Recall that Tables 4-8 display the marginal effects of a one point increase in the personality factor on use of the strategy in question. Fourth, Table 7 considers a bidder’s propensity to enter a bidding war, which we define as “repeatedly” submitting a bid at the same seller, once outbid, despite the presence of seller with a lower standing bid. Repeatedly is defined as at least twice within the same auction, which is a very inclusive definition yet still finds few bidding wars. This strategy is consistent with an attachment to a particular seller’s (homogeneous) good, which can be interpreted as a reaction to being outbid. Around 5% of bidder/auctions engage in any amount of bidding that is consistent with a bidding war, a proportion that falls to 1% when considering at least three repeated bids. Fifth, Table 8 considers a bidder’s propensity to bid in a way that we describe as increasing increments, which we define as, over the course of an auction, increasing the difference between a bidder’s bid and the minimum permissible bid at the seller that received the bid. Bidding such that this gap increases within an auction is inconsistent with several different models of bidding. This behavior could reflect inattentiveness, boredom, or a misunderstanding of the auction environment. Only 2% of bidder/auctions bid with increasing increments, a small proportion that suggests that bidders remained active and engaged in the experiment. We summarize behavior on these five strategies by the degree to which it is consistent with fully rational bidding models. To discuss the effect of gender and personality traits broadly across all five strategies, we hypothesize that rational bidding prescribes the following behavior: more likely to bid on the lowest-price seller (including PS06 and non-PS06 bidding) but less likely to squat, enter a bidding war, and bid with increasing increments. The results present a generally consistent picture irrespective of the strategy considered; however, the results present a starkly different picture by gender. We find important differences in the size, and often the sign, of the effects of personality on strategic behavior between male and female bidders. We discuss the sizes of these effects on PS06 bidding as representative of the pattern. 14

For females, a bidder’s propensity to use the PS06 strategy is affected as follows: from Table 5, a one point increase makes PS06 bidding 27 percentage points less likely for conscientiousness, 20 percentage points more likely for extraversion, and 13 percentage points less likely for neuroticism. The effects of openness and agreeableness on PS06 bidding are smaller and statistically insignificant. For context, the first column of Table 5 shows that 42% of bids by females are PS06 bids. Therefore, a female with a conscientiousness score at the mean of 3.61 has a PS06 propensity of 42%, while a female with a conscientiousness score one point higher at 4.61 has a PS06 propensity of 15%. This is a quantitatively large and statistically significant effect. For males, the majority of traits for the majority of strategies have quantitatively small effects that are statistically insignificant. The lack of statistical significance is not driven by low power; in contrast, we have a larger sample of males and similar variability in personality traits among males as among females (see Table 2). We argue that the findings for personality and strategies for males indicate a reduced role of personality in explaining bidding behavior for males and conclude that additional work is needed to understand the relationship between personality traits and market outcomes for females and males separately. These data indicate that low-conscientious, extraverted females follow more rational bidding strategies. Further, high emotional stability is associated with rational bidding among females but this finding is less robust than that for conscientiousness and extraversion in the sense that the evidence is less consistent across strategies.7 Our ex ante hypotheses did not anticipate an interaction of personality with gender. Further, none of our personality hypotheses held. Our post hoc interpretation of these results is that the competitive nature of our auction environment may explain the gender differences we observe in the predictive power of personality. Specifically, given that males are often found to be more competitive than females, one interpretation is that personality has an association with males’ behavior in noncompetitive settings but their willingness to engage in competition attenuates the association of personality and behavior in competitive settings.8 To further explore this personality-competitiveness mediation hypothesis, we sought corroboration for the personality-gender interactions that we find. First, in personal 7 Further, in unreported results, we rerun the regressions in Tables 4-8 separately for the early and late parts of a session to look for learning. Low-conscientious, extraverted females bid more rationally in both halves of a session. In contrast, emotionally stable females bid more rationally than neurotic females in the first half of a session but there is no quantitatively large or statistically significant difference across neuroticism in the second half. 8 We thank a referee for suggesting this interpretation.

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correspondence with the authors of Grebitus et al. (2013), it was noted that the relative predictive power of personality in Grebitus et al. (2013) differs for females and males, similar to our finding. Further, Grebitus et al. corresponded that these gender differences depend on whether the setting is competitive (an auction) or noncompetitive (hypothetical choice). Second, in personal correspondence with the author of Chlaß (2010, 2011), it was noted that personality traits have similar effects as in our study. However, in Chlaß (2011)’s noncompetitive setting (an auction with only one bidder), she does not find strong gender differences. We interpret these two sets of results, along with ours, in the context of the findings in M¨ uller and Schwieren (2012), who document that personality affects performance in a competitive environment, the real-effort tournament task of Niederle and Vesterlund (2007). The authors then demonstrate that personality (specifically neuroticism) affects individuals’ willingness to compete, concluding that personality mediates gender differences in competitiveness. We take our results, along with those of Chlaß (2011) and Grebitus et al. (2013), as evidence that there are gender differences in the effects of personality on behavior in competitive settings but not in noncompetitive settings.

5.2

Earnings

Subject earnings are easiest to analyze in experimental dollars because earnings in American dollars exhibit compressed variation in these data due to the dynamic exchange rate used to handle differences in completed auctions across groups. Tables 9 and 10 show raw ECU earnings for subjects below and above the median of each trait distribution, separately by gender. While these unconditional earnings are noisy in that they fail to control for confounds, they confirm the important finding that personality matters more for females than males in our setting. Regression results considering earnings in experimental dollars are from a single OLS regression, shown in two tables for ease of presentation.9 Table 11 shows the effects of covariates and strategies, while Table 12 shows the effects of gender/personality. The key findings are, in Table 11, the effects of bidding strategies on earnings and, in Table 12, the quantitatively small and statistically insignificant effects of personality of earnings. Taken together, these results imply that personality traits affect earnings via bidding strategies but, once controlling for strategies, personality does not have a direct effect on 9

An alternative specification is a Tobit regression with a mass point of zero, which treats winning bidders who bid above their value (who had negative earnings) the same as losing bidders (who earned zero). None of the results meaningfully change and these Tobit results are available from the authors upon request.

16

earnings. Importantly, this demonstrates the mechanism through which personality traits matter in determining auction outcomes. The specific findings for strategies can be interpreted by categorizing strategies into “rational” strategies (PS06 bidding and non-incremental bidding on the lowest-price seller) and “irrational” strategies (squatting, entering a bidding war, and increasing increments). A middle ground in our designation of strategies is bidding on a seller other than the lowest-price seller while not engaging in any of the listed irrational strategies, which is the omitted category in this regression. While conventional levels of statistical significance are reached for some but not all effects, the results are consistent with the rational/irrational designation. Specifically, bidding on the lowest-price seller with an incremental bid (PS06 bidding) weakly dominates doing so with a higher bid, which in turn is essentially equivalent in terms of earnings to bidding on a non-lowest-price seller. Among irrational strategies, increasing increments (bidding higher and higher amounts above the minimum permissible bid within an auction) is associated with the lowest earnings, followed by squatting (submitting a bid of the bidder’s value early in the auction), then entering a bidding war (repeatedly bidding on the same non-lowest-price seller’s good once outbid). Consistent with our claim that increasing increments make very little sense as a strategy, bidders who do so earn 11.04 ECUs less on average relative to the omitted strategy. For context, this translates to $9.74 lower take-home earnings in American dollars, which is calculated as follows: the earnings loss in experimental dollars of (11.04 ECUs) times the average number of completed auctions (8.21) divided by the average exchange rate (9.30). A loss of $9.74 is very large relative to an average earnings of $25. PS06 bidding increases earnings by $2.60 (take-home earnings in American dollars) but the effect is noisily estimated. Overall, these results on how strategies affect earnings support our hypotheses on which strategies should and should not work well. Most interestingly, poor bidding decisions are harmful to a greater extent than good bidding decisions are helpful. Table 12 suggests that females take home around $5.15 more in American dollars than males, which converts 5.83 ECUs to American dollars using the conversion described in the previous paragraph. This gender gap in earnings is quantitatively large and statistically significant. Further, it is novel relative to the previous literature that finds no gender difference in earnings in secondprice auctions but an earnings advantage for males in first-price auctions (Chen et al., 2013; Pearson 17

and Schipper, 2013). Relatedly, the existing literature provides evidence against some potential hypotheses for these findings. Chen et al. (2013) find that personality traits are not correlated with menstrual phases among their female subjects, while there are conflicting results regarding the predictive power of personality to explain risk and time preferences (Anderson et al., 2011; Deck et al., 2013). The latter results suggest that a claim that females are more risk averse cannot explain the gender differences in bidding behavior that we observe.10

5.3

Robustness to the Inclusion of Cognitive Abilities

After running our experimental sessions, we became aware of a protocol in which the experimenter obtains subjects’ consent to match experimental data with subjects’ student enrollment data in order to correlate academic performance with behavior in the lab.11 We ran an additional session following this protocol in order to test the robustness of our results by asking whether our observed correlation of personality traits and bidding behavior holds once we control for academic performance measures that proxy for subjects’ cognitive abilities. Subjects were asked for their student ID numbers and for their consent to obtain their enrollment records. They were told: “These records will be used in the statistical analysis of the data from the experiment to see if such things as GPA, academic major, etc. can enhance the predictive power of standard economic models typically used to analyze the data.” We use data only from male bidders to ask whether the low predictive power of personality in explaining bidding behavior among males holds once we control for cognitive abilities. Because only three females participated in the session where we matched with enrollment records, the data are not able to sort out the effects by gender. Table 13 shows the effect of personality on PS06 bidding for the 13 male subjects who participated in our fifth session, providing a total of 100 bidder-auctions observations. Only high school GPA has a statistically significant effect on PS06 bidding, where a one point increase in GPA increases PS06 propensity by 53 percentage points.12 More importantly, the results provide no evidence that controlling for cognitive abilities increases the power of personality traits in explaining bidding behavior among males; in fact, we find weak 10

Beyond these main results, the remaining findings for earnings are intuitive and a discussion of them is omitted. Linking experimental behavior with enrollments data has been done in Filiz-Ozbay et al. (2013), among other papers. We thank Erkut Ozbay for suggesting this robustness check. 12 Note that SAT score also positively affects PS06 bidding in a statistically significant way if the model does not control for high school GPA. 11

18

evidence that personality matters less when holding cognitive abilities constant. In this sample, we find that agreeableness has a meaningful effect on PS06 bidding when we do not control for cognitive abilities but has no effect when these controls are added. None of the other traits has an effect on bidding with or without controls for cognitive abilities. The imprecision of the estimated effects of personality on bidding for males is consistent with the main sample. In conclusion, we do not believe that our findings are driven by a relationship between cognitive abilities and bidding that is lurking in our findings on personality traits and bidding.

6

Conclusions We present an experimental analysis of a rich auction setting that allows us to understand

heterogeneous bidding behavior in a competitive environment. Our approach to quantifying differences among bidders uses a standard personality measurement tool from psychology, the Big Five. We find that personality traits have a meaningful effect on the strategies that a bidder uses in the auction and that these strategies have a meaningful effect on earnings. However, personality does not have a direct effect on earnings, controlling for strategies. Interestingly, strategies that we classify as “irrational” (e.g., entering a bidding war) reduce earnings to a greater extent than “rational” strategies raise earnings. The personality traits that have the largest effect on bidding behavior are conscientiousness and extraversion but these only matter for female bidders. For males, no personality trait has any meaningful effect on strategic behavior in this setting. We provide evidence in a robustness check that this finding also holds once we control for bidders’ cognitive abilities via their scores on standardized tests as well as high school and college grade point average. The findings for conscientiousness and extraversion among our female subjects are consistent with some evidence from the related literature. However, the existing literature provides limited guidance on the role played by personality in determining strategic behavior in competitive and noncompetitive settings and more work is needed to understand the driving forces. We believe that our analysis suggests several interesting directions for future research. For example, it is important to analyze the robustness of these personality traits affecting decision making in different economic environments. In an experiment with a noncompetitive decision

19

task, our hypothesis is that personality will interact with gender in different ways than in our environment of competitive, incremental bidding. Perhaps such work will offer new insights into differences between females and males in the effects of personality on decision making.

20

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Eroglu, C. and Croxton, K. L. (2010). Biases in Judgmental Adjustments of Statistical Forecasts: The Role of Individual Differences. International Journal of Forecasting, 26(1):116–133. Filiz-Ozbay, E., Ham, J. C., Kagel, J. H., and Ozbay, E. Y. (2013). The Role of Cognitive Ability, Personality Traits and Gender in Gift Exchange Outcomes. http://scholar.google.com/scholar? cluster=5438860487778690281. Fischbacher, U. (2007). z-Tree: Zurich Toolbox for Ready-Made Economic Experiments. Experimental Economics, 10(2):171–178. Gough, H. and Heilbrun, A. (1983). The Adjective Checklist Manual. Consulting Psychologists Press, Palo Alto, CA. Grebitus, C., Lusk, J. L., and Nayga, R. M. (2013). Explaining Differences in Real and Hypothetical Experimental Auctions and Choice Experiments with Personality. Journal of Economic Psychology, 36:11–26. Harstad, R. M. and Rothkopf, M. H. (2000). An “Alternating Recognition” Model of English Auctions. Management Science, 46(1):1–12. John, O., Naumann, L., and Soto, C. (2008). Paradigm Shift to the Integrative Big Five Trait Taxonomy. In Handbook of Personality: Theory and Research, volume 3, pages 114–158. Guilford Press. John, O. and Srivastava, S. (1999). The Big Five Trait Taxonomy: History, Measurement, and Theoretical Perspectives. In Handbook of Personality: Theory and Research, volume 2, pages 102–138. Guilford Press. Kagel, J. H. and Levin, D. (2008). Auctions: A Survey of Experimental Research, 1995-2008. In Handbook of Experimental Economics, volume 2. Princeton University Press. McAfee, R. P. (1993). Mechanism Design by Competing Sellers. Econometrica, 61(6):1281–1312. McCrae, R. and John, O. (1992). An Introduction to the Five-factor Model and its Applications. Journal of Personality, 60(2):175–215. M¨ uller, J. and Schwieren, C. (2012). Can Personality Explain What Is Underlying Womens Unwillingness To Compete? Journal of Economic Psychology, 33(3):448–460. Niederle, M. and Vesterlund, L. (2007). Do Women Shy Away From Competition? Do Men Compete Too Much? Quarterly Journal of Economics, 122(3):1067–1101. Pearson, M. and Schipper, B. C. (2013). Menstrual Cycle and Competitive Bidding. Games and Economic Behavior, 78:1–20. Peters, M. (1997). A Competitive Distribution of Auctions. Review of Economic Studies, 64(1):97– 123. Peters, M. and Severinov, S. (1997). Competition Among Sellers Who Offer Auctions Instead of Prices. Journal of Economic Theory, 75(1):141–179. Peters, M. and Severinov, S. (2006). Internet Auctions with Many Traders. Journal of Economic Theory, 130(1):220–245. 22

Swope, K. J., Cadigan, J., Schmitt, P. M., and Shupp, R. (2008). Personality Preferences in Laboratory Economics Experiments. Journal of Socio-Economics, 37:998–1009. Witt, L. (2002). The Interactive Effects of Extraversion and Conscientiousness on Performance. Journal of Management, 28(6):835–851. Wolinsky, A. (1988). Dynamic Markets with Competitive Bidding. Review of Economic Studies, 55(1):71–84.

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Table 1: Summary Statistics of Big Five Factors

O C E A N

Mean

Stnd Dev

Min

Median

Max

3.65 3.61 3.31 3.72 2.63

0.55 0.63 0.79 0.56 0.74

2.40 2.22 1.88 2.11 1.13

3.60 3.56 3.25 3.78 2.63

4.80 4.78 4.88 4.78 4.38

Notes: The summary statistics of the Big Five factors in our sample of 81 subjects are shown.

Table 2: Summary Statistics of Big Five Factors by Gender

O C E A N

Female

Male

Difference

3.58 (0.56) 3.58 (0.60) 3.41 (0.84) 3.67 (0.58) 2.75 (0.75)

3.67 (0.54) 3.62 (0.65) 3.28 (0.77) 3.74 (0.56) 2.59 (0.74)

-0.10 (0.14) -0.04 (0.16) 0.12 (0.20) -0.07 (0.15) 0.16 (0.19)

Notes: Separately by gender, the summary statistics of the Big Five factors in our sample of 20 female and 61 male subjects are shown. Standard deviations are shown in parentheses.

Table 3: Sample Correlations Among Big Five Factors

O C E A N

O

C

E

A

N

1.000 -0.045 0.136 0.108 -0.006

1.000 0.291∗∗ 0.263∗ -0.282∗

1.000 0.159 -0.427∗∗

1.000 -0.295∗∗

1.000

Notes: The correlations of the Big Five factors in our sample of 81 subjects are shown.

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Table 4: Prob(Bid on Low-Priced Seller | Bid) Mean Female Male Difference SEDiff

Marginal Effect of One Point Increase in Trait O C E A N

0.69 (0.04)∗∗ 0.66 (0.02)∗∗

-0.09 (0.11) 0.10 (0.05)∗

-0.24 (0.11)∗ 0.02 (0.04)

0.13 (0.07) -0.03 (0.03)

0.04 (0.10) -0.01 (0.04)

-0.06 (0.07) -0.05 (0.03)

0.03 (0.05)

-0.19 (0.12)

-0.26 (0.11)∗∗

0.17 (0.08)∗∗

0.05 (0.11)

-0.01 (0.08)

Notes: The strategy considered is whether a bidder places in a bid with (one of) the sellers whose standing bid is the lowest (within 1 ECU). In Tables 4-8, the regression analysis uses a Probit model with standard errors clustered at the subject level; ∗ and ∗∗ denote significance at the 5% and 1% level, respectively.

Table 5: Prob(Bid using PS06 Strategy | Bid) Mean Female Male Difference SEDiff

Marginal Effect of One Point Increase in Trait O C E A N

0.42 (0.04)∗∗ 0.38 (0.03)∗∗

-0.04 (0.09) 0.06 (0.05)

-0.27 (0.09)∗∗ 0.07 (0.05)

0.20 (0.06)∗∗ -0.01 (0.04)

0.02 (0.08) -0.03 (0.06)

-0.13 (0.06)∗ -0.02 (0.04)

0.04 (0.05)

-0.10 (0.10)

-0.34 (0.11)∗∗∗

0.21 (0.07)∗∗∗

0.05 (0.10)

-0.10 (0.07)

Notes: The strategy considered is whether a bidder places a PS06 bid: an incremental bid with (one of) the sellers whose standing bid is the lowest (within 1 ECU). Incremental bidding involves placing a bid such that the bidder’s maximum bid entered in the proxy bidding system is less than or equal to the second-highest standing bid among the three sellers’ standing bids.

25

Table 6: Prob(Bid using Squatting Strategy | Bid) Mean Female Male Difference SEDiff

Marginal Effect of One Point Increase in Trait O C E A N

0.03 (0.02) 0.05 (0.01)∗∗

-0.01 (0.04) -0.02 (0.02)

0.04 (0.04) -0.03 (0.02)

-0.04 (0.04) -0.02 (0.02)

-0.01 (0.03) -0.05 (0.02)∗

-0.00 (0.02) 0.00 (0.02)

-0.02 (0.03)

0.02 (0.04)

0.07 (0.04)

-0.02 (0.04)

0.05 (0.04)

-0.00 (0.03)

Notes: The strategy considered is whether a bidder places a bid equal to the bidder’s value in the first 75% of the bidder’s bidding opportunities (i.e., early) within the auction.

Table 7: Prob(Bidder Enters a Bidding War) Mean Female Male Difference SEDiff

Marginal Effect of One Point Increase in Trait O C E A N

0.05 (0.01)∗∗ 0.06 (0.01)∗∗

0.01 (0.04) -0.03 (0.02)

-0.06 (0.05) 0.02 (0.02)

0.04 (0.03) 0.00 (0.02)

0.09 (0.05) 0.05 (0.02)∗

0.04 (0.02)∗ 0.05 (0.03)

-0.01 (0.02)

0.04 (0.04)

-0.08 (0.05)

0.04 (0.03)

0.04 (0.05)

-0.01 (0.03)

Notes: The unit of observation is an individual bidder in an individual auction. The strategy considered is whether a bidder “repeatedly” places a bid with the same seller, once outbid, despite the presence of seller with a lower standing bid. Repeatedly is defined as at least twice within the same auction.

Table 8: Prob(Increasing Increments: Bid–MinBid Increases w/i Auction) Mean Female Male Difference SEDiff

Marginal Effect of One Point Increase in Trait O C E A N

0.02 (0.00)∗∗ 0.02 (0.01)∗∗

0.03 (0.02) 0.01 (0.01)

0.05 (0.01)∗∗ 0.00 (0.01)

-0.02 (0.01)∗∗ -0.00 (0.01)

-0.08 (0.02)∗∗ -0.02 (0.01)

-0.05 (0.02)∗∗ -0.00 (0.01)

-0.00 (0.01)

0.02 (0.02)

0.05 (0.01)∗∗∗

-0.02 (0.01)∗

-0.06 (0.03)∗∗

-0.05 (0.02)∗∗

Notes: The unit of observation is an individual bidder in an individual auction. The strategy considered is whether a bidder, over the course of an auction, increases the difference between her bid and the minimum permissible bid at the seller that received the bid.

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Table 9: Unconditional Earnings in Experimental Dollars by Big Five Factor, Females Only

Below Above Difference SEDiff

O

C

E

A

N

25.30 (8.08) 30.20 (9.75)

29.00 (5.03) 26.50 (12.04)

31.80 (7.67) 23.70 (8.86)

28.70 (10.29) 26.80 (8.12)

22.50 (7.78) 33.00 (7.21)

-4.90 (4.01)

2.50 (4.13)

8.10 (3.71)∗

1.90 (4.14)

-10.50 (3.35)∗∗

Notes: For females, earnings in ECUs are shown, only conditioning on a subject’s position in the personality trait distribution relative to the median.

Table 10: Unconditional Earnings in Experimental Dollars by Big Five Factor, Males Only

Below Above Difference SEDiff

O

C

E

A

N

23.56 (12.06) 26.21 (10.24)

25.76 (11.45) 24.17 (11.16)

24.03 (10.32) 25.69 (12.26)

25.50 (12.03) 23.84 (10.09)

25.71 (11.34) 23.62 (11.16)

-2.64 (2.86)

1.59 (2.95)

-1.66 (2.92)

1.66 (2.84)

2.10 (2.91)

Notes: For males, earnings in ECUs are shown, only conditioning on a subject’s position in the personality trait distribution relative to the median.

27

Table 11: Earnings in Experimental Dollars Average Value Average Bidder Order # of Bids Seconds Left Six-Subject Group High-Info Treatment PS06 Strategy Bid on Low, Not PS06 Bidding War Squatting Strategy Increment Increases

0.73 (0.02)∗∗ -0.93 (0.44)∗ -1.07 (0.31)∗∗ 0.03 (0.05) -12.03 (1.37)∗∗ 1.03 (1.11) 2.99 (1.70) -0.14 (1.42) -1.68 (2.89) -6.91 (1.94)∗∗ -11.33 (3.83)∗∗

Observations

680

Notes: The unit of observation is an individual bidder in an individual auction. An OLS regression analysis is shown of a subject’s earnings in ECUs in an individual auction. The effects of several covariates and strategies (as defined in earlier tables) are shown here, while the effects of personality traits are shown in the next table. Note that both sets of results are from the same regression analysis. As before, standard errors are clustered at the subject level.

Table 12: Earnings in Experimental Dollars, cont. Mean Female Male Difference SEDiff

Marginal Effect of One Point Increase in Trait O C E A N

26.77 (0.70)∗∗ 20.94 (0.62)∗∗

-0.16 (1.97) 0.02 (0.94)

-0.59 (2.10) 1.50 (0.98)

-0.23 (1.03) -0.07 (0.81)

1.26 (1.50) -1.74 (1.01)

0.88 (1.31) 0.50 (0.78)

5.83 (0.93)∗∗

-0.18 (2.17)

-2.09 (2.32)

-0.16 (1.44)

3.00 (1.81)

0.38 (1.47)

Notes: These results are from the same regression analysis as the previous table.

28

Table 13: Robustness Check: Prob(Bid using PS06 Strategy | Bid) O C E A N

(1)

(2)

-0.02 (0.16) 0.09 (0.11) 0.07 (0.11) -0.20 (0.08)∗ 0.09 (0.10)

-0.01 (0.10) -0.02 (0.07) 0.04 (0.12) -0.03 (0.12) 0.10 (0.06) -0.00 (0.00) 0.53 (0.09)∗∗ 0.09 (0.17)

449

449

SAT HS GPA College GPA Observations

Notes: The observations included are from the fifth session, which was run for this robustness check and includes only male subjects. The strategy considered is whether a bidder places a PS06 bid, with and without controls for cognitive abilities (as proxied by academic performance).

29

Figure 1: Screenshot of Low-Information Environment

30

Figure 2: Screenshot of High-Information Environment

31

.6 .5

.6

Density .3 .4

.5 Density .3 .4

.2

.2

.1

.1 2.5

3

3.5

4

4.5

5

2

3

4

Score

5

Score

Female

Male

Female

Male

Conscientiousness Score by Gender

Density 0

.1

.2

.2

Density .3

.4

.4

.6

.5

Openness Score by Gender

2

3

4

5

2

3

4

Score

Score

Female

Male

Female

Male

Agreeableness Score by Gender

0

.1

Density .2 .3

.4

.5

Extraversion Score by Gender

1

2

3 Score Female

4

5

Male

Neuroticism Score by Gender

Figure 3: Personality Trait Score Distributions by Gender of Subject

32

5

Appendix A

Experimental Instructions

We designed the instructions so that the same text could be used in all four treatments: lowinformation and high-information treatments as well as four-bidder and six-bidder treatments. In the low-information treatments (Figure 1), no information was given on the current number of entered bidders or the identities of the high bidders. Welcome! Today you will be participating in an auction experiment. You’ll be a bidder in an auction setting that closely resembles eBay. Three sellers have each listed one unit of the exact same good for sale. The other students that are in this room are also playing the role of bidders but may be participating in different auctions than you are. All dollar values in these instructions and during the experiment are expressed in terms of an experimental currency. Experimental dollars will be converted into American dollars at the end of the experiment and your take-home earnings will be paid in cash, including a $5 show-up payment for arriving on time. We will repeat the auction several times, each time called a round. For each round, the computer assigns you a number that we’ll call your Value. Your Value tells you how much you are willing to pay for each seller’s good. This Value is the same for all three sellers because they are selling the exact same good. You should consider your Value when you are deciding how much to bid. How much you earn in each round depends on your Value but we’ll tell you more about that below. Your Value changes from round to round. Your Value is always a number between $0 and $100, rounded to the nearest dollar ($0, $1 . . ., $99, $100). The computer randomly picks a value and each possible value is equally likely. That means that you are just as likely to have a Value of $1 as you are to have a Value of $99. Each seller has set a Starting Bid and you can enter any bid above this amount. Starting Bids change from round to round and are chosen randomly. You bid in this experiment just like you bid on eBay. When it is your turn to bid, you have the option to place a bid on any of the three sellers’ good. The bid must be at least $1 more than the Current Bid, but it may be any amount up to $100. As the auction proceeds, we compare your bid to those of the other bidders. When you are outbid, we automatically bid on your behalf up to Your Max Bid. We increase you bid by increments only as much as necessary to maintain your position as the highest bidder. The seller and other bidders don’t know Your Max Bid. If another bidder outbids you, you will have the opportunity to place another bid when it is your turn. For example, suppose the Current Bid for a good is $10, Tom is the high bidder, and Tom’s Max Bid is $12. When Laura views the good, she only sees that the Current Bid is $10 and that her bid must be at least $11. Suppose she places a Max Bid of $15. Tom’s bid is incremented to his maximum bid of $12. Laura’s bid is now $13. Laura is now the high bidder, and Tom now has the opportunity to place another bid if he chooses. You will be one of several bidders in the auctions. The computer randomly decides the order in which bidders participate and the order changes from round to round. You will always know when you will enter the auction by seeing on the screen “You are Bidder .”

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Each time it is a bidder’s turn, she has the following four choices: (1) place a bid with any of the three sellers if she is not currently the high bidder in any auction, (2) increase her bid if she is currently the high bidder in one of the auctions, (3) pass, or (4) drop out of the auction. If you choose to drop out of the auction, you will not be given another turn until the round ends. At the start of the next round, your order and Value will change. You cannot drop out of the auction if you are currently a high bidder on any sellers’ good. First Bidder 1 enters and acts. Next Bidder 2 enters. After Bidder 2’s turn, it is Bidder 1’s turn, then Bidder 2’s turn, then Bidder 1’s turn, etc. Once both players have passed, Bidder 3 enters. After Bidder 3’s turn, it is Bidder 1’s turn, then Bidder 2’s turn, then Bidder 3’s turn, then Bidder 1’s turn, then Bidder 2’s turn, and so on. This continues until all three bidders pass. Once all three bidders pass, then another bidder enters. The process repeats until all bidders have entered. The auction concludes once all bidders have entered and all bidders have chosen to pass. When the round is over, each good is sold to the Current High Bidder at the Current Bid. That means that if you are the high bidder on a seller’s good, you win that good and pay the Current Bid. Your earnings in the round are equal to your Value minus the Current Bid at the end of the round. If you are not the Current High Bidder on any seller’s good at the end of the round, your earnings in the round are zero. How You Get Paid For a particular round, you will earn experimental dollars if you are the high bidder on one of the sellers’ goods. In this case, your earnings at the end of the round are equal to your Value minus the Current Bid. If you bid more than your Value, this means that you may end up losing money and having to pay us out of your show-up payment. As long as you don’t bid above your value, you will not lose money. If you are not the high bidder on any of the three sellers’ goods, then your earnings at the end of the round are zero. We will go through a practice auction to help you get comfortable. Your earnings in this auction will not count in any way. After this practice auction, the real auctions begin and will continue until the time limit has been reached. The time limit makes sure that you will be done with the experiment and two questionnaires that follow in 90-120 minutes. You will be paid in cash at the end of the experiment. Your take-home earnings will be equal to the sum of your earnings in the real auctions, converted into American dollars, plus your $5 show-up payment. Experimental dollars will be converted into American dollars as follows: the exchange rate is equal to your group’s average earnings in experimental dollars divided by 20, which makes average earnings in American dollars equal to $20. This exchange rate makes sure that participating in more auctions does not increase or decrease your take-home earnings, so that your goal is to earn as much in experimental dollars as possible. [Insert Figure 1 for the low-information treatment or Figure 2 for the high-information treatment.]

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Legend [the information below corresponds to the high-information treatment and brackets denote what was omitted in the low-information treatments] In this example: “You are Bidder 3” is the order that you will enter the current auction. This changes from auction to auction. “Your Value: $48” is your willingness to pay for any of the three sellers’ goods in experimental dollars. This changes from auction to auction. [“3 out of 4 bidders have entered so far” tells you how many bidders are still waiting for their turn out of the total number of bidders in the auction. There will be either four or six total bidders and that number will not change from round to round. Here, one bidder is still waiting.] “You are the high bidder on object 3” is a message that changes depending on your current status in the auction. Here, you are the high bidder on seller 3’s good. “Your max bid is $34” tells you that the Max Bid you entered was $34 experimental dollars. Other bidders only see that the current bid on seller 3’s good is $3 experimental dollars because Your Max Bid is only seen by you. “You may only change your bid for this object” reminds you that you cannot bid on another seller’s good when you are currently high bidder on one good. “Seller 1: Current Bid = $15” shows that the Min Bid for Seller 1 is $15 experimental dollars and no bids have been placed on this object yet. “Seller 2: Current Bid = $19” shows that the Current Bid for Seller 2 is $19 experimental dollars but that may not be Bidder 2’s Max Bid. “Minimum Bid” is always the Current Bid plus $1 experimental dollar. “You have 25 seconds to make a decision” tells you how many of the 30 seconds are left before the computer passes for you. “Drop Out” button allows you to leave the auction completely and wait until the next auction to get a new order and Value. “Pass” button allows you to pass and wait until it is your turn again. “Bid” button allows you to enter a bid with a seller in any amount at least as large as the Min Bid or to increase Your Max Bid if you are already the high bidder on a seller’s good. Please do not talk with one another for the rest of the experiment. If you have any questions, please raise your hand. Are there any questions before we begin?

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