Bidding Behavior in Pay-to-Bid Auctions: An Experimental Study Michael Caldaray Department of Economics University of California, Irvine This version: 26 March 2012

Abstract This paper experimentally studies the pay-to-bid auction format and compares average revenues in the discrete time simultaneous decision model to average revenues in the continuous time setting experienced in pay-to-bid auctions on the internet. For both of the group sizes studied, 3 and 5, there is no di¤erence in the average revenues between the two environments. However, there is signi…cant over-bidding, as has been observed in pay-to-bid auctions on the internet, for both group sizes and this over-bidding depends on the number of participants. Over-bidding decreases with experience, and strategic sophistication plays a large role in the outcomes of individuals. Some of the least successful subjects cease auction participation all together, suggesting that the pay-to-bid auction mechanism can only sustain revenues above the value of the prize as long as new inexperienced participants can be attracted. JEL Classi…cations: C72, D03, D44 Keywords: All-pay, Internet Auctions, Strategic Sophistication, Experiments

This research was supported by grants from the Experimental Social Science Laboratory (ESSL) at University of California, Irvine. I thank Mike McBride, as well as participants from the 2012 IFREE Workshop in Experimental Economics, for comments and suggestions. y 3151 Social Science Plaza, Irvine, CA, 92697-5100, [email protected].

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Introduction

In recent years, a peculiar new auction format, the "pay-to-bid" auction (or "penny" auction), has surfaced on the internet. The auction format boasts average revenues well in excess of the value of the prize (e.g., Thaler 2009, Platt, Price and Tappen 2010, Augenblick 2011) and yet tens if not hundreds of individuals willingly participate in each new auction. This is in sharp contrast to the standard game theoretic prediction (e.g., Hinnosaar 2010, Platt et al 2010, Augenblick 2011) that average revenues will equal at most the value of the prize. An apparent key to the auction format’s success is its ability to e¤ectively exploit behavioral biases while still enticing new participants to join. This enticement stems from the generally great deal o¤ered to the high bidder (i.e., a High De…nition Television for $24:36, a $200 gift card for $17:45, a Blu-ray player for $1:71). It is the participants as a collective whole that lose, as the auctioneer collects a small non-refundable bid fee each time a bid is placed. In this example taken from a popular pay-to-bid auction website, the three auctions raised $2654:72 and retail price of the items was 779:98. With such lopsided outcomes it is no wonder the auction has been called "the evil stepchild of game theory and behavioral economics" (Gimein 2009). The pay-to-bid auction, which has similarities to the dollar auction (Shubik 1971), the war of attrition (e.g., Smith 1974, Fundenberg and Tirole 1986) and the all-pay auction (e.g., Krishna and Morgan 1997, Baye, Kovenock and de Vries 1996), is distinguished by the following features: Participants choose between bidding and not bidding. When a participant bids, the auction price increases by a small …xed increment and that participant is charged a non-refundable fee. The participant can bid multiple times during the auction, but must pay the non-refundable fee each time she bids. When there is no time left on the countdown clock, the last participant to bid wins the prize and pays the end auction price. Whenever a bid is placed in the last few seconds, a small amount of time (i.e., 15 or 20 seconds) is added to the countdown clock. Thus, the auction can be in the "last few seconds" inde…nitely (several hours is common). 2

It is clear from the structure of this auction that it is rife with the opportunity to make mistakes. The bid fees are a sunk cost, the monetary commitment of the active participants grows in small increments as the auction progresses, decisions must be made in a short window of time, and each decision to not bid risks losing the auction. Since the fees from past bids are lost forever, participants might fall victim to the sunk cost fallacy. If we try to model these sunk costs with prospect theory and loss aversion (e.g., Kahneman and Tversky 1979; 1991; 1992, Thaler 1980), excess revenues can be explained by risk seeking behavior in small losses (bid fees) from the reference point (the participant’s initial wealth).1 The growing monetary commitment of active participants may lead to further escalation of commitment as these participants try to dig themselves out of a hole. For instance, participants may be better able to rationalize unsuccessful bids through further bidding (e.g., Staw 1981, Wong, Kwong and Ng 2008). Additionally, the negative emotions that participants may encounter in this adversarial setting have been shown to increase the likelihood of escalation (e.g., Wong, Yik and Kwong 2006, Tsai and Young 2010) although if the participants are able to predict future regret (e.g., Wong and Kwong 2007, Ku 2008a), learn not to escalate from prior experience (e.g., Ku 2008b) or set a mental budget to limit participation (e.g., Heath 1995), this e¤ect may be mitigated. Lastly, the short time between decisions may lead to mistakes due to limited cognition (e.g., Simon 1976). While it is easy to develop a list of behavioral phenomena such as the sunk cost fallacy, escalation of commitment, bounded rationality, and loss aversion, that could explain the excess revenues of pay-to-bid auction websites, it is di¢ cult to determine theoretically whether these biases are driving excess revenues, and if so, which of these biases are the most salient. A variety of alternative theories have been proposed that can also explain excess revenues, including: Information asymmetries and imperfect information (e.g., Byers, Mitzenmacher and Zervas 2010), risk loving preferences (e.g., Platt et al 2010), shill bidding (e.g., Platt et al 2010, Byers et al 2010), and signalling strategies (e.g., Augenblick 2011, 1 Alternatively, Augenblick (2011) shows a similar result by explicitly modelling naive sunk cost fallacy in pay-to-bid auctions.

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Byers et al 2010). Furthermore, evidence from …eld data highlights the important in‡uence that individual heterogeneities have on individual outcomes. Both strategic sophistication and experience (Wang and Xu 2011)2 , and reputation and signalling behavior (Goodman 2011) have been shown to play a role in individual auction outcomes. While all of the above …ndings are plausible explanations for the excess revenues of pay-to-bid auction websites, this analysis is complicated by the complexity of the pay-to-bid auction format. For the sake of simplicity and tractability, the baseline pay-to-bid auction theory of (Augenblick 2011, Hinosaar 2010, and Platt et al 2010) makes many abstractions. But until the theoretical model is better understood, we have no way of knowing whether the game modelled by the baseline theory bears any resemblance to the game being played by the participants on the pay-to-bid auction websites. I seek to bridge this gap with the experimental method. By examining bidding behavior in pay-to-bid auctions in a controlled laboratory setting, I can test both the game modelled in the baseline theory, and a game that is closer to what is played on pay-to-bid auction websites in an environment where many of the confounding factors present in …eld data have been removed (i.e., imperfect information, asymmetries, unknown risk preferences, censored data). While this is the …rst paper to experimentally study the pay-to-bid auction format, this work …ts into a large body of experimental work on contests (e.g., Millner and Pratt 1991, Davis and Reilly 1998, Potters, de Vries and van Winden 1998, Gneezy and Smorodinsky 2006, Herrmann and Orzen 2008, Amaldoss and Rapoport 2009, Horish and Kirchkamp 2010, Muller and Schotter 2010, Sheremeta 2010; 2011, Sheremeta and Price 2011) and auctions (e.g., Coppinger, Smith and Titus 1980, Cox, Roberson and Smith 1982, Cox, Smith and Walker 1988, Kagel and Levin 1993). Much of the contest literature has found evidence of over-bidding in lottery and all-pay contests. As the pay-to-bid auction is a type of dynamic contest, we might expect to observe some over-bidding as well. Of key interest is the cause of any over-bidding, and whether 2

Wang and Xu use an adaptation of Camerer, Ho and Chong (2004) that is especially suited for measuring sophistication in pay-to-bid auctions.

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this over-bidding persists as subjects gain experience. For example, Sheremeta (2011) …nds evidence that mistakes play a role in over-bidding, Amaldoss and Rapoport (2009) attribute this over-bidding to strategic sophistication, Gneezy and Smorodinsky (2006) …nd that overbidding depends on the number of players, and Herrmann and Orzen (2008) link over-bidding with spiteful preferences. It is also possible that the dynamic nature of the pay-to-bid auction may turn this result on it’s head, as Horish and Kirchkamp (2010) do …nd over-bidding in the static all-pay auction, but …nd under-bidding in the dynamic war of attrition (despite the theoretical similarities). In addition, there is evidence that experience diminishes overbidding in the all-pay auction (e.g., Davis and Reilly 1998), and so we might expect any over-bidding to diminish with time. It is unclear whether sunk cost fallacy will play an important role in this setting. The fee structure of pay-to-bid auctions will clearly generate sunk costs, and so we might expect to observe sunk cost fallacy as has been observed in more general settings (e.g., Arkes and Blumer 1985) but other studies …nd the e¤ect to be small (e.g., Friedman, Pommerenke, Lukose, Milam and Huberman 2007) and the results of Sheremeta (2010) for multi-stage contests are inconsistent with sunk cost fallacy all together. Building o¤ this previous literature, I test bidding behavior in pay-to-bid auctions using a 2

2 design. The two key treatment variables are the number of auction participants ( n = 3

or n = 5) and the strategy space (discrete rounds with simultaneous bid decisions as in the baseline theory or continuous time with instantaneous feedback as in a pay-to-bid auction on the internet). I control for many of the confounding factors in internet pay-to-bid auctions by holding the remaining auction parameters constant, providing full information, and making the participants symmetric. The main observations of interest are average revenue under each treatment condition, the determinants of individual auction outcomes, and the presence of behavioral biases. In line with the previous literature, I …nd persistent over-bidding that tapers o¤ with time. Auction revenues in the n = 5 treatment are signi…cantly greater than auction revenues in the n = 3 treatment, consistent with the bidder mistakes hypothesis. I …nd no di¤erence between the auction revenues under the discrete rounds treatment and the

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auction revenues under the continuous time treatment, suggesting that the game modelled in the baseline theory is capturing many of the key strategic considerations present in a pay-to-bid auction on the internet. Risk aversion has the predicted e¤ect on number of bids placed relative to risk neutral participants, but the results for risk seeking participants are inconclusive. I …nd strategic sophistication to be a strong determinant of individual auction outcomes. I observe the use of signalling strategies, but not generally with success. This ine¤ectiveness may be in part to the shortened auction lengths and symmetries built in to the experiment design. Another key …nding is that many less successful participants cease participation entirely over the course of the session. The …ndings that overbidding decreases with experience and less successful participants learn to leave supports the hypothesis of Wang and Xu (2011) that pay-to-bid auction websites pro…t from a "revolving door of new bidders". For a …xed pool of participants, it does not appear that the pay-to-bid auction format can generate sustained revenues in excess of the value of the prize.

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Baseline Theory The Model

I …rst summarize the theoretical models presented in Augenblick (2011), Hinnosaar (2010), and Platt et al (2010). These closely related models can be used to characterize the symmetric equilibrium in a pay-to-bid auction. Each work models the pay-to-bid auction as a full information extensive form game, but a main point of departure between the three models is how to handle the possibility of ties. Platt et al assume the round ends immediately when a bid is placed and that potential bidders’decisions of when to act are distributed without atoms throughout each period. This treatment is conceptually closest to the continuous time setting in which the probability of a tie is zero and the round advances as soon as a bid is placed. Augenblick achieves a similar result by allowing multiple bids to be placed in a round and accepting one bid at random. This treatment, in which the bid fee is only paid if the bid is accepted, has the advantage of being easier to test in the laboratory while 6

providing an equivalent solution concept. Hinnosaar also allows multiple bids to be placed in a round but in his model all bids are accepted and the high bidder is selected at random. This treatment di¤ers from the other two models by adding the possibility of paying a bid fee without becoming the high bidder. Hinnosaar’s treatment captures an important consideration that participants face in a pay-to-bid auction. While the auctions do take place in continuous time where the probability of a tie is zero, it is quite common for a situation to arise where multiple bids are placed in a small window of time. For example, if a bidder is not trying to signal, a good strategy is to wait until the last possible second to place a bid. If several bidders are following this strategy then it is common for bids to be placed within a fraction of a second of one another. In this case, the actual order of bids will determine the high bidder, but from the perspective of a participant with a limited reaction time the order in which the bids are placed will appear random and the timing of the bids will appear to be simultaneous. Thus when placing a bid, the participant must consider the possibility of becoming the high bidder at an auction price multiple increments higher than the current auction price. Additionally, the participant must also consider the possibility of being charged a bid fee and then being immediately outbid by another bid that would have been placed anyway. These situations do not occur in the Augenblick or Platt et al treatments, but they may a¤ect bidding behavior in practice. For this reason, and since the Hinnosaar model is also easy to test in the laboratory, my treatment will utilize the Hinnosaar approach to tie-breaking.

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The baseline model is as follows. A single item is put up for auction. A non-participating auctioneer conducts the auction and a non-participating seller commits to sell the item at the end auction price. Any revenues generated by the auction will be divided in some manner between the auctioneer and the seller. There are n 3

2 participants in the auction,

This analysis makes no judgement as to which model should be preferred for other applications. A natural downside of the Hinnosaar model is that the symmetric equilibrium does not have an analytical solution and must instead be solved numerically using backwards induction. As this analysis is primarily concerned with revenue rather than the nature of the equilibria that are played, this downside is not problematic for my purposes.

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indexed by i 2 f1; 2; :::; ng, who share a known common value

for the item. The number

of participants n is …xed throughout the auction and n is known to all participants. The auction is conducted over a series of discrete rounds, indexed by t 2 f0; 1; 2; :::g. In all rounds t > 0, exactly one of the n participants is designated as the "high bidder", a title that is awarded based on the outcome of the prior round, and the remaining n

1 participants are

designated as "non-leaders." The auction starts in round t = 0 at initial price P0

0 with

no high bidder. In a given round t, non-leaders simultaneously choose between bidding and not bidding. The high bidder does not participate in the round. If a participant chooses to bid, the auction price increases by the price increment " > 0, the participant pays a non-refundable bid fee of C (" < C


under risk neutrality, I use

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and never exist equilib-

as a conservative baseline prediction to

compare against average revenue in my experiment sessions. If instead the assumed equilibrium is such that E(R)