Pay-Per-Bid Auctions with an Exit Option: An

Experimental and Empirical Investigation

Author: Tai Lam

Supervisor: Dr. Ben Greiner

A thesis submitted in partial fulfilment of the requirements for the degree of

Bachelor of Commerce/Economics (Honours)

School of Economics

24th October 2011

1

Declaration

I hereby declare that this thesis submission is my own work. Any contributions or

materials by other authors which are used herein have been appropriately acknow-

ledged. Furthermore, this thesis has not been submitted to any other university or

institution as part of the requirements for another degree or award.

Signed,

Tai Lam

24th October 2011

2

Acknowledgments

First and foremost, I would like to thank my supervisor, Dr. Ben Greiner, for his

knowledge and guidance throughout the year. If not for his encouragement and

passion for the topic, I would surely not have been able to see this thesis all the way

through.

I would like to acknowledge the generous support afforded to me by the NSW

Treasury Honours Scholarship and the grant from the ASBLab Small Projects Fund

without which there would not be any experiment at all.

Thanks must also go to Dr. Paul Pezanis-Christou, for the many helpful discus-

sions and insights provided in our meetings, and for acting as my discussant at the

Honours Colloquium. Much appreciated insights and comments were also received

from Dr. Bill Schworm. To all the other participants at the Honours Colloquium

and other honours presentations, thank you for your comments and suggestions.

To Dr. Andreas Ortmann and again Dr. Ben Greiner, thank you for igniting my

interest in behavioural and experimental economics.

Many thanks to my family for their support and understanding during this busy

year. Special thanks to my brother, Loune, for teaching me programming all those

years ago, it has been immensely helpful in many unexpected circumstances not

the least of which was this thesis, and for troubleshooting any and all programming

issues I encountered.

To the 2011 economics honours cohort, thank you so much for the many great

memories and fun moments. It is you people’s company, whether it is during lunch

eating noodles, or in the honours area talking about economics concepts so advanced

that not even a nobel laurete could follow, or just plain ranting on about thesis, that

have defined my economics honours experience.

3

Contents

1 Introduction 9

2 Auction Details 13

3 Literature 15

4 Model 18

4.1 Baseline Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

4.2 Exit Option . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

5 Empirical Investigation 24

5.1 Data Collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

5.2 Duration Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

5.2.1 Platform Comparison . . . . . . . . . . . . . . . . . . . . . . . 26

5.2.2 Exit and No Exit auctions . . . . . . . . . . . . . . . . . . . . 28

5.3 OLS Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

5.4 Auctioneer Profits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

5.5 Bidder Gains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

6 Experimental Investigation 38

6.1 Experimental Design . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

6.2 Summary Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

6.3 Duration Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

6.4 Probit Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

6.5 Auctioneer Profits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

6.6 Bidder Gains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

7 Discussion 53

8 Conclusion 56

A Empirical Regression Outputs 59

4

B Experimental Regression Outputs 60

B.1 Probability of Bidding . . . . . . . . . . . . . . . . . . . . . . . . . . 60

B.2 Probability of Exiting . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

C Experimental Documentation 62

C.1 Experimental Script . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

C.2 Experimental Instructions . . . . . . . . . . . . . . . . . . . . . . . . 64

C.3 Comprehension Test . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

C.4 Post Experimental Questionnaire . . . . . . . . . . . . . . . . . . . . 70

5

List of Figures

1 BidRivals.com website . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2 Payoff Schedule with Exit AV Option . . . . . . . . . . . . . . . . . . 22

3 Payoff Schedule with Exit BV Option . . . . . . . . . . . . . . . . . . 22

4 Kaplan-Meier Survival Estimates - Platform Comparison . . . . . . . 27

5 Hazard Rate Estimates - Platform Comparison . . . . . . . . . . . . . 27

6 Kaplan-Meier Survival and Hazard Rate Estimates - BidRivals.com

(giftcard) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

7 Kaplan-Meier Survival and Hazard Rate Estimates - BidRivals.com

(non-giftcard) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

8 Percentage Profit Histograms - Platform Comparison . . . . . . . . . 34

9 Revenue and RRP Scatter Plot - BidRivals.com . . . . . . . . . . . . 34

10 Auctioneer Gross Bid Revenue . . . . . . . . . . . . . . . . . . . . . . 35

11 Bidder Gains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

12 Experimental Auction Decision Screen . . . . . . . . . . . . . . . . . 40

13 Kaplan-Meier Survival and Hazard Rate Estimates - Experimental

Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

14 Average Predicted Probabilities of Decision to Bid . . . . . . . . . . . 48

15 Auctioneer Profits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

16 Auctioneer Profits and Cost of Goods . . . . . . . . . . . . . . . . . 51

17 Bidder Gains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

List of Tables

1 Summary Statistics - Empirical Data . . . . . . . . . . . . . . . . . . 30

2 OLS on Log-Transformed Final Bidding Rounds . . . . . . . . . . . . 32

3 Bidder Gains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4 Summary Statistics - Experimental Data . . . . . . . . . . . . . . . . 41

5 Bid Level Data Description . . . . . . . . . . . . . . . . . . . . . . . 45

6

6 Probit Marginal Effects of Decision to Bid . . . . . . . . . . . . . . . 46

7 OLS on Unique Bidders in an Auction: Coefficients . . . . . . . . . . 59

8 Probit Regression on Bidding Decision: Coefficients . . . . . . . . . . 60

9 Probit Regression on Exit Decision: Coefficients . . . . . . . . . . . . 61

7

Abstract

Online pay-per-bid or "penny" auctions are a relatively new type of auction

market which is rapidly gaining popularity online. The auction is character-

ised by small fixed bid increments, pay-per-bid bidding fees and a resetting

countdown timer with similarities to other all-pay auctions and the war-of-

attrition game. Empirically, estimates suggest that the auction allows the

auction operator (the sole seller of goods in the market) to collect average rev-

enues of up to 155% of the retail price, with average ending prices of around

25% of the recommended retail price. This paper seeks to extend the existing

literature by experimentally and empirically analysing the effect of an exit op-

tion, introduced by some operators, that allows participants to offset the cost

of purchasing the item at retail price with the sunk costs of previously paid

bidding fees. Our empirical analysis indicates that the exit option extends the

length of giftcard auctions while having an ambiguous effect on non-giftcard

auctions. Experimentally, we find the exit option provides auctioneers with

the potential for increased revenue through increased quantity sold per auc-

tion, along with lower volatility in earnings. Bidder welfare is also found to

be significantly higher, which suggests that the exit option may be pareto

improving.

8

1 Introduction

This paper investigates a relatively new type of online auction format that, as em-

pirical evidence suggests, allows the seller of a good to collect average revenues of

up to 155% of the value of the goods auctioned. The basic structure of the auction

is as follows:

• The price starts at zero and rises in fixed increments, the bid increment, (e.g.

$0.014) whenever a bidder places a bid.

• A fixed cost, the bidding fee, (e.g. $0.75) must be paid each time the bidder

places a bid.

• A count down timer, which resets (e.g. to 15 seconds) every time a bid is

placed, marks the close of the auction (once it reaches zero), the ending price

and the winning (last) bidder.

This auction was first introduced by Swoopo.com which began operations on Septem-

ber 2005. The mechanics of the pay-per-bid auction (also known as penny auctions

and pay-to-bid auctions) has parallels with the all-pay auctions and the war-of-

attrition game format. As with the classic all-pay auction (Shubik 1971), all bidders

pay a positive sum if they choose to participate in the auction, regardless of whether

they win or lose. The costly action required to become the winning bidder is also

reminiscent of the war-of-attrition game format. Key differences exists however, as

the main cost incurred by bidders come in the form of bidding fees, which are indi-

vidually small, and bidders are not required to place a bid every round in order to

stay in the auction.

However, what really sets this particular auction format apart from other non-

traditional auctions is the apparent success of its real world implementation, which

appears to be highly profitable for the website operator/auctioneer (who is the sole

seller of goods). As with other all-pay auctions, particularly the dollar auction, the

presence of sunk costs incurred from the bidding process seems to be a significant

9

factor in creating a dislocation between game theoretic predictions and actual ob-

served behaviour. Given the small bidding increments, empirical ending prices for

the auctions are typically 25% of the recommend retail price (RRP) of the item,

which when prominently advertised serves as effective enticement for potential bid-

ders. In effect, the losing bidders’ sunk bids subsidise the winning bidder’s payment

for the item with the remaining amount going towards the auction operator. The

auction can also be considered comparable to a lottery, where each bid is a lottery

on the chance that the timer will countdown to zero, or essentially the chance that

no one else places a bid/buys another lottery ticket.

Our paper focuses on one particular operator of this type of auction, Bid-

Rivals.com, which features a unique variation of the pay-per-bid auction. Bid-

Rivals.com offers the standard pay-per-bid auction with an exit option, the effect

of which has not been thoroughly studied within the existing literature.1 The exit

option allows bidders to purchase the item at the recommended retail price (RRP),

using their sunk bids in the auction to offset the cost of purchasing the item. This is

a unilateral option available to all bidders at any time during the auction and after

the auction ends, with the auction continuing unaffected should any bidder choose

to exercise it.

The exit option effectively caps the potential loss of the bidder to the RRP of

the good less their valuation and dramatically changes the characteristics of the

auction. Considering a bidder who would otherwise intend to purchase the item at

a retail store, the website allows the bidder to choose between purchasing the item

at a physical store (the inherent outside option, potentially below the RRP); or

some unknown chance of attaining the item at a price below RRP in the auction or

at a maximum of the RRP. The difference between the store price and RRP would

effectively be the cost of entering into the prospect.1The literature has thus far, with the exception of Byers et al. (2010), has not explicitly

addressed the implications of this exit option. Existing studies have thus far only concerned theoriginator of the auction format - Swoopo.com.

10

Our main questions deals with how bidder behaviour is affected by the presence

of the exit option and how this translates into differences in auction outcomes.

Secondarily, such differences may help explain why BidRivals.com, among other

operators, have decided to implement this feature.2

Given the particulars of this mechanism and its potentially exploitative design,

it is not surprising that there have been concerns about whether this type of market

should be treated as a form of gambling and regulated as such. The potential for

unlimited losses, in the standard auction, and an unknown chance of winning the

item would give weight to this particular argument (although it is worth considering

that these factors are not determined by the auctioneer but rather the actions of

the other bidders). The introduction of the exit option may represent a response to

such criticism.

Alternatively, operator profits may simply be higher for platforms which offer

this exit option. This would hold true to the extent that increases in revenue from

bidding and bidder participation offset bid revenues refunded from bidders exercising

the option.

Since this development in the growing online pay-per-bid auction space has not

yet been thoroughly explored and the feature dramatically changes the functioning

of the auction, it represents an interesting and important avenue of research.

This paper approaches the research question by utilising a mix of methods, firstly

by making theoretical predictions regarding the effect of the exit option on bidding

behaviour, then through the collection and analysis of empirical data on the auction

platform and lastly in utilising complementary experimental data to account for the

limitations of the theoretical and empirical analysis.

We find that the exit option does indeed influence bidding behaviour as predicted

by the theoretical model, resulting in longer lasting auctions. Bidder welfare is

unambiguously improved by the introduction of the exit option but auctioneer profits

from offering the exit option are heavily dependent profit margins of goods auctioned.2It is worth noting that Swoopo.com introduced this exit option in 2009 and a number of other

penny auction clones have also adopted this mechanism in recent years.

11

While Exit auctions provides the autioneer with lower bid revenues, more items are

sold per auction compared to No Exit auctions. Given a low enough cost of goods

sold, the Exit auction has the potential to be welfare pareto improving.

In Section 2, we provide further details regarding the auction. Section 3 presents

the existing literature on pay-per-bid auctions that we draw upon for our analysis.

Section 4 sets up the theoretical framework from which we form our predictions for

the exit option. In Section 5, empirical data of pay-per-bid auctions with an exit

option is compared to existing studies of the standard pay-per-bid auction. Section 6

details our experimental setup and analysis of experimental data. Section 7 contains

a discussion of our results and Section 8 concludes.

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2 Auction Details

In this section we provide some further details regarding the functioning and prac-

ticalities of BidRivals.com’s pay-per-bid auction website.

Potential bidders are able to view the progress of all currently running auctions

from the main web page where up to 10 auctions may be active at any one time.

Bidders may also view details of recently concluded auctions. The types of items

auctioned at any time range from $15 gift cards to high priced electronics like tele-

visions and smart phones (all brand new). Typically, auctions of high priced items

are interspersed with a greater quantity of low priced items. New items are seeded

on the site with a high initial timer, allowing bidders to see what potential items

may be actively bid upon in the future.

If bidders wish to place a bid, they must first create an account and pre-purchase

bidding packs of 20, 50 or 100 bids (at US$0.75 per bid). Every time a bid is placed,

the auction price increments by US$0.015 and the timer of that auction resets to 15

seconds if it is currently below 15 seconds.3 If the timer reaches 0 without any bids

being placed, the last leading bidder wins the auction and pays the auction price.

At any time, bidders are provided with information regarding the last 10 bidders

(username, price bid was placed and whether a BidAgent was used) with the timer

being updated in real time. An example is shown in Figure 1.

Figure 1: BidRivals.com website

As the pay-per-bid auction platform is accessible to any individual with an inter-3Since the price rises in fixed increments, it is not possible to engage in jump bidding.

13

net connection, the potential pool of bidders is essentially worldwide, with auctions

running 24 hours of the day. This also means that auctions can be in active bidding

(in the 15 second countdown phase) for a prolonged period of time. As such, an

increase in new entrants would likely lead to auctions lasting longer and a lower prob-

ability of winning. Country specific webpages (portals) provide localised prices but

differ only in the interface, allowing access to the same pool of auctions worldwide.

BidRivals.com, as is common practice among other operators, allow the use of

a BidAgent, which will automatically place bids based on parameters set by the

bidder. The BidAgent will place bids at approximately 10 seconds left in the timer,

for as many bids as the bidder dictates or until a maximum auction price set by the

bidder is reached, whichever is reached first. Multiple BidAgents within the same

auction will bid sequentially in different rounds of the auction.

At any time during or after the auction ends, the bidder can elect to exercise

the exit option. The RRP, total auction bids placed and net payment required to

purchase the item is calculated for the individual and shown on a separate section

of the bidding screen.

A shipping and handling fee of approximately 10% of the RRP must be paid if

an item is won or bought using the exit option regardless of whether the item is

physically delivered or not.

Some auctions also features special additional characteristics. No BidAgent auc-

tions disallow the use of a BidAgent, bonus auctions have a reserve price under

which bids are refunded at a rate of 150%, beginner auctions which only allow bid-

ding from users who have not won an item before and no-buy-now auctions which

do not allow the use of the exit option.

14

3 Literature

Since the pay-per-bid auction has only existed since 2005, the literature for this

auction format is still developing. Several papers have emerged in the last few years

to investigate the various theoretical and empirical aspects of the auction design.

To date, all papers have focused on Swoopo.com. In this section we present a brief

summary of the literature.

Augenblick (2009) presents one of the most comprehensive analyses of the pay-

per-bid auction format. The author characterises a theoretical model based on

fully symmetric Markovian bidders with a common valuation. A mixed equilibrium,

where bidders bid such that their expected profits from bidding equals their expected

losses, exists where bidders and auctioneers make expected profits of zero. It is then

extended through the consideration of naive bidders who experience regret and are

susceptible to the sunk cost fallacy. While the base model fails to account for the

amount of bidding that is empirically observed, the extensions to the model do

assist in explaining the over-bidding that occurs. Examination of the theoretical

and empirical hazard rates4, which diverge as the number of bids placed increases,

also leads the author to extrapolate that the sunk cost fallacy might play a role in

driving bidder behaviour in the auction. Further, supply side issues of the auction

design, like the examination of optimal supply given the number of active bidders

and the significant start-up costs of attracting a large user base serve as a barrier

to entry to most clones of the original site are discussed.

Ockenfels, Tillmann & Wambach (2010) augment their own base theoretical

model which is structurally similar to Augenblick’s (2009) and consider reference-

dependent preferences and loss aversion as potential explanations of the observed

bidding behaviour of participants within the auction. The authors find that the

reference-dependent model assists in explaining the abnormal bidding behaviour

seen within the empirical data. Additionally, an experimental form of the auction

game is conducted in order to test the reference-dependence hypothesis and the4The probability that an auction terminates at a given number of bids placed.

15

predicted effects of changing the number of bidders and the bidding increment.

Increase in bidders permitted to participate in an auction appears to increase the

overall bidding, but reduces per-participant bidding. The authors’ empirical and

experimental research also leads them to conclude that no obvious optimal strategy

exists for the auction format.

Byers, Mitzenmacher & Zervas (2010) take an alternative approach by utilising a

number of simulation models, which incorporate asymmetric information, to explain

the observed over-bidding. In particular, they find that asymmetries in bidding fees

and perceived number of bidders are responsible for the significant profits of the

auctioneer. The authors are also one of the few in the literature to consider the

impact of shill bidding and the exit option on the auction platform. They consider

the exit option under a situation where two separate classes of bidders exist to form

the bidder population. When one subset of bidders commits to purchase the item,

and to the extent that their bidding behaviour does not affect the bidding beha-

viour of non-committed players, overall bidding and auction length should increase.

The longer the player commits to stay in the auction, the higher the profit for the

auctioneer, although this may be offset by the cost of supplying an additional item

on the exercising of the exit option. Where two or more players commit to stay in

the auction, the auction devolves into a game of chicken which results in ambiguous

predictions for the profit of the auctioneer. Under the particular conditions imposed

in the system, the exit option has the potential to lead to higher auctioneer profits.

Platt, Price and Tappen (2010) observe that a significant majority of bidding

behaviour can be accounted for even under assumptions of risk neutrality. Bidding

in high price video game consoles is found to be the exception which would require

the presence of risk-loving participants. The authors equate the auction to an in-

cremental king-of-the-hall contest and discuss the possibility of using the auction to

model rent seeking behaviour.

Nanney (2010) provides a comprehensive theoretical exploration of the pay-per-

bid auction which includes the consideration of an asymmetric equilibrium, imperfect

16

information between bidding groups and a basic model of auction entry. The author

also considers the auction in the form of lottery to assist in explaining the over

bidding observed.

Since pay-per-bid auctions are essentially a type of all-pay auction, it is worth

noting the contribution of Shubik (1971) who laid the foundation for non-standard

auction formats with the introduction of the dollar auction. Consistent over bidding

in all-pay auction experiments as in Gneezy and Smorodinsky (2004) hold parallels

with the over bidding in pay-per-bid auctions. Despite this, theoretical support from

the existing all-pay literature is limited due to a distinct difference in the structure

of pay-per-bid auctions. Whereas standard all-pay auctions and war of attrition

games can be modelled as a static game (Baye, Kovencock and Vries (1996) and

Bulow and Klemperer (1999)), characterisation of the pay-per-bid auction is more

complex. This is due to the way in which bidding fees are incurred. In a war of

attrition game, for example, costs are a direct function of the number of rounds in

which participants choose to remain in the game. This allows for the reduction of

the game to a decision concerning the number of rounds to remain contingent on the

bidder’s valuation. In the pay-per-bid auction, the bidding decision can be made in

every round of the game regardless of whether they chose to bid previously or not.

17

4 Model

In this section, we briefly replicate the standard theoretical model developed by Au-

genblick (2009). Others, for example Platt et al. (2010), Ockenfels et al. (2010) and

Hinnosaar (2010), developed similar models. Despite the inability of the standard

model to explain the profitability of this auction format, it serves as an informative

baseline to which we can anchor our empirical and experimental analysis. Although

a complete model of the pay-per-bid auction with an exit option is beyond the scope

of this thesis, we also discuss the theoretical implications of this option on bidding

behaviour.

4.1 Baseline Model

We consider fully symmetric, rational and risk-neutral bidders who have full inform-

ation about the game. Let us define n as the number of bidders in the auction, each

of which share the same valuation v. The bidding fee f is paid each time a bid is

placed and accepted as the current highest bid. For simplicity, we assume that when

more than one bid is placed in any round t, the bid which is actually accepted is

randomly chosen with equal chance. We denote the bidding increment, the incre-

ment by which the ending price rises every time a bid is accepted, as m. As such,

the current ending price in any round t to be given by tm.

Within the theoretical framework, the auction begins at a price of 0 and in each

round t, all non-leading bidders make a decision whether to place a bid or not. If

all non-leading bidders do not place a bid, the game ends and the leading bidder in

the last round wins the auction and pays the ending price. Since the ending price

increments as the auction proceeds, there is a final round of the auction where no

bidders will bid. This occurs when the value of the item gained from winning v less

the bidding fee f is lower than the ending price of the auction that must be paid

tm. This is simply given by v − f = tm, which allows us to denote the final round

of t̄ = v−fm − 1.5

5Note that this only occurs if mod(v − f,m) �= 0. Where mod(v − f,m) = 0, there exist many

18

Knowing the last round of the auction allows us to employ backwards induction

to solve for the Subgame Perfect Nash Equilibrium. Since all bidders know that

no one will bid at the t̄th round as all players gain zero payoff from bidding, n− 1

bidders will bid with certainty in round t̄− 1 as being selected as the leading bidder

allows them to win with certainty. Given this, no one will bid in round t̄ − 2, and

the iterative process repeats until the start of the game where all bidders bid with

probability 1 at round 1 and cease bidding or no one bids, depending on whether k̄

is odd or even. However, this leads to a trivial equilibrium which unsatisfactorily

provides a prediction of no bidding.

Alternatively, we can look to a mixed equilibrium where bidders bid with a

probability such that they are indifferent between bidding and not bidding. This

mixed equilibrium is considered useful within the literature as it predicts positive

probability of bidding such that any round before the final round can be reached.

Since the end of an auction occurs when no bidders submit a bid, we can express the

termination probability in terms of each bidder’s probability of bidding. Each bidder

i’s Markov strategy set consists of a bidding probability for every period where he

is not a leader {pi0, pi1, pi2...pit̄} where pit ∈ [0, 1]. The hazard rate or termination

probability can therefore be given by:

h̃(t, lt) =

�ni=1(1− pit)

1− pltt

Where lt denotes the leader at time t. As no leader exists at t = 0, the hazard rate

at that time is given by h̃(t, lt) =�n

i=1(1− pit).

With the probability of bidding and probability of termination defined, we can

now state the point of indifference where the payoffs available to each bidder from

bidding and not bidding are equal given their bidding probability as h̃(t, lt).(v −

tm) = f . More succinctly, the hazard rate when the indifference condition is satisfied

is given by h̃(t, lt) = fv−tm . Which simply states that the probable payoff from

winning the auction must equal the cost of bidding in the auction. As all non-

equilibria.

19

leading bidders are symmetric, each individual bidder’s probability of bidding can

be backed out by the probability a bid is placed, split between each n−1 non-leading

bidders, pit = n−1

�1− f

v−tm .

The model also simplifies the situation by assuming that bidding will occur with

certainty in the first round. This is driven by the intuition that if no bidding occurs,

the auction operator can simply re-list the item costlessly and thus the auction never

actually terminates at t = 0.

As such, in equilibrium, the following holds:

pit =

1 for t = 0

n−1

�1− f

v−tm for 0 < t ≤ t̄

0 for t > t̄

and

h̃(t, lt) =

0 for t = 0

fv−tm for 0 < t ≤ t̄

1 for t > t̄

The revenue predictions for the model can be understood intuitively. As the ex-

pected profits for bidders in each round are zero, auctioneer profits from each round

are similarly zero. This particular aspect of the framework and its congruency with

the traditional auction literature on revenue equivalence adds to the attractive-

ness of this particular equilibrium. Augenblick’s (2009) theoretical model therefore

provides us with an informative baseline of bidding behaviour at which no profits

can be elicited.

4.2 Exit Option

As discussed previously, the exit option allows any bidder at any time during the

auction to unilaterally purchase the item at the recommended retail price (RRP)

20

less their sunk bidding costs in that particular auction.

Efforts to implement the exit option within the existing theoretical framework

yielded unsatisfactory results, with extensions leading to increased complexity and

associated difficulty in finding an equilibrium. This is due in part to payoffs from ex-

ercising the exit option changing based on past history which affects the probability

of bidding asymmetrically for individual bidders.

That said, there are a few predictions that can be made. In instances where

the RRP (i.e. the exit option price x) is lower than the value (we refer to this

situation as Exit AV (exit price above valuation)), and there is no other outside

option available to a bidder, then exiting the auction before t > t̂i = x−bifm is a

weakly dominated strategy (where bi represents number of bids placed by bidder i).

In other words, bidders should continue to bid in the auction, such that the Hazard

rate must equal 0 until t = max(t̂i). Things become more complicated when making

the more realistic assumption that the RRP is larger than the value, or if there exists

a viable outside option. Then, a bidder is essentially choosing between purchasing

the item at a physical store; or some unknown chance of either a) attaining the

item at some price below RRP in the auction, b) buying at the RRP after a certain

amount of bidding costs have been accumulated, thereby capping the losses, or c)

making a loss in the size of a smaller amount of bidding costs. We refer to this

situation as Exit BV (exit price below valuation).

Figures 2 and 3 on the following page depict the payoff schedule for bidders as

they incur sunk bids under Exit AV and Exit BV conditions, respectively. At each

state of sunk bids, the potential payoffs of winning the auction, losing the auction

(not bidding) and exercising the exit option are shown. The parameterisation as-

sumes a valuation of $20, a bidding fee of $0.50 and exit prices of $16 and $26,

respectively, for Exit BV and Exit AV.6 Payoffs from winning and losing decline

linearly as the number of sunk bids increase whereas payoffs from exercising the exit

option are invariant to sunk bids, as the latter are used towards offsetting the exit6We ignore bidding increments in this instance as the effect on the payoff schedule is minimal.

21

price payment.

Figure 2: Payoff Schedule with Exit AV Option

The exit option essentially caps the potential losses that can be incurred by

bidders. In the Exit AV example, once a bidder has incurred more than 12 bids,

the exit option can be exercised to cap losses at $6, which allows the bidder to bid

costlessly past that point. Bidding should therefore be a weakly dominant strategy

past this kink point (until gains from winning fall below the capped losses), which

we refer to as the Valuation Exit Threshold (b̂i = v−xf ).

Figure 3: Payoff Schedule with Exit BV Option

In the case of Exit BV auctions, bidding is a weakly dominant strategy from the

22

beginning of the auction. However, past 30 sunk bids, payoffs from bidding actually

falls below payoffs from exiting. Although bidding remains a weakly dominant

strategy till that point, given the diminishing gains from staying in the auction, cost

of effort may lead bidders to exit before reaching that point.

23

5 Empirical Investigation

Similar to other online auction operators and operators of the pay-per-bid auction

format, BidRivals.com displays a range of real time data for each auction in pro-

gress. On the auction level, each auction web page contains information about the

product being auctioned (product name, item description, RRP) and auction spe-

cific information (auction ID, auction type). On the bid level, real time information

is pushed through to the web page, with the current count down timer, current

ending price and information regarding the last 10 bidders (user id, time stamp, bid

agent indicator) being displayed.

Our analysis methodology involves the replication of the duration analysis un-

dertaken by Augenblick (2009). Although Swoopo.com and BidRivals.com feature

different bid increments, bidding fees and product composition, comparison of met-

rics across the two auction platforms is undertaken as a reference point to exist-

ing literature. Duration analysis is employed to characterise differences between

Exit and No Exit auctions and ordinary least squares regressions are carried out to

parametrically isolate the effect of the exit option. Additionally, our analysis also

highlights the shortcomings of the empirical data, and motivates the complementary

experimental analysis undertaken in Section 6.

In this section, we first describe the procedure undertaken to collect our data

and follow it up with a comparison between Swoopo.com and BidRivals.com. We

then investigate the differences between exit and no exit option auctions within

BidRivals.com. Lastly we provide some tentative analysis of the auctioneer profits

and bidder gains.

5.1 Data Collection

Since bid level data is displayed and discarded as new bids are placed, and auction

level data also expires relatively quickly, it was necessary to program a spider to

continuously monitor, track and record the data available on the website. The spider

was developed in C# using Microsoft Visual Studio 2010, and incorporates the use

24

of a SQL Server Database for the storage of data. Specifically, the spider monitors

JSON strings transmitted from the BidRivals.com’s server to the web browser and

parses the data stream to track updates to auctions and the bids placed within those

auctions. The information is then collated by the program and stored within the

database. By utilising the information sent from the server in its raw form, just as

the web browser does when it fetches information from the server, our dataset has

the advantage of ensuring that the data captured is consistent with the information

on which the auction operator actually acts upon. Consequently, our dataset should

possess a better signal to noise ratio in respect of timing and ordering data when

compared to other datasets employed in the literature which have been captured

second hand from the web browser.

Collection began 1 July 2011 and ended on 31 August 2011. The complete

dataset consists of 34,402 auctions comprising of 2,743,145 individual bids from

29,176 unique bidder accounts. Collection was undertaken through the Australian

web portal.7 Primary and backup servers were utilised simultaneously to minimise

the chance of missed or corrupted data. Missing data arising from hardware and

software failures were corrected by the merging of the separate databases. Essentially

all auctions recorded held complete records of all bids placed. In instances where

both the main and off site servers failed, incomplete observations (0.01%) were

removed from our analysis dataset.

For our duration and regression analysis, we disregard all “in house” goods auc-

tioned by BidRivals.com given the unique nature of the goods. These “in house”

goods include bid packs and discount cards for other auctioned items. Although

such items, which comprise of 83% of all items auctioned and are priced between

$15 to $100, are likely to influence bidder behaviour, we restrict our analysis to

auctions concerning tangible real-world goods for clearer interpretability of results.7Essentially all items accessible from the Australian web portal are items accessible from every

other country specific portal. The only issue of note is that No Exit auctions are not available forthe US portal. To the extent that the bidder base is internationally diverse, this should not posea significant issue, but this remains a potential source of bias for our analysis.

25

5.2 Duration Analysis

In this subsection we compare the hazard rates predicted by the theoretical frame-

work with empirical hazard rates observed in our dataset. Duration analysis seeks to

characterise the probability that auctions reach a particular ending price and allows

comparisons between theoretical and empirical hazard rates. Survival rate refers

to the percentage of auctions in the sample still undergoing bidding at a specific

normalised round. Hazard rates refer to the probability of an auction ending at

a specific normalised round conditional on it reaching that normalised round. We

approximate the empirical survival and hazard rates within our auctions using the

Kaplan-Meier product-limit estimator.8 Comparison of theoretical and empirical

survival estimates and hazard rates serves as a useful first point of analysis as it

provides an aggregate indication of the extent to which bidding behaviour differs

across auction platforms and from theoretical predictions.

5.2.1 Platform Comparison

Figure 4 on the next page presents Augenblick’s (2009) survival estimates for Swoopo.com9

(left-hand side graph) and survival estimates for auctions within our BidRivals.com

dataset (right-hand side graph) which disallowed the exit option. Despite Swoopo.com

and BidRivals.com featuring different bid increments, bidding fees and goods being

auctioned, a comparison can be made with the assistance of the theoretical baseline

(dashed line).

The analysis undertaken by Augenblick (2009) shows that auction survival rates

far exceed those predicted by the author’s theoretical model. Interestingly, our

BidRivals.com survival estimates do not lie entirely to the right of the theoretical

prediction. For normalised rounds less than 20, the proportional of auction surviving

up to that round is actually less than suggested by theory. For normalised rounds8Auction data is normalised by setting each auction’s ending number of bids relative to their

RRP value normalised to 10, see Augenblick (2010). This normalisation allows comparison ofhazard rates across goods of different values.

9Survival estimates reported here pertains to auctions (n=7861) with a bid increment of $0.01(Augenblick 2009). Underlying data for the Augenblick graphs could not be obtained.

26

Figure 4: Kaplan-Meier Survival Estimates - Platform Comparison

Swoopo.com (Source:Augenblick 2009) BidRivals.com (No Exit auctions only)

Theoretical (Dashed), Empirical (Solid)

greater than 20, the survival rates deviate in a manner more similar to Swoopo.com.

Figure 5: Hazard Rate Estimates - Platform Comparison

Swoopo.com (Source:Augenblick 2009) BidRivals.com (No Exit auctions only)

Theoretical (Dashed), Empirical (Solid)

Figure 5 reports Swoopo.com and BidRivals.com’s respective hazard rates for No

Exit auctions. Smoothed hazard estimates show that the termination probability

at any normalised round is less than predicted.10 The lower than predicted survival

probabilities observed previously are no longer present after smoothing, although

early normalised round hazard rates remain relatively high. Both platforms’ hazard

rates seem to maintain a termination probability around half that of the theoretical

predictions.

For the most part, results for Swoopo.com and BidRivals.com are fairly similar,

with both exhibiting survival and hazard rates that deviate from the theoretical10The sharp increase in hazard rates above the theoretical prediction past 150 normalised rounds

is attributed to the lack of observations at that level.

27

prediction.

5.2.2 Exit and No Exit auctions

We now turn to differences between Exit and No Exit auctions within BidRivals.com.

For this analysis we separated auctioned items between categories and observed sig-

nificantly different effects of the exit option for giftcards being auctioned in com-

parison to the other items on offer. Giftcards auctioned range from $15 to $100 and

are redeemable at a range of prominent online retailers like Amazon.com. These

giftcards are essentially pure common value items which allows for a cleaner ana-

lysis.11 Non-giftcard auctions are in contrast subject to less predictable valuations,

with the analysis of the category complicated by a wide range of consumer goods

with uncertain valuations.

We report survival and hazard rate estimates for giftcard auctions in Figure 6.

Figure 6: Kaplan-Meier Survival and Hazard Rate Estimates - BidRivals.com (gift-card)

The effect of the exit option is clear, survival estimates across all normalised

rounds are strictly higher for Exit auctions compared to No Exit auctions. The

effect on hazard rates show that termination probabilities in the Exit auction are

initially much lower than the No Exit auction. However, as the auction progresses

the Exit auction hazard rates proceed to cross over and back under those of the11Recall that since shipping and handling must still be paid, the giftcard auction is an Exit AV

auction. The value of the giftcard may also be worth less to the individual depending on theirpropensity to shop at that particular retailer. The pure value nature of the items also closelyresembles our experimental implementation in Section 6.

28

No Exit auction. The difference between No Exit and Exit auctions are significant

according to a Mantel-Cox test with a p-value of 0.0000.12 A possible explanation

would be that bidders are initially attracted by the fail-safe provided by the exit

option, which drives termination probability down. This may be a result of increased

participation by bidders or increased in bids per bidder. Bidding is then maintained

by bidders entering the Valuation Exit Threshold until bidders begin exercising the

exit option. From the perspective of the No Exit auctions, the naive sunk cost

fallacy argument proposed by Augenblick (2009) appears to apply with termination

probability decreasing, relatively to the theoretical prediction, as bids are placed.

The cross over of hazard rates would seem to suggest that an exit option encourages

initial bidding, but nullifies the sunk cost effects experienced further into the auction.

It is however important to note the tentative nature of such an analysis as normalised

rounds represent the aggregate number of sunk bids distributed non-evenly among

many potential bidders.

Figure 7 depicts survival and hazard rate estimates for non-giftcard auctions.

Figure 7: Kaplan-Meier Survival and Hazard Rate Estimates - BidRivals.com (non-giftcard)

In contrast to gift cards auction, the exit option for remaining items (consist-

ing mostly of consumer electronics worth $100 - $1500) significantly reduce survival

probability (p-value of 0.0236). Hazard rates for Exit auctions are also consist-

ently higher than those of the No Exit auction. For the No Exit auctions, survival12In the absence of censored data, as in our sample, the Mantel-Cox logrank test is equivalent

to a Mann-Whitney U test.

29

probabilities are strictly higher than predicted. A possible explanation for the dif-

ference may be that the predominately higher priced items in this analysis leads to

a stronger susceptibility to the sunk cost effect, which overshadows any effects of

the exit option in encouraging bidding.

5.3 OLS Analysis

To further isolate the effects of the exit option, we undertake ordinary least squares

parametric analysis on the number of bids (round) reached by each auction. Sum-

mary statistics broken up by giftcard and non-giftcard auctions are displayed in

Table 1

Table 1: Summary Statistics - Empirical DataObs. Mean Std Dev. Min Max

Giftcard auctions 3664Bids 63.09 125.82 2 2127RRP 28.21 19.10 15 100

Beginner Feature 0.05 0.21 0 1Bonus Feature 0.00 0.02 0 1Exit Feature 0.16 0.37 0 1

No BidAgent Feature 0.17 0.38 0 1Unique Bidders 4.62 3.35 1 40

BidAgent Bids % 0.43 0.31 0 0.99BidAgents % 0.44 0.32 0 1

Non-giftcard auctions 2107Bids 484.72 1211.75 2 19909RRP 261.15 291.47 26 1599

Beginner Feature 0.02 0.12 0 1Bonus Feature 0.28 0.45 0 1Exit Feature 0.87 0.17 0 1

No BidAgent Feature 0.00 0.05 0 1Unique Bidders 18.41 27.63 1 395

% of BidAgent Bids 0.63 0.26 0 0.99% of BidAgents 0.34 0.19 0 1

******** ******** ******** ********Note: % of BidAgent Bids refers to the percentage of bids made by BidAgents

Note: % of BidAgents refers to the percentage of bidders who used a BidAgent at least once

Of note in our summary statistics, exit option auctions are far more prevalent in

non-giftcard auctions (87%) compared to giftcard auctions (16%). The value of the

30

goods are also a point of distinction between the two classes of auctions. BidAgent

bids also make up a larger percentage of non-giftcard auctions (63% vs. 43%) despite

less bidders employing the use of a BidAgent (34% vs. 44%).

Our regression analysis on log-transformed (non-normalised) final bidding rounds

(Table 2) corroborates the effects found in our duration analysis. Models (GR1) and

(NR1) isolate the effect of having an exit option for giftcard and non-giftcard auc-

tions, respectively, whilst models (GR2) and (NR2) incorporates separate dummies

for each observed type of auction (where one auction may contain more than one

feature). For giftcard auctions, the presence of an exit option increases the length

of the auction by a significant 30.16% holding all other variables constant. For

non-giftcard auctions, the effect is not significant. Auctions with both an exit and

no BidAgent feature increases final bidding round by a significant 142% in giftcard

auctions.

We also observe that the ending round increases by 4.2% for every 1% increase

in the proportion of BidAgent bids. Conversely ending round decreases by 2.4% for

every 1% increase in the proportion of bidders who employ a BidAgent.

31

Table 2: OLS on Log-Transformed Final Bidding RoundsGiftcard Non-giftcard

(GR1) (GR2) (NR1) (NR2)RRP 0.0197*** 0.0173*** 0.0022*** 0.0020***

(0.0010) (0.0010) (0.0001) (0.0001)No BidAgent 0.8227***

(0.0711)Exit 0.3501*** 0.3016*** -0.4024** -0.4980

(0.0507) (0.0539) (0.1650) (1.1306)Exit and No BidAgent 1.4153*** 3.3351

(0.1273) (1.2202)Bonus 0.1148

(1.1362)Bonus and Exit -0.3207

(1.1283)Beginner -0.3706***

(0.0967)Beginner, Bonus and Exit -0.4620 -0.5751

(0.7451) (1.1488)% of BidAgent Bids 0.0384*** 0.0422*** 0.0438*** 0.0447***

(0.0009) (0.0010) (0.0012) (0.0012)% of BidAgents -0.0261*** -0.0235*** -0.0247*** -0.0242***

(0.0009) (0.0009) (0.0017) (0.0017)Constant 1.9912*** 1.6558*** 2.7287*** 2.7489**

(0.0447) (0.0625) (0.1835) 1.1330

Adjusted R2 0.4350 0.4722 0.5490 0.5630N 3664 3664 2107 2107

Note: * p-value < 0.10, ** p-value < 0.05, *** p-value < 0.01

Additionally, a OLS regression on the number of unique bidders show that the

Exit auctions attracts an extra 2.29 unique bidders for giftcard auctions (p-value

of 0.000) and non significant numbers for non-giftcard auctions (regression output

available in Appendix A on page 59). This result is consistent with the exit option

being an attractive feature for bidders as it caps any potential losses.

5.4 Auctioneer Profits

An obvious metric of interest for auction market mechanisms and particularly pay-

per-bid auctions is the revenue and profits that can be obtained.13 We restrict our13Since BidRivals.com has its headquarters in the US, we restricted our analysis to the US Dollar.

To the extent that a majority of bidders originate from the US, this should not greatly affect our

32

calculation to revenues given the difficulties associated with determining the op-

erating costs and wholesale per unit costs of obtaining the items for the operator

(with the exception of the Swoopo.com and BidRivals comparison). On the surface,

our estimations indicate that as a whole, bids and ending price payments provide

revenues of 155% of the RRP, which appears consistent with the level of profitab-

ility reported in the no exit pay-per-bid literature.14 To arrive at this number, we

multiplied all bids placed in our dataset by the bidding fee of AU$0.70 and added

on revenues owing to the final ending price paid by the winner.

It is worth noting there exists clear limitations to calculations of the profitability

of (most) pay-per-bid auctions. Given the international nature of a website auction

and localised portals for individual countries, revenue can be influenced by currency

fluctuations. Country specific portals charge localised prices for bidding fees but no

information is available on the origin of bidders. Additionally, items of equivalent

value may be substituted in localised auctions despite bids being pooled across all

portals. As such, revenue calculations may be exaggerated or understated.

Even more importantly, with our focus of the exit option, the use of this exit

option is not reported by the auction operators. The effect of the exit option on

profitability would not only depend on the frequency of use and when individuals

exercise the option but also on the secondary effects of enticing (or discouraging,

if bidders feel there will be increased competition) bidders to place additional bids.

Since an exercise of the exit option does not necessary reduce the revenues from the

bidder if the sunk costs are less than the difference between the wholesale value and

the RRP (exit price), it is not clear whether our calculations actually overstate or

understate total revenues and profits.

Figure 8 on the next page shows Swoopo.com and BidRivals.com have markedly,

different profit percentage profiles and this is likely owing the differing item compos-

analysis. For this aggregate analysis only, we also include “in house” items previously excluded toadjust for bids won rather than bought.

14Augenblick (2010) reported auction revenues of over 150% of the lowest market price of thegoods (from amazon.com). Nanney (2010) computed an average 70% profit margin in the Byerset al. (2010) dataset.

33

Figure 8: Percentage Profit Histograms - Platform Comparison

Swoopo.com (Source:Augenblick 2009) BidRivals.com

ition presented on the respective platforms. BidRivals.com features a larger range

of low price (filler items) which more easily end with no bids being placed, which

accounts for the spike seen in the graph. The notably noisier distribution may be a

symptom of the ending behaviour of the distinctly different classes of goods on offer

(high price electronics versus low price filler items).

Figure 9: Revenue and RRP Scatter Plot - BidRivals.com

Figure 9 provides a representation of the composition of items auctioned in Bid-

Rivals.com in terms of RRP and ending prices reached. A large proportion of items

auction are below US$500. It is also clear that the pay-per-bid auction format

provides the potential for extremely high earnings for auctioneers on individual

products. Case in point, the highest data point in Figure 9 comes from the auction

34

of a high end “iPad” which held a RRP of US$1,199. That particular auction ended

at an ending price of US$312.48, with 20,893 bids having been placed, leading to

revenues of US$15,936.48 for the auctioneer. The winner of that particular auction

placed a total of 89 bids, at a cost of US$66.75 which when combined with the end-

ing price paid results in a price saving of approximately 58%. This is of course an

extreme example, but it highlights the potential for profits in this auction for both

the auctioneer and the winner at the cost of the losers.

Figure 10: Auctioneer Gross Bid Revenue

In terms of Exit and No Exit auctions, revenues as a percentage of good value

is as expected given the preceding analysis of bids. Exit auctions for giftcards earn

auctioneers higher bid revenue compared to No Exit auctions.

5.5 Bidder Gains

A variation on the investigation of revenues earned by the auction operator is the

gains and losses incurred by the participating bidders. Figure 11 on the following

page depicts the profits and losses incurred by each unique bidder (ordered by net

gain ascending from left to right) within our dataset, over the course of collection.

We assume all bidders value the item at the RRP in calculating their net gain or loss.

Since we do not observe the use of the exit option, net losses are likely over-stated

in this analysis. As expected given the auction format, a large majority of bidders

(96.12%) incur losses and only a small minority makes gains, although such gains

can be significant for a proportion of such bidders. A significant majority of bidders

35

place very few bids and appear to never bid again.

Figure 11: Bidder Gains

Net gain of zero (Dashed Line)

Interestingly, bidders at the extremes of gains and losses in our sample have

similar characteristics in terms of bids placed and value of items won. Given the

limited time frame during which we captured data, it may be possible that these

“experienced” bidders fluctuate around incurring large losses and large gains. Over

the long term, this may be indicative of a bidding strategy and outcome that reflects

bidding as predicted by the theoretical model. As such the transient bidders who

place a low volume of bids and win few items, may actually form the bulk of the

operator’s revenue base. These characteristics are consistent across both giftcard

and non-giftcard auctions as well as Exit and No Exit auctions.

36

Table 3: Bidder GainsObs. Mean Std Dev. Min Max

Giftcard No Exit auctions 1521Cost of Bids 109.40 359.53 0.75 6748.50

Value of Items Won 99.05 286.51 0 3554.00Net Gain/Loss -10.35 169.14 3194.50 1028.50

Giftcard Exit auctions 721Cost of Bids 156.25 407.18 .75 4452.75

Value of Items Won 113.52 406.50 0 4510.00Net Gain/Loss -42.75 216.11 -2202.75 1785.50

Non-giftcard No Exit auctions 3874Cost of Bids 264.78 1009.51 0.75 18820.50

Value of Items Won 191.74 1120.42 0 28560.00Net Gain/Loss -73.04 558.12 -12797.25 13764.75

Non-giftcard Exit auctions 820Cost of Bids 123.25 323.92 0.75 4997.26

Value of Items Won 71.04 448.15 0 7252.00Net Gain/Loss -52.22 319.57 -2092.00 4497.75

******** ******** ******** ********

Summary statistics for bidder gains separated by giftcard and non-giftcard auc-

tions and Exit and No Exit auctions are reported in Table 3. While mean bidder

losses are larger for Exit auctions compared to No Exit auctions for giftcards, the

opposite holds true for non-giftcard auctions. However, few solid conclusions can be

drawn from this when bidder’s use of the exit option is not observed.

37

6 Experimental Investigation

Given the key limitations of the empirical study of pay-per-bid auctions, notably,

the lack of data on use of the exit option, it is difficult to empirically analyse the true

effects of this change in auction mechanism. As such, an experimental study serves

to complement the existing analysis through the examination of factors of interest

not typically observable in the empirical data, whilst allowing for the control of

factors outside the scope of our analysis.

As standard with experimental studies, our analysis of experimental data will

focus on treatment effects of the control and with exit option treatment as opposed

to metrics within treatments. Our conclusions should be robust to the extent that

inherent differences in conditions within a laboratory environment and the abstrac-

tions made in the implementation of the auction format are not correlated with our

variable of interest, the exit option.

In this section we begin by detailing our experimental design and implementation

and presenting summary statistics of interest. Then we undertake auction level

duration analysis which is designed to describe aggregate behaviour in the auctions,

bid level probit analysis which isolates individual drivers of bidding behaviour and

conclude with a short discussion of the experimental results.

6.1 Experimental Design

A basic treatment-and-control between-subject design is utilised to experimentally

test the effects of the exit option on outcomes of the pay-per-bid auction format.

In our experimental implementation of the pay-per-bid auction, participants were

randomly assigned into groups of 5 to bid for a coupon, which is redeemable for

$20.00. Following the theoretical model, bidding took place in discrete stages, with

participants being given an initial 10 seconds, which was reduced to 5 seconds after 5

rounds, to make a decision whether to place a bid or not. The time limit is reflective

of the decision time constraints faced by bidders in the online auction and also limits

round time and associated participant fatigue. At the end of each discrete round,

38

one out of all bidders who opted to place a bid is selected to be the leading bidder

and is charged a bidding fee of $0.50. Each bid increments the ending auction price

by $0.05.

Participants were given an initial endowment of $15 from which they could spend

on bidding fees. Earnings consisted of participant’s remaining endowment, their

gains from attaining coupons, and a $5 show-up fee. Potential losses for participants

were therefore restricted and participants were paid a minimum of $5 for their time

in the lab. Due to the $15 endowment, bidding is likewise limited to 30 bids per

participants.

In the exit option treatment, participants were allowed an additional option to

“purchase” the coupon at any time at an exit price less the amount of bidding fees

they have already incurred in the auction. Exit prices ranged from $16 to $26

and were fixed for the duration of an individual auction. Having both auctions

with exit prices above and below valuation allows us to better isolate the effects of

the exit option for a range of items. In the Exit AV auctions, once a bidder has

placed bidding fees up to the difference between their valuation, $20, and the exit

price, and the Valuation Exit threshold, individual bidding aggressiveness should

increase. Likewise, for Exit BV auctions, this should hold true immediately for all

participants.

Time permitting, participants took part in up to 8 auction matches. To alleviate

potential wealth effects from distorting behaviour across auctions, a random pay-

ment mechanism selected one auction out of all the auctions played to be paid out

at the end of the experiment. Although participants remained in the same groups

throughout all auctions, Bidder IDs were randomised across auctions.

Consistent with the theoretical model, participants are aware of the symmetric

nature of the auction and are also provided with full information regarded bidding

histories and exited players.

The experiment was programmed and conducted with the software z-Tree (Fisc-

hbacher 2007) with all auction interactions conducted on lab computers. Figure 12

39

depicts the auction decision screen participants made their decisions in. Recruitment

was undertaken via ORSEE (Greiner 2003), with 185 students from the University

of New South Wales participating. The average payment for each participant for

the 2 hour session was $21.73. Our sample consisted of 48% females, 53% business

faculty students and 82% international students.

Figure 12: Experimental Auction Decision Screen

A short comprehension test was conducted to assist participants in understanding

the auction and an exit questionnaire was used to elicit demographic variables and

measures of risk aversion.15 Experimental instructions, experimental script and

post-experimental questionnaires are available in Appendix C.

Rather than designing the experimental auction such that it more closely rep-

licates the real world implementation (e.g. with the presence of a timer countdown

and allowing for continuous bidding rounds), we instead implement a simplified ver-

sion of the auction which closely mirrors the theoretical framework discussed above.

The advantages of this method are two fold: firstly, this allows us to more closely

test the theoretical predictions of the model within a controlled environment and

in turn eliminate theoretical simplifications of the auction as a source of deviation;

and secondly, the discrete nature of the theoretical model lends itself to more eco-

nometrically palatable data collection and analysis.15We use the standard instrument per Holt and Laury (2002).

40

The use of a coupon with a common valuation simplifies the analysis and rep-

resents a realistic replication of a range of goods offered in the online platform with

well known retail values (gift cards, consumer electronics). The restriction of auction

groups to 5 also limits our analysis on the dimension of participation. In the online

auction, bidding behaviour is likely to be influence by the potential entrance of new

participants. Never-the-less, experiment participants can still profit by not parti-

cipating in the auction and simply taking home their endowment and this should

account for some variability in participation.16

Although limiting spending on bids to their initial endowment has the poten-

tial to distort bidding behaviour, ethical concerns and the practical implications of

requiring participants to pay out their losses took precedence.17

6.2 Summary Statistics

Table 4: Summary Statistics - Experimental DataObs. Mean Std Dev. Min Max

No Exit Auction 110Unique groups 19Ending round 33.52 35.75 0 146

Exit BV Auction 36Unique groups 18Ending round 45.56 35.01 0 123

No. exited 3.80 0.84 2 4Bids refunded 28.06 28.86 0 114

Exit AV Auction 45Unique groups 18Ending round 42.60 38.52 0 126

No. exited 1.51 1.19 0 4Bids refunded 18.82 27.34 0 99

****** ****** ****** ******

We present auction level summary statistics in Table 4. Both types of Exit16Ockenfels et al. (2010) found overall bidding increased when group sizes increase from 2 to 4

but less bids placed per participant.17Ockenfels et al. (2010) noted resistance in getting participants who experienced net losses to

pay the experimenter back.

41

auctions result in higher average ending rounds when compared to the No Exit

treatment. As expected, the number of exiting bidders and bids refunded per auction

are higher in the Exit BV auction than in the Exit AV auctions.

6.3 Duration Analysis

In our duration analysis, we examine aggregate auction level metrics to tease out

differences that occur across auction types, our treatment and control. Kaplan-Meier

survival estimates are presented for our experimental data in Figure 13, stratified

by treatment type. We report survival and smoothed hazard estimates for the exit

and no exit treatments, separating the exit treatments according to auctions with

exit prices above valuation and exit prices below valuation. Theoretically computed

survival estimates and hazard rates for the no exit option auction are also displayed.

Figure 13: Kaplan-Meier Survival and Hazard Rate Estimates - Experimental Data

Our aggregate survival estimates illustrate that at essentially every round, sur-

vival rates for our exit option auctions dominate that of the No Exit auction. This is

consistent with expectations that the presence of an exit option makes entry into the

auction relatively more attractive. Interestingly, survival rates for the No Exit auc-

tion in our experiment do not deviate as much from theoretical predictions as those

in the empirical analysis. Particularly, auction survival rates for the early rounds

are much lower than predicted, although this deviation reverses as additional bids

are placed. A Mantel-Cox logrank test for equality of survivor functions finds no

statistically significant differences between the theoretical and experimental survival

42

estimates (p-value of 0.26).18

Focusing on the more readily interpretable hazard rates, which have been smoothed

using a 20 bid running average, both Exit auction variations display a distinctly lower

hazard rate at the early stages of the auction comparative to the no exit control.

Auctions with exit prices above valuation maintain a consistently lower hazard rate

than No Exit auctions throughout the analysis time while auctions with exit prices

below valuation cross both other hazard curves around 50 bids placed.

The Exit AV and No Exit difference in hazard rates is consistent with our theor-

etical predictions about the effect of an exit option on bidding behaviour. The pres-

ence of an exit option increases bidder participation and bidding, resulting in lower

hazard rates, which is maintained once bidders enter the Valuation Exit Threshold

(not directly observable in total bids placed).

For auctions with exit prices below valuation, where bidding is a strictly dom-

inant strategy, termination probability in the beginning are lower comparative to

both No Exit and Exit AV auctions as expected. Relative to Exit BV auctions, Exit

AV auctions should initially display higher termination rates as bidding remains a

potentially costly action, but then exhibit similar termination rates as individual

bidders reach their exit-price-valuation gap. Interestingly however, the termination

probability exceed those of the No Exit and Exit AV auctions past 50 total bids

placed in the auction. This may be attributed to participants recognising that bid-

ding is likely to continue till all participants have exhausted their endowment, at

which point the payoff for winning is essentially equal to exiting immediately. Where

remaining potential gains outweigh cost of effort required to stay in the auction, par-

ticipants become more likely to exit.

The Mantel-Cox logrank test, stratified across No Exit, Exit BV and Exit AV

auctions, do not find statistically significant different survival rates (p-value of 0.19)

between the three auctions.19 Pairwise comparisons between No Exit, Exit BV18In the absence of censored data, as in our sample, the Mantel-Cox logrank test is equivalent

to a Mann-Whitney U test.19In this application the Mantel-Cox logrank test is equivalent to a Krushal-Wallis test.

43

and Exit AV also yielded no significant differences.20 Alternatively, semi-parametric

testing through a Cox proportional hazard regression, clustered at the group level,

is conducted to better isolate the effects of each auction type on hazard rates. With

No Exit auctions as the baseline, Exit AV auctions had a proportional hazard rate

of 0.77 with a p-value of 0.0950. This means that, at any round, Exit AV auctions

are 33% less likely to terminate than No Exit auctions.21

6.4 Probit Analysis

In our probit analysis, we utilise the experimental bid level data to investigate

how participant behaviour with regards to the decision to bid changes across our

treatment and control. A key advantage of experimental data over the empirically

collected data is the degree to which we can actually observe and capture data

regarding decisions made by participants. Since participants make a distinct decision

to place or to not place a bid each round, a probit analysis is feasible. We also

briefly examine the decision to exit and the probability of a bid being a winning

bid. Table 5 on the next page presents the bid level variables collected within our

experiment. Each data point represents a participant’s decision in one specific round

of an auction.

We estimated a variety of probit models to analyse how the probability of bidding

was influenced by auction related factors. We account for potential within-group

interaction effects by clustering standard errors at the group level. Observations

where bidders were leading or had exited were excluded from the analysis as the

bidding choice is not made in those circumstances.

The marginal effects of these models at sample means are presented in Table 6 on

page 46 (regression coefficients are available in Table 8 in Appendix B.1). The base

probit model (B1) incorporates basic auction and bidder state variables including20P-value of 0.1683 between No Exit and Exit BV, 0.1397 between No Exit and Exit AV and

0.8636 between Exit BV and Exit AV (paired test).21A Schoenfeld residuals test of the proportional hazards assumption, however, rejects a pro-

portional hazards relationship between No Exit and Exit BV auctions which precludes Exit BVauctions from the analysis.

44

Table 5: Bid Level Data DescriptionVariable Type DescriptionSubject Discrete Subject Unique IDGroup Discrete Group Unique IDBid Binary 1 if the subject placed a bid, 0 otherwiseWin Binary 1 if the bid placed was a winning bid, 0 otherwiseExit Binary 1 if the subject chose to exit, 0 otherwise

Sunk Bids Discrete Current number of own bids placed by the bidderRound Discrete Current round / total number of bids already placed in the auctionMatch Discrete The current auction match being played

Exit Option Binary 1 if the auction allowed an exit option, 0 otherwiseExit Price Gap Discrete Valuation less exit price

Bid Lag Binary 1 if the subject placed a bid in the previous stage, 0 otherwiseActive Bidders Discrete Number of bidders in the group who placed a bid last roundLeading Lag Binary 1 if the bidder was the leading bidder in the previous round, 0 otherwiseNo. Exited Discrete Number of subjects who have exitedThreshold Binary 1 if the subject has reach the Valuation Exit Threshold

the number of sunk bids submitted by the bidder, total auction bids placed, auction

type, the valuation relative exit price and the round of auction to control for learn-

ing/order effects across auctions played.22 Model (B2) has the addition of lagged

(previous stage) variables, to account for behaviour influenced by past information

and behaviour, and the Value Exit Threshold (the point from which bidding is a

weakly dominant strategy - see Section 4.2) and (B3) accounts for non-linearity in

the main continuous variables. Finally, model (B4), from which we draw our analysis

henceforth (unless stated otherwise), controls for any residual exit option treatment

effects.23 Each iteration of model is tested for goodness of fit and explanatory power

using the Wald test (p-values displayed in Table 6).24

22Note that with the inclusion of the Exit Price Gap, we necessarily force opposing effectsbetween Exit AV and BV auction. Estimations with each exit price as a separate dummy yieldsqualitatively similar results.

23The exit option dummy is interacted with sunk bids, auction bids placed, round, active bidders,leading lag and no. exited.

24The more typical LR Test is forgone since clustering of standard errors does not produce truelikelihoods. A more conservative Bonferroni adjusted test also produces results consistent with theWald test - Korn and Graubard (1990).

45

Table 6: Probit Marginal Effects of Decision to Bid(B1) (B2) (B3) (B4)

Sunk Bids 0.0572*** 0.0759*** 0.1736*** 0.1867***(0.0038) (0.0087) (0.0226) (0.0233)

Sunk Bids ^2 -0.0073*** -0.0089***(0.0020) 0.0022

Sunk Bids * Threshold -0.0235*** -0.0406** -0.0581**(0.0079) (0.0215) (0.0221)

Sunk Bids ^2 * Threshold 0.0040** 0.0055**(0.0020) (0.0022)

Round -0.0107*** -0.0101*** -0.0219*** -0.0209***(0.0007) (0.0007) (0.0013) (0.0014)

Round ^2 0.0001*** 0.0001***(0.0000) (0.0000)

Match -0.0113* -0.0091* -0.0066 -0.0061(0.0060) (0.0048) (0.0042) (0.0039)

Exit Option 0.0557** 0.0229 0.0263 0.0263(0.0260) (.0255) (0.0243) (0.0243)

Exit Price Gap -0.0066 -0.0118** -0.0095 -0.0136*(0.0049) (0.0056) (0.0066) (0.0071)

Bid Lag -0.0871*** -0.0757*** -0.0830***(0.0119) (0.0112) (0.0108)

Active Bidders 0.0524*** 0.0404*** 0.0399***(0.0066) (0.0055) (0.0062)

Leading Lag 0.1732*** 0.1086*** 0.1074***(0.0234) (0.0191) (0.0286)

No. Exited 0.0479** 0.0554** 0.0361(0.0205) (0.0274) (0.0308)

Demographics yes yes yes yesExit Interactions no no no yes

Pseudo R2 0.1518 0.1772 0.2303 0.2325Wald test p-value 0.0000 0.0000 0.0450

Note: * p-value < 0.10, ** p-value < 0.05, *** p-value < 0.01

Note: p-value for variables with quadratic terms pertains to joint significance

Although the exit option is statistically significant at the 5% level and positively

signed as expected (with the exit option increasing the probability of bidding) in

model (B1), the effect becomes insignificant as we account for additional auction lag

and polynomial terms. Where significant, the exit option only increases probability

of bidding by 5.72% (at the mean value of the sample of 67 sunk bids). This suggests

that bidding behaviour as a whole is not strongly influenced by the mere presence

of the exit option alone when additional drivers of behaviour (both treatment and

46

non-treatment related) are accounted for.25

The exit price gap variable captures the relative effects of the exit price, between

auctions with differing exit prices, on bidding behaviour on top of what is captured

by the exit option dummy. Auctions with a positive exit price gap (Exit AV auctions)

are correlated with a lower bidding probability relatively to negative exit price gap

(Exit BV auctions).26

By far the most important effect of the exit option on the decision to bid is

captured by the Valuation Exit Threshold variable. As discussed in Section 4, the

Valuation Exit Threshold marks the point at which bidders have sunk bids greater

than or equal to the difference between their valuation and the exit price. The

threshold variable captures whether the bidder has entered this state of bounded

losses where costless bidding is possible and the dominant strategy is to bid. We in-

teract this threshold variable with sunk bids to obtain the additional effect, reaching

this Valuation Exit Threshold, has on bidding behaviour as bids sunk increases. We

find significant additional effects of this threshold variable in addition to the already

significant sunk bids variable. Given the difficulty of analysing marginal effects at

means of continuously variables, we compute average predicted probabilities of the

probability to place a bid over our sample and report the results in Figure 14 on the

next page.27

For the No Exit auction case, as sunk bids increase from 0 to 10, the probability

of bidding rises from 20% to 80%. The effect is however diminishing with bidding

probability falling back to 20% at 20 bids placed and 0% past 25 bids placed. The

positive correlation between sunk bids and bidding probability lends some evidence

to the argument that bidding behaviour in pay-per-bid auctions is due to suscept-

ibility to the naive sunk cost fallacy. To the extent that auction, bidder state and25A joint test of significance for the exit option and all exit option interaction terms returns a

p-value of 0.0702 for model (B4).26The formulation of the exit price gap variable necessarily forces an opposing relationship

between Exit AV and Exit BV auctions. A check against estimation of the probit regressionwith categorical variables for each Exit auction price supported this relationship.

27The average predicted probabilities are calculated by using our estimation results to predictback into the sample and graphing the corresponding average predicted probabilities over sunkbids.

47

Figure 14: Average Predicted Probabilities of Decision to Bid

strategic variables have been properly controlled for within our probit regression,

participants become more likely to place bids when they have incurred irrecoverable

costs.28 This potential escalation of commitment appears to diminish as parti-

cipants approach the maximum bids that can be placed by participants (given $15

endowment and $0.50 bidding fees). This is possibly consistent with a desire by

participants to conserve their remaining endowment for strategic bidding and loss

mitigating purposes.

In comparison, the Exit with Threshold average predicted probabilities capture

the effect of sunk bids on bidding probabilities for participants who have reached the

Valuation Exit Threshold.29 The average predicted probability profile is markedly

different, with an increasing propensity to bid which exceeds a 95% chance of bidding

past 10 sunk bids. The key effect of reaching the threshold is that the decreasing

probability of bidding in higher values of sunk bids seen in the No Exit case, which

may be attributed to loss mitigation and strategic conservation, is nullified by the

presence of the exit option. This sustained high probability of bidding drives the

lower hazard rates observed in exit option auctions.28Even if participants were to anchor their bidding strategy to spending some fraction of their

endowment, such behaviour should not lead to an increasing bidding probability over sunk bids.29Although statistically not significant, the Exit auction case, where we only consider the static

effect on bidding probability of participating within an auction with an exit option, does predicthigher bidding probability over all values for sunk bids.

48

Bidding behaviour in both the Exit and No Exit auctions are affected positively

by an increase in sunk bids, but it is worth noting the differing effects at work.

Increase in bidding under the No Exit auction may be attributed to naive sunk cost

fallacy, but an increase in bidding under Exit auction may be reasonable considering

the zero marginal costs of doing so once the Valuation Exit Threshold is reached.

In terms of the current round, which captures the effects of the current auction

price and the total bids placed by all auction participants, the probability of bidding

falls at a decreasing rate as auction bids placed increases which reflects the increasing

cost of winning the item.

The control for auctions rounds, which investigates whether any order or learning

effects occur across successive auctions, results in both statistically and economically

insignificant effects once additional factors are controlled for.

The effect of the bid lag variable (8.30% less likely to bid), which captures the

probability of bidding if the participant had bid in the previous stage but was not

selected as the winner, suggests that there is no persistence in the bidding process if

no costs are incurred. The leading lag estimate, which measures the effect of bidding

after being outbid in the previous stage, returns a significant 10.74% increase in

bidding probability. With the bid lag controlled for, this suggests a competitive

effect of the auction, where being “dethroned” by another bidder, increases bidding

propensity.

We find no significant effects of bidding behaviour attributable to the level of

risk aversion as measured by the Holt and Laury (2002) risk instrument.30 From a

sample mean of 5.1, an additional unit of risk aversion results in participants being

0.44% less likely to place a bid.

No significant effects were found when controlling for demographics (gender,

student locality and field of studies).30The instrument was not financially incentivised and was carried out as part of the post ex-

perimental questionnaire. The assessment was given to and completed by subjects in half oursessions (n=115). A separate (B4) model with the subsample of subjects was estimated with therisk measure. No significant changes in coefficients and standard errors were observed.

49

6.5 Auctioneer Profits

In addition to understanding how drivers of individual bidding behaviour change

across Exit and No Exit auctions, it is worth stepping back to examine how such

behaviour translates to outcomes for the auctioneer/operator. The distribution of

auctioneer profits per auction arising from our experiments are displayed in Figure

15. Auctioneer profits are calculated by assuming the item is acquired at costs

equal to the valuation of bidders and represents the net profit after deductions for

additional items sold and bidding fees refunded where applicable.

Figure 15: Auctioneer Profits

Similar to Ockenfels et al. (2010), our auctioneer experienced slight negative

profits (mean of -$3.24) in the No Exit auctions.31 This is contrasted with mean

losses of -$11.66 and -$34.56 respectively for the Exit AV and Exit BV auctions.

Although the auctioneer profits cannot be interpreted directly as they are a product

of our experimental setup, we can analyse the difference in profits between the

auction types to get a sense of how profits may change from the implementation

of an exit option. It appears that the implementation of an exit option does not

attract a sufficiently greater amount of bids to compensate for loss in bidding revenue

(refund of bids) arising from the exercising of the exit option.

However, the above method of comparing profits ignores a key difference between31The lack of over bidding within our experiment is contrary to experiments involving standard

all-pay auctions, e.g. Gneezy and Smorodinsky (2004). However, this may simply be a consequenceof our chosen experimental parameters.

50

Exit and No Exit pay-per-bid auctions. In the case of No Exit auctions, profits are

wholly a function of bid revenue, ending price and cost of goods. For Exit auctions,

bid revenue, exit price, refund of bidding fees, cost of goods sold and number of

items sold all factor into the profit equation. Since more than one item may be sold

for every Exit auction, the relative impact of the cost of the goods is greater with

respects to Exit auctions. Figure 16 depicts mean profits as cost of goods sold is

varied away from the valuation.

Figure 16: Auctioneer Profits and Cost of Goods

As the profit margin of the good sold increases, Exit AV profits rise steadily

as gains from goods sold cover diminished bidding revenue. Although it would be

difficult to extrapolate such an analysis to the real world to pin point a particular

break-even point between offering of the exit option and a standard pay-per-bid auc-

tion, this does suggest that there is a reason why the exit option could be beneficial

to auctioneers.

It is also worth noting that the standard deviation of Exit AV auction profits

(10.31) are significantly lower (p-value of 0.0000) than that of the No Exit Auction

across cost of goods sold. A tighter variation in profits, for an auction platform that

is characterised by volatile earnings, represents a significant reduction of risks which

further increases the potential attractiveness of offering such an option.

51

6.6 Bidder Gains

Just as pertinent as auctioneer outcomes are bidder outcomes. Figure 17 illustrates

the distribution of bidder gains per auction in our experiment. We calculate bidder

gains as the value of the voucher, minus the bidding fees, minus auction or exit price

paid.

Figure 17: Bidder Gains

Average bidder gains from the Exit AV auctions (2.13) significantly outweigh

gains for those who participated in the No Exit auctions (-1.01).32 Although the

standard deviation of Exit AV auctions (6.08) are larger than that of No Exit auc-

tions, the added variation appears to be right skewed towards higher bidder gains.32Exit BV auctions unsurprisingly result in far higher bidder gains of 6.99.

52

7 Discussion

With respect to our empirical analysis of the exit option, we find giftcard auc-

tions last longer while non-giftcard auctions actually end earlier than their No Exit

counterparts. Given the pure common value nature of giftcard auctions and the un-

observed, potentially very heterogeneous private valuations in non-giftcard auctions,

it would be reasonable to put more weight on the results of the giftcard auctions. In

this sense, the exit option appears to increase bidding aggressiveness, particularly

in the early rounds of the auction.

The discrepancy between the two groups of auctions may however be attributed

to an exponential effect of sunk cost fallacy in response to higher valued items in

non-giftcard auctions. If bidders are more susceptible to the naive sunk cost fallacy

when the value of items are higher, then it is possible this effect, which is eliminated

in an exit option, that would cause No Exit auctions to last relatively longer. This

would suggest some level of interplay between sunk costs effects and exit option

effects of reaching the Valuation Exit Threshold.

Likewise, due to the higher value of items, bidders may be more reluctant or

have a smaller probability of reaching the Valuation Exit Threshold and this would

reduce the effect of the exit option. Another reason for the difference may be the

interplay of strategies between bidders with asymmetric valuations. If one bidder

reaches the threshold significantly sooner than the rest, their bidding aggression may

deter bids from other participants. This is in contrast to giftcard auctions where

multiple bidders are likely to reach the threshold with relatively fewer bids placed

and within a few rounds of each other.

However, the lack of data on the use of the exit option limits our empirical ana-

lysis of No Exit auction outcomes for auctioneers and bidders. Crucially, while the

Exit auction increases bidding, auctioneer profits and bidder gains hinges on the

frequency and point at which the exit option is used. This serves to motivate our

experimental investigation which not only allows for a cleaner test of the theoret-

ical formulation of the auction, but also resembles the giftcard auctions analysed

53

empirically.

Our experimental evidence suggest that the introduction of an exit option to the

pay-per-bid auction affects behaviour in the ways predicted within the theoretical

section. Overall bidding increases with the exit option and this leads to longer

lasting auctions and higher gross bid revenue for the auctioneer. Participants take

advantage of the exit option as expected, increasing bidding aggressiveness once they

reach the Valuation Exit Threshold leading to higher welfare gains for bidders. We

observe that the effect of entering the threshold on bidding dominates the sunk cost

effect of the No Exit auction. However, the implications for the auction operators

are less clear and are highly contingent on profit margins on the goods auctioned.

While the Exit auction results in reduced bidding revenue, additional quantities

of the goods sold per auction compared to the No Exit auction could potentially

make up for the difference. To the extent that profit margins on goods are sufficient

there appears to be potential welfare gains for both auction operators and auction

participants, with a more equitable split of efficiency gains from trade.

Such a result has important implications for the regulatory treatment of pay-per-

bid auctions. Since the exit option appears to eliminate the reliance on exploiting

bidders’ naive sunk cost fallacy, caps potential losses and improves bidder welfare,

there may be a lessened need to intervene in the online pay-per-bid auction market.

Duration analysis undertaken shows that qualitatively, our experimental data

matches our empirical observations with respects to giftcard auctions, which gives

strength to the external validity of our experimental conclusions. Particularly, ter-

mination rates for Exit auctions in early rounds are lower than No Exit auctions

in both experimental and empirical analyses. However, given budget limitations,

questions remain regarding the effect of the exit option on items of high value as in

non-giftcard auctions. Further research could therefore be undertaken to isolate how

the effects of Exit and No Exit auctions change as the value of the item is scaled.

It is worth noting that a key abstraction made in our experimental setup is

the fixing of bidder numbers within our auction. Although bidding is not enforced

54

within our experiment and bidders still earn a payoff if they choose not to bid, it

stands to reason that the potential pool of bidders are different between platforms

offering the exit option and those which do not offer it. When faced with a choice of

auction platforms, the exit option might attract a greater number of participants,

as basic evidence in our empirical analysis suggests. The experimental setup may

therefore be understating bid revenues for the Exit auctions.

A possible extension of the experimental design would be to allow participants

to choose between the two auction platforms or even multiple Exit and No Exit

auctions. This may lead to further differences between the Exit and No Exit auction

outcomes and may provide an alternative explanation to why certain operators have

decided to offer the Exit auction. From an institutional choice perspective, if one

auction platform offers the exit option, it may force all other operators to do the

same to retain their bidders.

55

8 Conclusion

In this paper, we investigate how bidding behaviour and auction outcomes change

in pay-per-bid auctions when an exit option is made available to bidders. The exit

option, which allows bidders to purchase the item at the recommended retail price

less sunk costs, is predicted to increase bidding propensity when the bidder has

reached the Valuation Exit Threshold. Empirically, we find evidence that supports

our conjectures in pure common value giftcard auctions. Giftcard auctions with the

exit option are found to last longer than their No Exit counterparts. Experimental

data which isolates individual bidder behaviour corrobates the effect of the exit

option. The increase in bidding in the Exit treatment displaces and dominates

the potential sunk cost effects in the No Exit auctions. This results in unambiguous

welfare gains for bidders. Auctioneer profits are however heavily dependent on profit

margins as the exit auction trades-off bid revenues for more items sold per auction.

Provided profit margins are sufficiently large, the Exit auction has the potential to

be pareto improving.

56

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58

A Empirical Regression Outputs

Table 7: OLS on Unique Bidders in an Auction: CoefficientsGiftcard Non-giftcard

(GU1) (GU2) (NU1) (NU2)RRP 0.0715*** 0.0687*** 0.0542*** 0.0566***

(0.0025) (0.0026) (0.0017) (0.0024)No BidAgent 0.0677

(0.1397)Exit 2.1996*** 2.2943*** -25.8453*** -26.4918

(0.1323) (0.1448) (3.0190) (20.9921)Exit and No BidAgent 0.1417*** -3.0949

(0.3207) (22.6313)Bonus -2.9784

(21.0969)Bonus and Exit -28.8138

(20.9502)Beginner -1.3380

(0.2304)Beginner, Bonus and Exit -1.1067 -27.5901

(2.0433) (21.3185)Constant 2.2508*** 2.3896*** 29.3757*** 29.9491

(0.0865) (0.0896) (3.1803) (21.0134)

Adjusted R2 0.2477 0.2557 0.2477 0.4281N 3664 3664 2107 2107

Note: * p-value < 0.10, ** p-value < 0.05, *** p-value < 0.01

59

B Experimental Regression Outputs

B.1 Probability of Bidding

Table 8: Probit Regression on Bidding Decision: Coefficients(B1) (B2) (B3) (B4)

Sunk Bids 0.1464*** 0.1948*** 0.4440*** 0.4777***(0.0097) (0.0223) (0.0581) (0.0600)

Sunk Bids ^2 -0.0186*** -0.0226***(0.0052) (0.0057)

Sunk Bids * Threshold -0.0604*** -0.1038* -0.1486***(0.0202) (0.0551) (0.0567)

Sunk Bids ^2 * Threshold 0.0102** 0.0141**(0.0050) (0.0056)

Round -0.0274*** -0.0259*** -0.0559*** -0.0534***(0.0018) (0.0017) (0.0031) (0.0036)

Round ^2 -0.0003*** 0.0003***(0.0000) (0.0000)

Match -0.0289* -0.0234* -0.0168 -0.0155(0.0153) (0.0124) (0.0108) (0.0100)

Exit Option 0.1428** 0.0587 0.0672 0.0393(0.0667) (.0655) (0.0622) (0.1223)

Exit Price Gap -0.0169 -0.0302** -0.0243 -0.0347*(0.0127) (0.0144) (0.0169) (0.0182)

Bid Lag -0.2236*** -0.1936*** -0.2123***(0.0308) (0.0313) (0.0276)

Active Bidders 0.1345*** 0.1034*** 0.1020***(0.0167) (0.0140) (0.0159)

Leading Lag 0.4624*** 0.2832*** 0.2801***(0.0639) (0.0505) (0.0759)

No. Exited 0.1229** 0.1418** 0.0924(0.0527) (0.0703) (0.0789)

Constant 0.2269*** -0.0542 -0.0488 -0.0277(0.0786) (0.0814) (0.0648) (0.0842)

Demographics yes yes yesExit Interactions no no no

Pseudo R2 0.1518 0.1772 0.2303 0.2325N 25279

* p-value < 0.10, ** p-value < 0.05, *** p-value < 0.01

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B.2 Probability of Exiting

Table 9: Probit Regression on Exit Decision: Coefficients(E1) (E2) (E3)

Sunk Bids 0.0214*** 0.0206*** -0.0123**(0.0054) (0.0056) (0.0170)

Sunk Bids ^2 0.0012**(0.0005)

Round -0.0003 -0.0003 -0.0079*(0.0016) (0.0016) (0.0047)

Round ^2 0.0001**(0.0000)

Match -0.0123 -0.0172 -0.0194(0.0213) (0.0208) (0.0204)

Exit Price Gap -0.0455*** -0.0498*** -0.0534***(0.0065) (.0073) (0.0077)

Bid Lag 0.0624 0.0531(0.0660) (0.0663)

Active Bidders -0.2059*** -0.1773***(0.0324) (0.0302)

Leading Lag 0.0324 0.0762(0.0829) (0.0850)

No. Exited -0.0622 -0.0610(0.0384) (0.0407)

Constant -2.4515*** -2.0647*** -1.8942***(0.0726) (0.0985) (0.0929)

Demographics yes yes yes

Pseudo R2 0.0319 0.0537 0.0670N 25279

* p-value < 0.10, ** p-value < 0.05, *** p-value < 0.01

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C Experimental Documentation

C.1 Experimental Script

If you are here for the experiment, could you please form a line and ready your

student id cards so that we can record your attendance and get you seated.

[Wait for participants to be seated]

You should find three pieces of paper in front of you, a participant information

sheet which you should read, an informed consent form which you should sign and

a payment receipt form which you will need at the end of the experiment

[Wait for participants to complete forms]

We will now collect the consent forms before we distribute the experiment in-

structions.

[Wait for collection of consent forms]

We will now distribute the instructions for the experiment. Please read and

understand the rules carefully as this will help you make the decision that is best

for you. Before the experiment begins, there will also be a short comprehension

test to assist your understanding of the rules of the experiment. If anyone has any

questions please just raise your hand and we will come over to assist you.

[Wait for participants to finish reading instructions]

We will now start the comprehension test, if you have any difficulties with an-

swering the question, please just raise your hand and we will come over to assist

you.

[Wait for participants to complete comprehension test]

The experiment will begin shortly. There will be a welcome screen, once all

participants have clicked the OK button, the auction will begin immediately. Please

note that there may be a waiting period between each auction as the program waits

for all groups to finish an auction before continuing. You can raise your hand at any

point in the experiment if you need help, we will come out to assist you.

[Wait for participants to complete experiment]

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The experiment is now over, we now need to randomly select the auction that is

paid out. I have an eight-sided die here which I will need a volunteer to roll. The

number facing up will be the auction number that is paid out for real.

[Dice roll]

While we prepare the payments, we will distribute some questionnaires for you

to complete. If you have any thoughts about the experiment, you can write them

on the back of the questionnaire.

[Prepare payments]

Note that the seat number is the number on the wall of your station, not your

bidder id.

Please also fill out your receipt form with your details, you can leave the amount

paid blank for now, we will fill that in when we call your seat number up for payment.

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C.2 Experimental Instructions

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C.3 Comprehension Test

Questions were administered via the computer terminals.

Q1) When more than one bidder decides to place a bid in a stage, how is the leading

bidders in the next stage decided? Only one of the following is true:

• All bidders who placed a bid become leading bidders.

• The bidder who places their bid first during the countdown becomes the leading

bidder.

• The leading bidder is selected randomly from the bidders who decided to place

a bid during the countdown in the previous stage.

• The bidder who placed their bid last during the countdown in the previous

stage becomes the leading bidder.

Q2) When is the bidding fee of $0.50 deducted from your endowment? Only one of

the following is true.

• Immediately after you decide to place a bid, before the stage ends.

• After the stage ends whether you are the leading bidder or not.

• After the stage ends whether you decide to place a bid or not.

• After the stage ends, if you place a bid AND is randomly selected as the leading

bidder.

Q3) Who will win the auction and obtain the voucher at the current price if no bids

are placed in a stage? Only one of the following is true.

• All the bidders who decided to place a bid in the previous stage.

• The bidder in the last stage who decided to place a bid and was selected as

the leading bidder.

• Any bidder who was selected as a leading bidder at any stage of the auction.

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• A randomly selected bidder out of all the bidders.

Q4) How do you calculate your balance at the end of an auction? Only one of the

following is true.

• $20 if you have a voucher. $0 if you have no voucher.

• $20 if you have a voucher, less the price you paid for your voucher. $0 if you

have no voucher.

• $20 if you have a voucher, less the price you paid for the voucher, plus your

remaining endowment.

• Just your remaining endowment.

Q5) How much will you be paid at the end of the entire experiment which is made

up of multiple auctions? Only one of the following is true.

• The sum of all your balances at the end of each auction.

• Your balance in one randomly selected auction.

• The average of all your balances in all the auctions.

• Only if you have won a voucher.

Q6) At the start of a new auction, only one of the following is true.

• You will start the new auction with your remaining endowment from the pre-

vious auction.

• You will start the new auction with a voucher if you won one previously and

will be able to accumulate vouchers.

• You will not be able to bid if you previously obtained a voucher.

• You will start the new auction with a a separate new endowment and none of

the actions from the previous auction will carry forward to this new auction.

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Q7) What happens when you choose to buy the voucher now? Only one of the

following is true.

• The auction will end for everyone and only you will get the voucher at the buy

now price.

• You will obtain the voucher at the buy now price and you will no longer be

able to place a bid in any new auctions in the future.

• You become the winning bidder and pay the current price to obtain the

voucher.

• You will obtain the voucher at the buy now price less your bidding fees paid.

Q8) If you have $1.00 of remaining endowment and the buy now price after discount-

ing the bidding fees paid is $6.00, will you be able to buy the $20 voucher now?

Q9) You have an initial endowment of $15, the bidding fee is $0.50 and the voucher

is worth $20. You decided to place 5 bids, was successful in placing a bid (selected

as the leading bidder) 2 times and you won the voucher at $1.50. What would your

balance be at the end of the auction?

Q10) You have an initial endowment of $15, the bidding fee is $0.50, the voucher is

worth $20 and the initial buy now price is $22. You decide to place 10 bids and was

successful in placing a bid (selected as the leading bidder) 8 times but did not win

the auction. What would your balance be at the end of the auction if you chose to

buy now at the end of the auction?

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C.4 Post Experimental Questionnaire

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