AN EXPERIMENTAL ANALYSIS OF SUNK-COST EFFECT AND
LOSS AVERSION THROUGH COMMON VALUE AUCTIONS
SURAJEET CHAKRAVARTY† & SUDEEP GHOSH‡§
Abstract. Contrary to expectations that rational economic agents would always
ignore the effect of sunk costs, the failure to ignore them seems to be quite pervasive. We use a common value auction mechanism to detect presence of sunk costs
and loss aversion in strategic decision making. Apart from the standard first and
second price auctions, we run several other treatments; a fixed (exogenous cost)
entry fee one, a bidding (endogenous cost) in order to participate in the auction
and all-pay auction. We find that bids statistically differ in the treatments when
the subjects have to pay in order to participate compared to when the subjects do
not pay to enter the auction. Interestingly, in the first price auction with entry fee,
the average bid falls in comparison to the auction without the entry fee, while in
second price auction with entry fee the average bid increases in comparison to the
auction without the entry fee, consistent with the implications of the sunk-cost effect. Also auctions bids are negatively correlated to their entry bids (endogenous
entry cost), further strengthening the sunk-cost hypothesis. Finally we observe
a significant (negative) correlation between endowments and bids in the all-pay
auction suggesting loss aversion.
Keywords: Experiments, Common Value Auctions, Sunk Cost Effect, Loss Aversion
†
Department of Economics, University of Exeter, Exeter EX4 4PU, UK. E-mail:
[email protected]
‡
Department Of Economics & Finance, City University of Hong Kong, Hong Kong. E-mail:
[email protected]
§
We thank Ngai Ho Lam for providing programming assistance with the experiment and Gauthier
Lanot for comments on the paper. We also thank various conference participants for their comments and suggestions. Finally support for the experiment through a Research Grant from City
University is acknowledged.
1
1. Introduction
The sunk cost effect is defined as a phenomenon where people demonstrate a greater
predilection for sticking to those endeavors, where a previous allocation of unrecoverable (i.e., sunk) money, time or effort has been made. Such behavior seemingly
contradicts economic rationality or for that matter any normative cost-benefit paradigm of decision-making. Hence, it is assumed that rational economic agents would
always ignore the effect of sunk costs or past decisions while making decisions about
the future. But contrary to such expectations, the sunk cost fallacy, i.e. the failure to ignore sunk costs, seems to be quite pervasive (Staw and Ross (1987)). The
evidence of this are the numerous studies, mostly in the nature of surveys conducted by psychologists, that show sunk cost effect. Behavioral explanations are
provided as the probable explanation for the supposed sunk cost fallacy. Prospect
theory (Thaler 1980), mental accounting (Thaler 1985), loss aversion (Kahneman
and Tversky, 1991) and internal justification (Staw, 1976) are existing explanations
for decision makers failing to ignore sunk costs. In a similar vein, Loewenstein &
Prelec (1998) and Gourville & Soman (2002) analyze a theory where decision makers mentally track costs of purchase and prefer to pay and then enjoy consumption
rather than have the pain of payment hanging over their head. Such a preference
can lead to over reliance on sunk cost when decisions are made.
Number of phenomena are cited by decision scientists as evidence of sunk costs
affecting future decisions. Staw and Hoang (1995) and Camerer & Weber (1999) both
find that the position where basketball players in the NBA (the major league in the
USA) are drafted affects their subsequent playing time. Janssen and Scheffer (2004)
argue that sunk cost behavior played an important role in the demise of ancient
civilizations. Also, the so called “Concorde Effect” is a prime example (Arkes and
Ayton, 1999). While the venture of flying the Concorde was loss generating, the
venture was not abandoned given the huge investment in it. Psychologists have also
talked about escalation effects. Gamblers spend more time trying to recover their
money even if they are losing (Thaler and Johnson, 1990), or businesses do not
change their policy once they realize they are losing money or cheaper policies can
2
be instituted if they have already spent considerable amount of money in a given
business practice. Colombo & Delmastro (2000) look empirically at exit behavior of
firms and find that the sunk investment plays a significant role in the decision to exit.
Firms are less likely to exit if sunk costs are higher. Sunk costs may also have an
effect reverse of the escalation effect on the decision-makers. Decision-makers behave
more conservatively after incurring sunk costs(van Dijk and Zellenberg, 1997). While
Genesove and Mayer (2001) find loss aversion the reason for home owners delaying
home sales if the market price is lower than the price at which they have bought
their house.
In our paper we look at individual decision making in a strategic context, with
decision makers participating in perfect information common value auctions. The
main aim of the paper is to look for evidence of sunk costs in a single decision
problem. We look at behavior in auctions, since it provides us with a fairly simple
decision problem and that it is a well studied problem with existence of extensive
experimental work on decision making in auctions. We construct an experiment
where agents make a payment at the door to enter the auction. This entrance fee
or cost is equivalent to the sunk cost. We study if this entry fee has an effect on the
bid of the subject when she participates in the actual auction. Rational behavior
would suggest that the entry fee should not have any effect on the bidding behavior.
We run sealed bid first price and second price auctions for Hong Kong $25, where
all players are aware of the value of the prize. In each, first price and second price,
we run a base treatment where all subjects participate in the auction and in the
second treatment subjects have the choice to enter or not and if they want to enter
the auction they have to make a payment at the door. In addition, for first price
auction we look at two extra treatments One, we endogenize the auction entry by
making the subjects bid for the right to enter in one. In the other, we have an
all-pay auction where subjects pay the bids irrespective of the outcome.
Individuals in the experiment make two key decisions, one to enter the auction
or not (if any) and the other, the bid in the auction. The main finding is that
individual payments made at the door does influence the bids made in the auction.
Interestingly, in the first price auction, the average bid in the auction with entry
3
fee falls in comparison to the auction without the entry fee, while in second price
auctions, the average bid in the auction with entry fee increases in comparison to
the auction without the entry fee. This difference is due to the nature of the auction institutions. In a first price auction, increasing one’s bid not only increases
the probability of winning but it also reduces the expected earnings conditional on
winning. In contrast, for a second price auction increasing one’s bid while increasing the probability of winning does not necessarily decrease the expected earnings.
Therefore, if the subjects incur sunk cost, they bid more conservatively in the first
price auction to off-set it, while in case of second price auction they behave more
aggressively with the belief that this increases their probability of winning and thus
the chances of recovering the sunk cost. We use a very simple model from Thaler
(1980) to explain the bidding differences between the treatment when subjects enter
without paying and when they enter after a paying a fee.
The other key decision, apart from the bid decision, is the entry decision of the subjects. In our design, subjects if they choose the sub-game perfect strategy then the
subjects when asked to pay a fee of HK$5 would not enter. We find that considerable
amount of subjects enter both the first price and the second price auctions. While
forty percent do not enter in the first price auctions, about sixty percent choose
to remain out in the second price auction. One possible behavioral explanation
is optimism. Camerer and Lovallo (1999) discuss the possibility of overconfidence
amongst players in explaining excess entry. Players ignore the strategic behavior on
entry by all other subjects and therefore over estimate on their winning chances.
We do study the optimism or overconfidence in our paper, but invoke it in order to
provide a possible explanation for entry. The likely reason for significant percentage
of the subjects not entering the auction is loss aversion which players experience
if they pay the entry fee to enter the auction1. We find further evidence of loss
aversion amongst the subjects when the subjects participated in an all-pay auction
treatment. Given that in the all-pay auction subjects realize the loss of the bids,
1
As shown by Phillips et al. (1991), the fact that players entry behavior is different depending
upon whether there is an explicit entry fee or an implicit one of the same amount further strengthens
our assertion that loss aversion is the overwhelming reason for non-entry behavior.
4
we find that the loss realized in the previous period affects the next period bids. To
this end we present a very simple model from Thaler (1980) to explain the bidding
differences between the treatment when subjects enter without paying and when
they enter after a paying a fee.
Our paper we believe has an important contribution to the literature, since most
of the existing evidence for the sunk cost fallacy is of anecdotal nature. Also since
most of the psychology experiments in this area were in the nature of surveys,
there might exist alternative “rational explanations” for some of their conclusions.
Regarding previous experimental work searching for evidence of sunk cost effect,
Plott (1987), Miller, Plott & Smith (1977) and Forsythe, Palfrey & Plott (1982) look
at the aggregate behavior of the market. They find evidence that while individuals
may exhibit irrationality and not ignore sunk costs, for the market as a whole they
do not matter. For evidence of individual decision makers exhibiting sunk cost
fallacy, Keasey & Moon (2000) show that if the investors have made sunk costs then
even if the project is poor the investors will likely go ahead with it. Friedman et.
al. (2003) on the other hand find that sunk cost matters little. Using a similar
hypothesis as the previous paper, that players will spend more time on a project
where they have invested more, the authors find that sunk cost actually plays a
minimal role in the decision of the players. Tan & Yates (1995) found that the
subjects in their study, business and accounting students who were exposed to the
sunk cost effect, were more likely to ignore sunk costs on “business” problems, but
just as likely to fall prey to the sunk cost effect on “non-business” problems. Our
paper here is probably nearest in spirit to the study by Phillips et al. (1991),
where the authors look at decision making in two environments; one, in a lottery
and two, in an auction. While in their lottery treatment a fifth of the subjects do
not ignore sunk costs, in the auction treatment only 5% of subjects do not ignore
sunk costs. But there are some major points of departure between our paper and
theirs. Our design of a common value auction with perfect information is of utmost
simplicity and hence our results have very little scope for ambiguity. We introduce a
variable entry fee treatment to examine whether any monotonicity of sunk cost effect
exists. Furthermore, we run both second price and and first price auctions to explore
5
differences in bidding strategies between them due to sunk-cost effect. Finally, we
also run an all-pay auction treatment to capture any potential endowment effect
(through loss aversion) in a continuous manner.
In addition, this paper also adds to the extensive experimental literature on common value auctions. Significant part of this has focussed on the winner’s curse (Dyer,
Kagel and Levin, 1989 and Lind and Plott, 1991). Cox, Dinkin and Swarthout (2001)
look at entry, exit and bidding behavior in common value auctions. While in order
to separate out the effect due to sunk costs we limit our analysis to looking at the
bidding behavior and the entry divisions given the entry fee in perfect information
common value auctions.
The paper is organized in the following way: in section two we present a brief
description of the theory and the equilibrium predictions, in section three we develop
our major hypotheses, followed by the design. In section five, we discuss the results
of the experiment and finally we conclude.
2. Theory and Equilibrium Predictions
We consider common value auctions with perfectly informed players, where we
draw upon previous results of common value auction to develop the theoretical
predictions for our auction treatments2. All participating bidders know the value
of the object they are bidding for so there is no uncertainty about the value of the
good. Let there be n = 2 bidders, bidding for a single object with value V . We
will assume that the bidders are risk averse where ti is the risk averse parameter of
player i. The players make a bid bi . In case of the first price auction, the highest
bidder gets the object and pays the bid and if the bids are equal each have half
probability of getting the object. So the expected return if the player i bids bi is
Πi (bi ) = G(β −1 (b))(u(V, ti ) − bi )
and u(V, ti ) is the Bernoulli function. Let the symmetric equilibrium strategy be β,
and the G be the distribution of ri = maxj6=i bj . And the optimal bid is given by
2
See for example Krishna (2002) for a comprehensive treatment of these and other auction types.
6
b∗i ∈ arg max Πi (bi , ti ). Assuming β(0) = 0 and ignoring the index i for the players
1
b = β (u(V, t)) =
G(u(V, t))
∗
∗
Z
u(V,t)
sg(s)ds
0
With another auction mechanism, the second price auction, where the highest
bidder wins the auction but pays the second highest bid. In second price auction
the players will make an optimal bid such that β(u(V, t)) = u(V, t).
In case of entry fee, players have a choice to pay a fee F and enter the auction or
remain out of the auction. If they pay F, they enter and make a bid for the object.
Given the auction is similar to the ones discussed above the optimal bidding behavior
in case of first price is bF ∗ ∈ arg max [G(β −1 (b))(u(V, t) − b) − F ] . the optimal bid
in this case with the entry fee is equivalent to that without the entry fee,
bF ∗ = b∗
Similarly in case of the second price the bidding behavior does not change if the
entrant pays a fee to enter the auction.
In order to explain bidding behavior, we develop a behavioral model similar to
Thaler (1980). Thaler proposed that decision makers take decisions in order to the
maximize the value of prospects. While valuing the prospect, decision-makers may
have different value function for their gains and and losses. In the first price auction
with out entry fee, players gain the value of the prize and lose the bid if they win,
and if they fail to win the auction then there is no gain or loss. And in case the
players pay an entry fee before entering the auction, if they win, they gain the value
of the prize and lose the bid and the entry fee and if they lose, the gain is zero but
they lose the entry fee. So let us assume that the value function for the gains is ω
and the losses is v, given that probability of winning is G(β −1 (b)), the value of the
prospect in case of no entry is
G(β −1 (b)) (ω(V, ti ) + v(−bi ))
and in case the player pays an entry fee F , the prospect value is
G(β −1 (b)) (ω(V, ti ) + v(−bi − F )) +
7
1 − G(β −1 (b)) v(−F )
In greater detail the functions ω(·) and v(·) are such that ω(x) = 0 if x = 0, ω(x) > 0
if x > 0 and ω(x) < 0 if x < 0, ω ′(·) > 0, ω ′′(·) < 0, we assume that v(x) = 0 if
x = 0, v(x) < 0 if x < 0 , v ′ (·) > 0, v ′′(·) > 0.
3
Here the function ω is similar to a
standard concave, risk averse Bernoulli function. Let,
b∗P ∈ arg max G(β −1 (b)) (ω(V, ti) + v(−bi ))
and
bFP ∗ ∈ arg max G(β −1(b)) (ω(V, ti ) + v(−bi − F )) +
1 − G(β −1 (b)) v(−F )
This implies that b∗P ≤ bFP ∗ . In the auction without the entry fee, marginal increase
in the bid results in higher chance of winning, but also raises the cost of the bid in
case of winning. This is similar to the standard auction optimal bid. With entry
fee though, a marginal increase in the bid, raises the chance of winning, but also
raises the cost of the bid on winning. But an increased bid also means that there is
a lower probability that the player will incur only the loss of the entry fee. So with
entry fee since the marginal benefit actually increases due to the reduced chances of
making losses but the same time there is increased marginal costs due to the higher
loss suffered on winning. Given the property v(x) < 0 if x < 0 , v ′ (·) > 0, v ′′ (·) > 0,
of the v function, the increase in marginal cost will be larger than the increase in
the marginal benefit. Therefore, the bid, if entrance fee is paid will be smaller than
the bid when no entrance fee is paid.
For the second price auction, we can see that the value of the prospect will be:
[(Pr(win)) (ω(V, ti ) + v(−bj ))
in case of no entry fee, and
(Pr(win) (ω(V, ti ) + v(−bj − F )) + ((1 − (Pr(win)) v(−F ))
for the auction with entry fee, where bj is the second highest bid and Pr(win) is the
probability of winning. Let,
b∗∗
P ∈ arg max [(Pr(win)) (ω(V, ti ) + v(−bj ))]
3Note
here that we do not develop a sophisticated model of loss aversion or prospect theory. For
a more advanced treatment check Koszegi & Rabin (2006).
8
and
bFP ∗∗ ∈ arg max [(Pr(win) (ω(V, ti ) + v(−bj − F )) + ((1 − (Pr(win)) v(−F ))]
Here a marginal increase in the bid causes the probability of winning to increase
but at same time increases the probability of payment. Note here it does not increase
the payment itself unlike in the first price auction. Now in case of the second price
auction, a marginal increase of the bid causes the probability of winning to go up
as does the probability of payment, but the higher bid also decreases the chance
of not winning and losing only the entry fee. So here bid will actually increase in
comparison to the auction without entry fee, bFP ∗∗ ≥ b∗∗
P .
3. Hypothesis
Now we construct our hypothesis in order to check sunk cost effect and loss aversion.
3.1. Sunk Cost. Decision makers exhibit sunk cost if past decisions affect future
actions. Future decisions should be based only on future expected benefits and
future expected costs. The way we construct this hypothesis here is quite broad.
We put no restrictions regarding what effect the sunk costs can have on bidding
behavior. For instance, past sunk cost may make decision makers more aggressive in
their bidding or make them more careful or conservative. So for example if a decision
maker has made considerable investment in a business, then even if the future of
the business may not be very bright, the decision maker may keep investing more
in order to recoup that investment. In other circumstances, the decision maker may
behave more conservatively if he has made some investment in the past.
As discussed earlier, the standard auction theory predicts no effect on bids because
of entry fee and hence the bids should be HK$25 in both first and second price
auction with or without entry fee. But if sunk costs were to matter then then we
would observe a difference between the bids in entry fee and no-entry fee treatments.
Furthermore, the prospect theory based sunk cost model we developed earlier implies
not only a difference in the bids due to the introduction of an entry fee but also
a change in direction of the bids going from first price to second price auction.
9
Specifically, with entry fee the bids in first price auction would fall, while in second
price they would rise.
From the above discussion we develop the following hypotheses:
(1) The bid in the first price (FPA-NEF) and second price (SPA-NEF) no entry
fee should be different from the first price (FPA-FEF) and second price (SPAFEF) fixed entry fee respectively.
(2) The bid in first price auction auction with entry fee (FPA-FEF) is lower than
the bid in the no entry fee one (FPA-NEF).
(3) The bid in second price auction auction with entry fee (SPA-FEF) is higher
than the bid in the no entry fee one (SPA-NEF).
(4) The auction bid in the first price variable entry fee (FPA-VEF) treatment is
correlated to the entry bid in the same treatment.
We test these hypotheses through OLS regressions discussed later.
3.2. Loss Aversion. The second behavioral hypothesis is regarding loss aversion.
Loss aversion is exhibited by agents in case they value differently losses in respect
to gains. As a result what we expect is that the behavior of players will change
regarding their future decisions with respect to the past losses and make them more
conservative. By taking into account the past losses what we expect is that the
agents will be less willing to lose money in their future decisions. There are two
decisions which the players make, one to enter the auction or not and next to bid if
they do enter. Thus if the subjects in the above classroom experiments are bidding
for HK$25 and if they pay entry fee in order to participate then we expect the players
not enter. So we construct the following hypothesis
(1) If players are loss averse, subjects will not make Nash bids.
(2) In an all-pay auction where the subjects realize losses even when they do not
win the auction, cumulative earnings from the previous round will influence
the bids. In order to check this we look at all-pay auction data, where allpay auctions were run with subjects from the same student population. We
construct a hypothesis that the explanatory variable cumulative earnings
10
from the last round participated will be a significant in explanation of the
round bids.
(3) If subjects are loss averse they will not enter the first price or second price
winner pay auction. Given that they will lose money by entering and they
are entering a common value auction, subjects will try to avoid the loss by
not entering. Note here that it is rational/Nash to not enter in the designed
auctions. But if it can be shown that the subjects are not rational then we
get infer, though a weak one, that subjects show loss aversion.
Using the dependant variable BID, which is the auction bid by subjects in each
treatment we estimate the following regression equation for the first price auction:
BID = α1 +β1 D1+β2 D2+β3 BEGEARN+β5 D1∗BEGEARN+β6 D2∗BEGEARN+ε
The variable BEGEARN is the subject’s cumulative earning at the beginning of
each round and D1 and D2 are the dummy variables, where D1 is the dummy
for the fixed entry fee and D2 is the dummy for the all pay auction respectively.
The two product variables D1*BEGEARN and D2*BEGEARN measure the relative
effect of BEGEARN on bids in the entry fee and all pay treatment respectively
compared to the effect in the no entry fee treatment on bids. In other words β5
measures how significantly a subject’s endowment affects bids at the beginning of
each round in the entry fee treatment, relative to the same effect in the no entry fee
treatment. Similarly, β6 measures how significantly a subject’s endowment affects
bids at the beginning of each round in the all pay treatment, relative to the same
effect in the no entry fee treatment. Therefore, if the coefficient on D1 is significantly
different from zero, then that provides evidence for the sunk cost effect. Also if the
coefficient on D2*BEGEARN is negative and significantly different from zero, then
that provides evidence for loss aversion. This is due to the fact that subjects with
higher endowments would be more loss averse and hence more likely to bid low
amounts in order to protect themselves against large losses.
11
Similarly, using the dependant variable BID, which is the auction bid by subjects
in each treatment we estimate the following regression equation for the second price
auction:
BID = α1 + δ1 D1 + δ2 BEGEARN + δ3 D1 ∗ BEGEARN + ε
As before, the variable BEGEARN is the subject’s cumulative earning at the beginning of each round and D1 is the dummy variable for the fixed entry fee treatment.
The product variable D1*BEGEARN measures the relative effect of BEGEARN on
bids in the entry fee treatment compared to the effect in the no entry fee treatment.
Like before, if sunk cost effect exists then the coefficient on D1 must be significantly
different from zero.
Finally, we estimate a regression for the variable entry fee treatment given by:
BID = α1 + γ1 ENT RY BID + γ2 BEGEARN + ε
where, As before BID is the auction bid by each successful entrant and BEGEARN
is the endowment at the beginning of each round. ENTRYBID is the bid made by
each individual towards entering the auction. A value for the coefficient δ1 significantly from zero would be evidence of the prevalence of sunk cost effect.
4. Design
We ran two player complete information common value auctions with common
value of HK$25. The subject pool was drawn randomly on a volunteer basis from
students at City University of Hong Kong. First, all subjects make entry decisions
or entry bids (if any). After the entry decisions are made, all entrants are randomly
assigned to groups of two, wherein subjects make their bid decisions. In case of odd
number of subjects one group is assigned three subjects. If only one subject enters,
then there is no auction. All the subjects are re-matched after every round.
There were both first price and second price auctions. And in first price there were
the following treatments: with no entry fee, with fixed entry fee, variable entry fee
and an all-pay auction with no entry fee. There were similar treatments regarding
second price auction with no entry fee, with fixed entry fee, and an all-pay auction
12
with no entry fee. In case of no entry fee the subjects entered the main auction
and bid for the prize. In case of the fixed fee auctions, for both second price and
first price, subjects had a choice to enter the auction or not enter the auction. If
the subjects wanted to enter the auction then they had to pay HK$5 and then they
participated in the auction. For the variable fee auctions, the participants first had
to participate in an auction where the highest 60% bids were allowed to enter the
auction and bid for HK$ 25. Note the variable fee treatment was run only as first
price auction. For the first price all pay auction treatment, they were designed to
reflect standard first price auctions where the subjects entered without any entrance
fee and then made a bid which had to be paid, either win or lose. In the second price
all-pay, this represented a standard war of attrition. The players bid sequentially
in subsequent rounds. The bids increased every round at increments of HK$1 or$2.
Players were given a large endowment at the start and if they went bankrupt then
they stopped participating in the auction. Most treatments were repeated for eight
rounds. To summarize, the following treatments were run:
• First Price Sealed Bid Auctions
– No entry fee [FPA-NEF]
– Fixed entry fee of HK$5 [FPA-FEF]
– Variable entry fee, where players bid to enter [FPA-VEF]
– All pay auction with no entry fee [FPA-AP]
• Second Price Auctions
– Sealed bid with no entry fee [SPA-NEF]
– Sealed bid with fixed entry fee of HK$5 [SPA-FEF]
5. Results
For the results, we are interested in both the aggregated and disaggregated behavior of subjects. Initially, we look at the descriptive statistics of the aggregated
13
Table 1. Aggregated Data for First Price & Second Price Auctions
First Price
Second Price
Auctions
Auctions
NEF
FEF
VEF
AP
NEF
FEF
# of Auctions
451
365a
240
632
661
141a
Non-entrant %
na
41.66
40b
na
na
60
28.1
33.45
33
43.27
Mean Bid (entrants)
19.95 18.23 20.13 10.45
Mean Bid (winers)
21.9
Mean Bid (losers)
18.04 16.55 19.03
5.14
23.4
24.54
Mean Buyer Earnings (all)
1.54
-2.54 -0.36
1.97
0.87
-4.95
Mean Buyer Earnings (winners)
3.1
0.02
9.16
1.75
-4.91
0
-5
0
-5
-0.87
5.11
Mean Buyer Earnings (losers)
Mean Seller Earnings (entrant)
19.98 21.23 15.84
-1.54 5.18
a post-entry
-0.40
-0.30 -5.14
0.36
-1.96
b fixed by experimenter
behavior across different treatments for both the first price and second price auctions. Focusing on the first price auctions to begin with, we see from table 5 that
the average bid for the first price auction (FPA) with no entry fee (NEF) is 19.95,
with the average bid of ultimate winners being 21.9 and losers being 18.04. Looking
at the frequency of bids in figure 1 we observe only 3.5% of bids are near (up to
50 cents less) the equilibrium predicted bid of $25. Around 69% of the bids are
between 20-24.5, with most of these near $20. One of the reasons why the equilibrium predicted bid is not played is due to the fact that even though it increases the
probability of winning, but the actual earnings are zero (or close to). Therefore,
14
Table 2. Regression Results for First Price Auction
Coefficient
S.E.
t-stat
P-value
Constant
20.3661
0.3046 66.8536
D1 (Dummy for FEF)
-1.5903
0.3631
D2 (Dummy for AP)
-7.2689
0.4119 -17.6457
BEGEARN
-0.0107
0.0048
-2.2345
0.0255
D2*BEGEARN
-0.0635
0.0071
-8.8804
0
-4.3795
0
1231E-8
0
subjects willingly make the trade-off in favor of increases potential earnings at the
cost of lower chance of winning.
In the fixed entry fee (FEF) treatment where the subjects have a choice of entering
by paying a fee of $5, we observe from table 5 that around 58% of subjects choose
to enter and their average bid falls to 18.23 compared to the no entry fee case. The
average bid of winners and losers is also lower, similar to the average overall bid.
As can be observed from figure ??, the entry data disaggregated over rounds reveals
that entry falls from a high of around 75% in round 1 to less than 50% in round
8. This could be interpreted as subjects “learning" to stay out of an auction whose
equilibrium predicted expected earnings are negative, i.e. equal to the entry fee.
Looking at the frequency of bids in figure 1 we observe more clearly the significant
fall in average bids compared to the no entry fee case. The overwhelming majority of
the bids, around 77.5% are between 15-20 compared to the majority the bids being
in the 20-25 range for the no entry fee case. A t-test for the hypothesis regarding
the difference between the bids in the NEF treatment and the FEF treatment being
zero is rejected, with the t-statistic being 2.99. Hence, the difference in the average
bids is significant. Another noticeable observation is the fact that less than 1% of
bids are near (up to 50 cents less) the equilibrium predicted bid of $25.
The significant difference in average bids between the first price auctions with no
entry fee and the one with a fixed entry fee of $5 is consistent with the hypothesis
that there exists a sunk-cost effect. From table 5 we observe that the coefficient of
15
D1, i.e. the dummy for the entry fee treatment, is negative and significant (p-value
is almost zero), which provides evidence for a sunk cost effect. Also the negative
coefficient implies that compared to the no entry fee treatment, the subjects bid more
conservatively in this treatment. Subjects are willing to bid lower so that they can
increase their net earnings (subject to winning) and thereby recoup more money
in order to compensate for the entry costs. Of course by doing so they decrease
their chances of winning, so from an individual perspective the net effect on their
expected earnings is uncertain. But since there is a fall in overall average bids, we
would expect buyers to earn more in the FEF treatment post entry, i.e. before the
$5 entry fee is accounted for. Looking at the data on buyer earnings in table 5, we
see that this is indeed the case. The mean buyer earning in the NEF treatment for
the auction winners is 3.1 and obviously zero for the losers, thus resulting in average
buyer earnings of around 1.55. The mean buyer earnings of auction winners in the
FEF treatment net of entry costs is close to zero and obviously -5 for those who lost
the auction, resulting in average earnings amongst all auction entrants of around
-2.5. But this implies that earnings in the actual auction itself (i.e. ignoring the
entry fee) is 2.5 for all buyers and 5 for the winners, i.e. higher earnings from the
auction itself in the entry fee case compared to the no entry fee case.
Figure 1. Frequency Distribution of Bids for FPA (NEF & FEF)
Our above hypothesis that in a first price auction the sunk-cost effect leads to
less aggressive bidding in the presence of an entry fee gets further reinforced by
16
Table 3. Entry Bid Data for Variable Entry Fee FPA
FPA-VEF
Mean entry bid (all)
1.49
Mean entry bid (entrants)
2.28
Mean entry bid (non-entrants)
0.30
Mean entry bid (auction winners)
2.17
Mean entry bid (auction losers)
2.34
the evidence from the variable entry fee (VEF) treatment. In this treatment all
subjects had to first bid an amount for the right of entry in order to participate in
the subsequent auction. By design the highest 60% bidders were allowed to enter,
where each entrant had to pay the amount they bid after being declared eligible for
entry. From table 5 we observe that on average the subjects bid $1.49 for the right to
enter, an amount much smaller than the fixed entry fee of $5 in the FEF treatment.
Amongst those who were successful in entry the average bid was 2.28. As discussed
earlier our hypothesis that in a first price auction the sunk-cost effect leads to less
aggressive bidding in the presence of an entry fee was supported by the data from
the FEF treatment. Now for this hypothesis to hold true in the VEF treatment, it
must be true that subjects who paid higher entry fees had auction bids on average
lower than those who paid less to enter in the VEF treatment. From our regression
results in table ??, we find a significant negative correlation between entry fees and
auction bids.
Finally we note that the difference between the average auction bid in the VEF
treatment of 20.13 and the average bid of 19.95 in the no entry fee auction is not
statistically different. The likely reason could be that for the case of VEF, the
average entry payment of 1.49 is not significantly large enough to trigger a significant
sunk cost effect. But an entry payment of HK$5 has a considerable effect on the
17
Table 4. Regression Results for FPA-VEF Treatment
Coefficient
S.E.
t-stat
P-value
Constant
20.9442
0.1965 106.586
0
ENTRYBID
-0.2593
0.0508 -5.1027 4.84E-07
BEGEARN
-0.0042
0.0019 -2.1726
0.0302
bids of the subjects and hence the significant difference between the average bids in
NEf and FEF treatments.
Another possible explanation for the negative relationship between auction bids
and entry fees could be due to “loss aversion.” The subjects who entered the FEF
treatment after paying $5 (or the VEF treatment after paying different amounts),
had a subsequent valuation of the object 5 dollars less than the original valuation.
This would explain the fall in average bids due to the entry fee, i.e. since the subjects
have already made a payment/loss in order to enter the auction they reduce the final
bids so that they do not risk losing or paying more, as in the first price auction their
bid is directly related to their net earnings. While the loss aversion explanation holds
true in the auction decisions, this fails to explain why so many players (around 60%)
enter the auction in the FEF treatment in the first place. Similarly if loss aversion
held true, then subjects should entry bids of zero in the VEF treatment. Therefore
loss aversion is not consistent with the entry decisions of the subjects.
Coming to the aggregated behavior of subjects across different treatments of the
second price auctions, we see from table 5 that the average bid across 661 auctions
with no entry fee (NEF) is 28.1 , with the average bid of ultimate winners being
33 and losers being 23.4. Given that the valuation of all subjects would be $25, we
notice that there is significant overbidding compared to the true valuation, with the
mean overbidding over true valuation being around 12%. Kagel (1995) reports that
there is in general around 11% overbidding in second price auctions averaging across
numerous studies [Kagel et al (1887), Harstad (1990), Kagel & Levin (1993)]. Our
data on overbidding is therefore highly consistent with the magnitude of overbidding
18
reported in the literature. One of the common reasons in the literature attributed
to over-bidding is the so-called “Winner’s Curse.” But it should be noted that since
we have a common value auction without any noise regarding the true value, hence
there is no “Winner’s Curse" in our design. Therefore, the fact that we still observe
similar levels of overbidding implies that this phenomena is quite pervasive. In all
our treatments there were no restrictions on overbidding, except for an upper limit
of 100 on bids4, hence theoretically the magnitude of overbidding could have been
even higher.
Figure 2. Frequency Distribution of Bids for SPA (NEF & FEF)
Looking at the distribution of bids in the no entry fee (NEF) auction in Figure 2
we see that a little more than 50% of the bids were at the (weak) dominant strategy
of bidding the true value5 (5 cents either side). Around 20% of the bids were below
the dominant strategy and 27% were above. Therefore, even though bidding the
true value was by far the most prevalent strategy and both under and overbidding
were significant, yet the greater extent of overbidding and it’s higher range lead to
a mean bid which was significantly above the true value.
Comparing the results of the no entre fee (NEF) treatment to that of the entry
fee ($5) treatment (FEF), we see significantly higher mean bids. For the regression
results we see from table 5 that the coefficient for the dummy variable D1 is positive
4This
was primarily meant for restricting the effect of huge outliers distorting the data
536.5%
of bids were exactly at $25, the (weak) dominant strategy.
19
Table 5. Regression Results for Second Price Auction
Coefficient
S.E.
t-stat
P-value
Constant
28.1002
0.9982 28.1493
0
D1 (Dummy for FEF)
6.6810
1.4772
4.5226
663E-8
BEGEARN
-0.0022
0.0156 -0.1435
0.8858
D1*BEGEARN
-0.0425
0.0281 -1.5085
0.1316
and significant. This indicates evidence for the sunk cost effect. Also as can be
seen from table 5, average bid was 33.45 (32.47 for the truncated data), with the
average bid of ultimate winners being 43.27 and losers being 24.54. A t-test for
the hypothesis regarding the difference between the bids in SPA-NEF and SPAFEF being zero is rejected, with the t-statistic being -3.109. Even the frequency
distribution of bids in Figure 2 reveals the more aggressive bidding with entry fee.
While the percentage of true value bids drops to 33%, the frequency of overbids is
more than 38% with around 13% of them being bids of more than $50. Note that
while in first price auction bids decreased with entry fee, in second price auctions the
bids increased with entry fee. This could be due to the fact that from an individual
bidder’s perspective, aggressive bidding in a first price auction not only increases the
probability of winning but also necessarily decreases the value of the net earnings.
But, in a second price auction, aggressive bidding while increasing the probability
of winning does not necessarily decrease the net earnings, though if very bidder
becomes more aggressive then the net effect is a decrease in earnings. Therefore, we
argue that the aggressiveness of bidding that gets reinforced with the introduction of
an entry fee is evidence towards the prevalence of a sunk-cost effect in bids. Subjects
seem to be more willing to bid higher in order to increase their chances of winning
and hence get back the money paid for entry.
After looking at the characteristics of the aggregate data for all treatments above,
we now focus our attention on the disaggregated data, where we segment the whole
20
population of subjects into different cohorts, separately for both the first price and
second price auctions, based on the subjects likelihood of entry in the fixed entry
fee treatment. In other words, given that subjects in the fixed entry fee treatment
of the first price auctions played 8 rounds in every session, we calculate the entry
percentage for each subject in all the sessions. Similarly we calculate the entry
percentage for subjects in the fixed entry fee treatment of the second price auctions,
where the subjects played 6-9 rounds depending on the session. On aggregate around
60% and 40% of subjects chose to enter in the first price and second price auctions
respectively (see table 5). Figure 3 provides the frequency distribution of entry for
both first and second price auctions.
Figure 3. Frequency Distribution of Entry for FPA & SPA
Our objective in separating the population of subjects into different likelihood of
entry cohorts is to discern any “behavioral patterns” within the population, where the
“behavioral pattern” we are particularly interested in is whether a subjects predilection to a higher likelihood of entry has any impact on bidding behavior, as opposed
to the impact of entry on bidding behavior in a particular round which we have
already discussed earlier. Furthermore we are not just interested in the correlation
between entry % and bids in the fixed entry fee treatment, but also on the correlation between the likelihood of entry for a subject in the fixed fee treatment and the
bidding behavior for the same subject in the no entry fee treatment. This is relevant
because once we take into consideration the fact that subjects with a higher/lower
21
Table 6. Correlation Coefficients for First Price & Second Price Auctions
Correlation Coefficients
First Price Auctions Second Price Auctions
entry and NEF bid
0.09
0.194
entrya and FEF bid
0.014
-0.121
a entry fraction is > 0.
predilection to entry, when faced with an entry fee, might potentially demonstrate
a behavioral trait towards more/less aggressive bidding, then that trait should be
demonstrated irrespective of whether there actually exists an entry fee or not6. To
find such correlations we first isolate the population of subjects who were common
between both the no entry fee and fixed entry fee treatments for each of the two
auctions. For the first price auction, we have 94 common subjects and for the second
price auctions we have 108 common subjects common between the two treatments.
From table 5, we have the correlation data for likelihood of entry (in fractions)
and bids in both NEF and FEF treatments for each of the two auctions. We observe
that the correlation between entry fractions (i.e. absence or presence of innate
predilection towards entry) and magnitude of bids (average across all rounds for
each subject) is close to zero for both the NEF and the FEF7 first price auction
treatments. We can comprehensively reject the hypothesis that any innate tendency
towards higher likelihood of entry has a negative or positive impact on bidding
behavior of subjects. For the second price auctions, the correlation between entry
and NEF bid is a little higher than the corresponding value for the first price auction,
but it still is sufficiently close to zero that we can easily reject the hypothesis that
6Note
that the impact of an innate predilection to entry (if it exists) on bidding strategy (if any)
is a behavioral trait, while the impact of actual entry (if any) in a particular auction on bidding
is a strategic consideration. Our current concern is with the former, while the discussion in the
previous paragraphs on aggregate data was concerned with that latter.
7For the FEf treatment we ignore the data for subjects whose entry percentage is zero, since
their average bids would be necessarily zero, thus skewing the correlation.
22
predilection to entry has any impact on bidding. For the correlation between entry
and FEF bid, we get a small negative value. But again it is very close to zero and we
can easily reject the above hypothesis. Therefore from all our correlation data, we
are unable to discern any within population behavioral traits, based on innate entry
predilections, that have impact on subjects attitude towards bidding more or less
aggressively in the auctions. Therefore in our opinion the only explanatory factor
that is able to consistently account for the data across all the auctions is a prevalence
of what can be construed as a “sunk-cost effect." Loss aversion is another potential
explanatory factor but is unable to account for the presence of such high levels of
entry in both auctions, especially since average buyer earnings in fall substantially
in both auctions, the fall being especially high in the second price auction, due to
the more aggressive bidding in the entry fee treatment.
Coming to the first price all-pay auction we see from table 5, that the average
bid of 10.45 in the first price all-pay auction is actually less than the equilibrium
predicted average of 12.5, i.e. there is lack of individual over-dissipation. Also,
sellers expected revenue in the all-pay auction is significantly less than zero. This is
somewhat consistent with the results of Potters et. al (1988) but in contrast to most
other experimental results in all pay auctions where there is over-dissipation in rents
[Davis & Reilly (1998), Gneezy & Smorodinsky (2005), Lugovsky et al. (2005)]. Our
design for the all-pay auctions matched more closely that of Potters et. al (1988)
in terms of number of bidders (2 in all our all-pay sessions). Also unlike some of
the other experiments, our subjects were given an endowment once at the beginning
of the session and not before each treatment. Both these could help explain the
dissipation of rents results.
We ran the all-pay treatment to identify the “endowment effect” on bids, which
works through the loss aversion of subjects. Subjects with higher earnings (or endowments) are more loss averse and hence are likely to bid lesser amount s in all-pay
auctions, since if they lose they will have to pay their bids. From table 5 we observe
that the coefficient of D2*BEGEARN8 is negative and significant. This provides
8In our regression we
observed that the coefficient for D1*BEGERAN was not significant. There-
fore we dropped it from our regression.
23
evidence for loss aversion behavior, since this implies that subjects endowments or
cumulative earnings at the beginning of the round affects bids negatively and significantly more compared to the effect of the same for the no entry fee treatment,
where the effect is insignificant to begin with. From table 5 we observe a negative
correlation between earnings at the beginning of a round and bids in that round of
-0.32, which is a significant negative correlation. Therefore this again supports our
loss aversion hypothesis.
6. Conclusions
It has been suggested that decision makers ignore past sunk costs while making
decisions. Decision makers take into account the future benefits and costs and ignore
the past costs. This issue regarding sunk costs has been discussed and analyzed over
the past few decades, with evidence for and against the existence of presence of
sunk costs. In addition there has been studies about escalation of commitments
and wealth effects (Staw, 1981 and Camerer and Weber, 1999). In this paper, we
report the subjects’ failure to ignore sunk costs while making future decisions. The
subjects make their decisions in an market environment, bidding for an object of
known value. The design is motivated by both simplicity of the decision making
environment and individual choice in a market environment. We find that sunk
costs do affect bidding behavior or future decisions. The bidding behavior of the
subjects, on average, is influenced by the entry fee they pay at the door. We find this
effect present in both first price and second price auction. The sunk-cost effect result
is strengthened by the fact that we have a significant negative correlation between
entry bids (endogenous entry fee) and actual bids in the first-price auctions, i.e.
(endogenous) cost of entry negatively affects bids.
Various behavioral reasons have been given for decision making, including mental
accounting, prospect theory or reference dependence and loss aversion. Interestingly,
we find that bidding behavior is more aggressive in second price auctions and more
conservative in first price auction with respect to the bids where subjects pay no
entry fee. This suggests that the possible factor, influencing the decision making
is the sense of loss for the decision makers both in the sunk cost, as well as future
24
expected loss. For in the second price auction the subjects realize that they may
not have to pay the amount they bid while this increases the chance of winning the
auction and in the first price auction the subjects have to pay the amount they bid.
This results in more aggressive bidding in order to recover the loss of entrance fee
or sunk cost in second price. Subjects seem to value losses differently than gains.
Upon closer analysis of loss aversion in the players, we find that the subject pool
does exhibit loss averse behavior. The loss averse behavior we find is primarily
through the endowment effect, with the cumulative earnings during the bid decision
influencing the bidding behavior.
25
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