The effect of competition on the evaluation of lotteries.
Shavit, Tal ; Shahrabani, Shosh ; Benzion, Uri 等
I. Introduction
Many experiments carried out in various contexts have repeatedly
demonstrated the endowment effect (e.g., Kahneman et al., 1990; Thaler,
1980, Horowitz & McConnell, 2002). The endowment effect refers to
the disparity between the Willingness-To-Pay (WTP), which represents an
individual's buying price for a product, and the
Willingness-To-Accept (WTA), which represents an individual's
selling price for a product. According to the endowment effect, people
have a psychological feeling of belonging towards an asset they own and
as a result ask for a higher price than its value when they sell it. For
this reason, the selling price is higher than the buying price, even
though both should be equal and reveal the participants' true
value.
The purpose of our study is to analyze the impact of risk
preference on participants' bids for lotteries (WTP and WTA) within
a second-price auction (henceforth, SPA) mechanism (Vickery, 1961). The
SPA is a sealed bid auction in which the highest bidder in a buying
auction wins the final prize and pays the second highest bid. The lowest
bidder in a selling auction wins the final prize and pays the second
lowest bid. This mechanism provides participants an incentive to reveal
their true valuation, because they must buy the good if their bid wins
the auction (Vickrey, 1961). The theoretical nicety of the second-price
auction, first pointed out by Vickrey (1961), is that bidding one's
true value is a dominant strategy. In the WTP case, overbidding in the
SPA increases the likelihood that individuals will have to pay more for
the commodity than desired, while underbidding increases the chances
they will not win what they could have won if they had stated their true
preferences (Shogren et al., 2001).
Using financial assets represented by lotteries, we examine whether
the endowment effect (WTA>WTP) is valid as a general phenomenon for
all participants. In addition, we identify participants who place higher
WTP bids and lower WTA bids simply for the sake of winning an auction,
where WTP is higher than WTA (the "reversed" endowment effect:
WTA<WTP). These participants are defined as win-lovers. In the
literature, win-loving behavior has been described as the
"top-dog" effect (Shogren & Hayes, 1997), or the "joy
of winning" (Goeree & Offerman, 2003). Using financial
assets/lotteries with a known distribution, we test the consistency of
win-loving behavior for different lotteries and in buying and selling
positions.
Moreover, we test whether individuals who are win-lovers in
auctions tend to be more competitive than others in the social
comparison context. We constructed a questionnaire to measure
participants' degree of competitiveness, describing how much an
individual "enjoys competition." We find a strong relation
between the competitive index and win-loving attitude in the
Second-Price-Auction.
The paper is organized as follows. Section 2 reviews the
experimental literature, and Section 3 discusses the theoretical
background and develops the main hypotheses for the experiments. Section
4 describes the experimental procedure and methods, while Section 5
presents the major results and offers some possible explanations.
Section 6 presents the second experiment and its results regarding
win-loving behavior and the competitiveness index. Finally, Section 7
summarizes the paper and presents its conclusions.
II. Literature Review
The endowment effect has been demonstrated repeatedly in many
experiments and in various contexts (e.g., Katmeman et al., 1990,
Thaler, 1980, Kahneman et al., 1991, Loomes and Weber, 1997, and Weber
et al., 2000). Horowitz and McConnell (2002) examined evidence on the
experimental features of WTA/WTP and concluded that high WTA/WTP ratios
are not the result of experimental design. They found that ratios in
real experiments are not significantly different from hypothetical
experiments. Yet, the results of Plott and Zeiler (2005) show no
significant gap in experiments using the Becker-DeGroot-Marschak (BDM)
mechanism (Becker et al., 1964), a procedure applicable both to real
products and to risky assets. In auctions based on the BDM mechanism,
individuals buying an asset declare their maximum buying price (WTP). If
the bidding price is higher than a drawn number, the individual pays the
drawn number and buys the asset. When selling an asset, individuals
declare their minimum selling price (WTA). If the bidding price (WTA) is
lower than a drawn number, the individual receives the amount of the
drawn number and sells the asset. Plott and Zeiler (2005) question
whether the gap between WTA and WTP can be attributed to an endowment
effect. They argue that experimental procedure is critical in
controlling participant misconceptions.
In another experiment, Shogren et al. (2001) measured WTP and WTA
values of auction goods such as coffee mugs and candy bars using three
auction mechanisms: the Becker-DeGroot-Marschak (BDM) mechanism (Becker
et al., 1964), the second-price-auction (SPA), and the random nth-price
auction. According to the nth-price auction, bids and offers are
displayed in real time, and continuously crossed to yield a provisional
clearing price and quantity while the market is open. When the trading
period ends, all trades become binding at the price and quantity
standing at market close. Their results show that the endowment effect
can be eliminated with repetitions of the SPA or the random nth-price
auction.
In the context of lotteries, Kachelmeier and Shehata (1992)
confirmed the endowment effect, which influences the bidding pattern of
individuals. They reported dramatically different results depending on
whether the choice task involves buying or selling lotteries. Horowitz
and McConnell (2002) mentioned that lotteries have lower WTA/WTP ratios
on average than ordinary private goods, while no significant difference
between WTA and WTP was observed when the goods are monetary, as in
experiments using tokens (Kahneman et al. 1990).
Nevertheless, several studies argue that participants overbid in
common value auctions (where the object's true value is the same
for all bidders) because they may fall prey to the "winner's
curse." The "winner's curse" occurs if winners of
auctions systematically bid above the actual value of the objects and
thereby systematically incur losses (Kagel & Levin ,1986, Lind &
Plott, 1991).
An alternative explanation for overbidding in auctions is "joy
of winning" behavior or competitiveness behavior. This type of
behavior, reflected by the "top-dog" effect (Shogren &
Hayes, 1997; Cherry et al., 2004, Shahrabani et al., 2008), is said to
exist if bidders submit bids to win for winning's sake. They might
bid up on WTP and down on WTA simply to walk out of the auction as the
"top-dog" among their peers. In repeated trials of SPA
auctions, Corrigan and Rousu (2006) showed that some participants will
dramatically increase their bids for a candy bar, not only to obtain the
product but also to be the highest bidder.
The experiments of Corrigan and Rousu (2006), however, refer only
to the buying position (WTP) of real products, while in the current
study we also seek to examine the "top-dog" effect in the
context of the selling position (WTA) of financial assets. Moreover,
none of the above mentioned studies used risk classification to analyze
the bidding behavior of individuals and the endowment effect. We feel
that risk classification and win-loving are important variables that may
affect an individual's bidding behavior, especially in a
competitive environment. Hence, our paper considers these variables in a
theoretical framework and in experiments as well. As in previous
experimental works, we use the SPA mechanism, a popular mechanism in
laboratory valuation experiments (e.g., Krahnen et al., 1997; Shavit et
al., 2001; Shahrabani et al., 2008), to reveal participants'
private values (WTP and WTA) (Kagel, 1995). The advantage of using SPA
is that it creates a competitive environment between bidders, which is
absent in the BDM mechanism.
III. Theoretical Framework and Hypotheses
We use the framework of Expected Utility (EU) to measure
participants' risk-aversion in the context of bidding in a lottery
representing financial assets. (1) In this framework, we conform to the
prevalent economic approach of analyzing decision-making under
uncertainty, where gambles are the standard approach for obtaining EU
estimates (Morrison, 2000). In addition, in a series of experiments Hey
and Orme (1994) found that the best model of individuals' responses
is EU plus white noise.
We focus on a simple lottery L that pays [W.sub.j] > 0 with
probability [a.sub.j] where [n. summation over (j=1)] [a.sub.j] = 1. The
expected payoff from lottery L is: E(L) = [n. summation over (j=1)]
[a.sub.j] * [W.sub.j], and the Decision Maker's (DM) utility from
the value W is: U(W).
Definitions:
WTP--The maximal amount a DM is willing to pay for lottery L.
WTA--The minimal amount a DM is willing to accept to sell lottery L
he or she owns.
We define the DM as a "win-lover" if WTP > WTA because
"win-loving" causes people to lower their WTA if they are
selling, and to raise their WTP if they are buying, simply to increase
their chances of winning the auction. In addition, for every lottery L,
the DM is defined as being risk averse when the utility from the
lottery's expected value is higher than the utility from the
lottery itself, U(E(L))>E(U(L)), and as a risk-seeker when the
utility from the lottery's expected value is lower than the utility
from the lottery itself, U(E(L))<E(U(L)). Hence, since the WTP and
the WTA should be equal to the subjective certainty equivalent, the
definition of a risk-averse individual is as follows: WTP < E(L) and
WTA < E(L).
For example, Lottery L pays an outcome of 100 NIS with a
probability of 50%, or 50 NIS with a probability of 50%. The expected
payoff (value) of lottery L is E(L) = 100*0.5 + 50*0.5 = 75 NIS.
Individuals with WTP or WTA lower than 75 are defined as risk averse,
while individuals with WTP or WTA higher than 75 are defined as
risk-seekers.
The following Hypotheses 1 and 2 are based on the Expected Utility
framework and on the win-loving effect, while Hypothesis 3 presents some
restrictions for the existence of the endowment effect. Finally,
Hypothesis 4 refers to the relation between win-loving behavior in SPA
and the degree of competitiveness among participants in other contexts.
Hypothesis 1: WTP increases as risk-seeking increases and as
win-loving increases.
The intuition behind this hypothesis is that risk-seekers will
prefer the lottery ticket (or the risky asset) over the sure amount (the
expected value of the lottery ticket). Hence, their willingness to pay
for the lottery ticket will increase as they seek greater risk. In
addition, we expect that participants higher on win-loving will raise
their WTP simply to increase their chances of winning the auction. This
hypothesis is based on the findings of Corrigan and Rousu (2006) that
some participants dramatically increase their bids for candy bars not
only to obtain the product but also to be the highest bidder (the top
dog). Hypothesis 1 is also consistent with Goeree and Offerman (2003),
who showed that in a second-price private value auction with value
uncertainty, loss/risk aversion predicts a downward shift in the bidding
function, while the "joy of winning" leads to an upward shift.
In our experiments we examine our hypothesis for the different risk
attitude groups in the context of financial assets.
Hypothesis 2: WTA increases as risk-seeking increases and as
win-loving decreases.
The intuition behind this hypothesis is that risk-seekers will
prefer the lottery ticket over the sure amount (the expected value of
the lottery ticket). Therefore, risk-seekers will tend to keep a risky
lottery ticket and raise their WTA. Hence, we expect that greater
risk-seeking will increase a participant's WTA. We also predict
that higher win-loving will decrease a participant's WTA simply to
increase the chances of selling the lottery ticket (that is, of winning
the auction).
Hypothesis 3: Relation between WTP and WTA--The Endowment Effect:
In the case of financial assets, the endowment effect (WTA>WTP) does
not exist for all participants. For the win-loving group the reversed
endowment effect (WTA < WTP) consistently exists.
While some previous studies have found large disparities between
WTP and WTA for lotteries (e.g., Kachelmeier & Shehata, 1992),
others have shown that this disparity is small or not significant at all
for lotteries or for money instead of private goods (Kahneman et al.
1990, p. 1328, Horowitz & McConnell, 2002). Our hypothesis is that
the endowment effect is not a general phenomenon for financial assets.
However, when we classify participants according to risk attitude and
win-loving behavior, we expect to find this effect only among those who
are risk-averse (who bid lower WTP), while for other participants we do
not expect to find it in the context of lotteries. Moreover, we expect
that the reversed endowment effect (WTA < WTP) exists (consistently)
for the win-loving group in all lotteries, simply because participants
want to increase their chances of winning the auctions by increasing
their WTP and decreasing their WTA for the same lotteries.
Hypothesis 4: Win-lovers in auctions are more competitive in the
social comparison context than are non-win-lovers.
Another question of interest to us is the relation between
win-loving behavior in financial auctions and individuals'
competitiveness attitude in the social comparison context. Hypothesis 4
assumes consistent behavior among participants in different activities
(e.g., auction and social context).
IV. Experimental Methods
1. Experimental design and procedure--Experiment 1
Eighty-six undergraduate economics students from Ben-Gurion
University and The Max Stem Academic College of Emek Yezreel
participated in the first experiment. The experiment took place in class
and lasted approximately one hour. The participants were divided into
two groups (Group 1 included 41 participants and Group 2 included 45
participants). The lottery values and initial balances for Group 1 (see
Appendix 1 for examples) were multiplied by 10 to get the lottery values
and initial balances for Group 2. Participants in both groups were
asked: (a) to bid the maximum price they are willing to pay (WTP) for
different lotteries, and (b) to ask the minimum price they are willing
to accept for different lotteries they own (WTA).
The lotteries we chose represent stocks and options; however to
avoid any labeling effect, we did not mention the financial terms
"stock" and "option." In the instructions,
participants were told that the assets (lotteries) will be sold and
bought from them using a Second-Price-Auction (SPA), which is a sealed
bid auction. In the case of an SPA buying auction, the participant with
the highest bidding price wins the auction, but pays the second highest
bidding price in the group participating in the auction. In the case of
a selling auction, the participant with the lowest asking price wins the
auction, but receives the second lowest asking price in the group
participating in the auction. Before the experiment began, we explained
why participants should optimally bid their own private values in the
SPA. In the WTP case, overbidding in the SPA increases the likelihood
that individuals will have to pay more for the good than desired, while
underbidding increases the chances they will not win what they could
have won had they stated their true preferences (Shogren et al., 2001).
In each auction, each participant received an initial balance. In
the case of selling problems, participants owned the initial balance and
the lottery. To avoid an income effect in the selling problems with high
expected value lotteries (Lottery A in Table 1), participants'
initial balance was lower than in the buying problems (2).
Before the experiments began, we handed out the written
instructions (see Appendix 2), including examples, and gave the
participants ten minutes to read them. We then read the instructions
aloud, explained the examples on a board, and answered questions. The
auctions were presented in random order to avoid any order effect
(except for auction 1, which was used for risk attitude measurement).
Each problem or assignment was typed on a separate page, so participants
answered one assignment at a time and inserted the completed page into
an empty envelope. This procedure was carried out to avoid the
possibility of returning to previous answers while answering a current
problem.
Participants were told that at the end of the experiment, a
computer program would randomly divide them into groups of five. Using
the SPA, the five participants in each group competed on buying
lotteries and selling lotteries. To provide concrete incentives, we told
all participants that one of the problems would be randomly selected at
the end of the experiment and that we would pay them according to their
final balance in the selected problem. The average payment was 20 New
Israel Shekels (approximately $4.50 US). Participants in Group 1 were
told they would be paid 10% (in New Israeli Shekels) of the final
balance for the selected problem, while participants in Group 2 were
told they would be paid only 1% (in New Israeli Shekels) of the final
balance. The concrete incentives were the same for both groups, because
Group 1 's lotteries values and initial balances were multiplied by
ten to get Group 2's lotteries values and initial balances.
2. Description of the Auctions
The nine auctions presented in the experiment (see Appendix 1 for
examples) are described in Table A.1 (see Appendix 3). All assets are
presented in two positions: buying and selling (problems 2 to 9), while
the first three auctions are used as control auctions with no relation
to the other auctions in the experiment. The main assets are described
in Table 1.
Lottery A, which represents a stock, pays 120 with probability 0.4,
80 with probability 0.4, and 25 otherwise. Lottery B (Call-Option (70))
can be described as a call-option on the stock (lottery A). In a
call-option, the holder of this option has the fight to buy the stock at
a certain price, in this case -70. Therefore, the option outcome of
Lottery B can be described as MAX (0, Lottery A's outcome minus
70), or more specifically, Lottery B pays 50 with probability 0.4, 10
with probability 0.4, and 0 otherwise.
Lottery C (Put-Option (90)) can be described as a put-option on the
stock (Lottery A). In a put-option, the option holder has the fight to
sell the stock at a certain price, in this case -90. Therefore, the
option outcome of Lottery C can be described as MAX (0, 90 minus Lottery
A's outcome). More specifically, Lottery C pays 10 with probability
0.4, 65 with probability 0.2, and 0 otherwise. Lottery D (Put-Option
(120)) is the fight to sell Lottery A (the stock) at 120. Therefore, the
option outcome can be described as MAX (0, 120 minus Lottery A's
outcome). More specifically, Lottery D pays 40 with probability 0.4, 95
with probability 0.2, and 0 otherwise.
3. Classification of Participants According to Risk Attitude and
Win-Loving
Problem 1 was used to obtain a participant's risk attitude. In
this problem, we asked each participant to bid the maximum price he or
she is willing to pay for a lottery that pays 200 with probability 1/3,
100 with probability 1/3 and 0 otherwise. Consistent with previous
studies, which infer risk aversion by eliciting buying and/or selling
prices for lotteries in experiments (Holt & Laury, 2002; Anderhub et
al., 2001; Shavit et al., 2001), we define risk attitude by comparing a
participant's WTP to the expected value of the lottery. According
to the WTP for the lottery in problem 1, we divided the participants
into three groups. One-third of those with the highest WTP (an average
ratio of 1.29) were defined as risk-seeking (29 participants). For
participants in this group, the WTP was higher than the expected payoff
from the lottery. Another third, those with the lowest WTP (an average
ratio of 0.55), were defined as risk-averse (29 participants). The WTP
for those in this group was lower than the expected payoff from the
lottery. The remaining third, those whose WTP fell between that of the
risk-seeking and the risk-averse groups (average ratio of 0.98), were
defined as risk-neutral (28 participants). The reason for choosing three
equal risk attitude groups was to emphasize the difference between the
risk-averse, risk-neutral and risk-seeking groups, and to avoid a
situation where risk-neutral participants (with limited prices) are
included in the risk-seeking group. We do not show the risk-neutral
results separately, since we want to emphasize the differences between
the two extreme risk attitude groups (risk-averse and risk-seekers).
Nevertheless, we include this group in all the results and in the
regression analysis. For this reason, we divide the risk-seeker group
into two sub-groups. Half of the risk-seekers with WTA < WTP (those
with the highest difference between WTP and WTA in Lottery A) were
defined as "win-lovers" (14 participants). (3) Those in the
other half of the group were simply defined as risk-seekers (15
participants). We should emphasize here that the win-loving group is not
a distinct group separate from the standard risk categories; rather it
is a sub-group of the risk-seekers. It is possible that win-loving
behavior influences risk-averse and risk-neutral participants. However,
the size and impact of this effect seem to be higher for the
risk-seekers group. Therefore, we divided only the risk-seekers into two
equal groups to highlight win-loving behavior and to show that
risk-seekers may in fact be win-lovers.
V. Experiment 1 Results
Table 2 describes the relative price (buying or asking price for
the expected values) for Lotteries B, C and D for the different risk
attitudes and win-loving groups, and Table 3 describes the results of
the Mann-Whitney U-Test on the hypothesis that the bidding prices are
equal between the sub-groups. In analyzing the results, we combined
Groups 1 and 2 into a single group, since we did not find any essential
differences between the two groups. In addition, Lottery A is not
included in the results, since we used this lottery to measure the
win-loving effect among participants. We used the ratio between the
bidding (or asking) price and the lottery's expected value instead
of the price in New Israeli Shekels.
Tables 2 and 3 strongly confirm the first part of Hypothesis 1,
that is, that WTP increases as the risk-seeking measure increases for
all lotteries. For example, Table 3 shows that the difference in the
average ratio of price to expected value (WTP) between risk-averse and
risk-seeking participants is significantly negative for all lotteries
(-3.76, -3.63, and -3.95, for Lotteries B, C, D, respectively). In other
words, the WTP of risk-seekers is significantly higher than the WTP of
risk-averse participants.
The results in Tables 2 and 3 also confirm the second part of
Hypothesis 1, that win-loving behavior increases the WTP. Table 2
indicates that the WTP of the win-lovers group is the highest among all
groups for all the lotteries. In addition, Table 3 shows that the
difference in the average ratio of price to expected value (WTP) between
that of all participants excluding the win-lovers group and that of the
win-lovers group is significantly negative for all lotteries (-3.50,
-2.38, and -2.53, for lotteries B, C, D, respectively). Inother words,
the results in Table 3 confirm that win-lovers bid significantly higher
than all other participants in all lotteries in the buying position.
The overbidding pattern we found for some participants is
compatible with controlled laboratory experiments that have provided
evidence for overbidding in common value auctions (Lind & Plott,
1991). In addition, our finding that risk-averse individuals will more
likely tend to decrease their WTP is compatible with the prediction that
risk/loss aversion causes a downward shift in bids in SPA auctions
(Goeree & Offerman, 2003). Moreover, we suggest that in the context
of the competitive environment of a second-price private value auction,
participants' WTP is influenced by their risk attitude as well as
by their win-loving behavior.
Our second result addresses Hypothesis 2. In the results shown in
Tables 2 and 3 we cannot separately control for win-loving, endowment
effect, and risk aversion. Therefore, the findings do not reflect any
significant differences in WTA among the different groups. Two opposite
effects emerge. Greater risk-seeking increases the WTA, while greater
win-loving decreases the WTA. Therefore, it is possible that the two
effects offset one another for some participants.
Based upon the Wilcoxon-Signed Ranks test, the results in Table 3
show:
(a) The endowment effect (WTA>WTP) holds only for risk-averse
participants.
(b) The endowment effect is reversed (WTA< WTP) for the
win-lovers group.
In general, the results (Table 2) confirm Hypothesis 3, i.e. for
all participants the endowment effect in financial assets considered in
this study does not exist (column 6). Moreover, for all participants,
without taking win-lovers into consideration, the difference between the
WTA and the WTP is positive and significant (last column--5%
significance level for Lotteries B and C, and 10% significance level for
Lottery D). When we examine the difference (WTA-WTP) for each risk group
separately, however, a clearer picture emerges. For risk-averse
participants, the endowment effect exists in all the lotteries at the 5%
significance level (Table 2). For risk-seekers, the endowment effect
does not hold, while for the win-lovers sub-group, we found the
existence of a "reversed" endowment effect (WTA < WTP) for
all financial assets in this study (at the 5% (Lottery C) or 10%
(Lotteries B and D) significance level).
These results are compatible with the findings of Kahneman et al.
(1990, p. 1328) that for money instead of private goods, the disparity
between WTA and WTP is not significant. We add to this finding by
showing that the endowment effect is valid only for one group and
reversed for another group. Therefore, we emphasize the importance of
separating participants into different risk attitude and win-loving
groups to explain the differences in magnitude of the disparity between
the WTP and the WTA in financial assets.
VI. Win-Loving and Competitiveness Index
Bidding in SPA tends to reveal the competitive nature of an
individual in that particular context. An important issue is whether
such behavior is also related to competitive behavior in the social
context. To examine this relationship, we constructed a competitive
index based on a questionnaire, and participants were tested both on the
questionnaire and on the SPA. Our hypothesis is that individuals who are
win-lovers in auctions will tend to be more competitive than others in
the social comparison context as well.
1. Experimental Design--Experiment 2
The participants in the experiment were 85 undergraduate economics
students from the Max Stern Academic College of Emek Yezreel. The
experiment took place in class, and lasted approximately half an hour.
In the first stage of Experiment 2 we repeated the stages of Experiment
1, this time using only Lottery A. In the second stage of Experiment 2
we administered a questionnaire based on the "competitiveness"
dimension questionnaire of Krebs et al. (2000). The questionnaire
included six questions (see Table A.2 in Appendix 4) to measure
participants' degree of competitiveness, which describes to what
extent an individual "enjoys competition" in the social
comparison context. The questionnaire also included seven questions used
only for purposes of distraction. Questions were measured on a 5-point
Likert-type scale, with possible responses as follows: strongly agree
(5), agree (4), neither agree nor disagree (3), disagree (2), and
strongly disagree (1). Negative items were reverse scored so that high
scores indicated higher level of competitiveness. The scores were
averaged for each participant to form the "competitiveness
index." Next, as in the first experiment we divided the
participants into three groups according to the difference between WTP
and WTA in Lottery A. We show the results for two groups only:
win-lovers and non-win-lovers.
2. Experiment 2--Results
The main results of Experiment 2 are presented in Table 4. The
table shows that the win-lovers group has a significantly higher
competitiveness index than the non-win-lovers group (3.65 versus 3.2).
In addition, we found the following reverse relation: Individuals with a
higher competitiveness index exhibit a significantly greater difference
between WTP and WTA. Table 5 indicates that WTP-WTA is 0.48 for the
competitive group versus 0.19 for the non-competitive group.
These results confirm Hypothesis 4, that win-lovers in auctions
have a higher competitive index in the social comparison context. The
importance of this result is that an individual who is competitive in
one situation tends to be competitive in other situations as well. If
this is true, then SPA behavior may to some extent predict behavior in
other contexts as well.
VII. Discussion and Conclusions
Our results indicate that the endowment effect (WTA>WTP) exists
for risk-averse individuals, does not hold for risk-seekers, and is
reversed (e.g., WTA<WTP) for the sub-group of win-lovers. Thus, we
conclude that the endowment effect seems to be weaker for financial
assets.
The outcomes of our experiments show that win-lovers consistently
tend to reduce the price they are willing to accept for their own asset,
and increase the price they are willing to pay for buying the same
asset. This finding is compatible with the evidence provided by Corrigan
and Rousu (2006) regarding the "top-dog" effect in repeated
trials of SPA auctions for real products (coffee mugs and candy bars).
However, our experimental results show that the win-loving effect exists
in non-repeated games and is consistent over different lotteries
representing financial assets. Moreover, we show that win-loving
behavior has an impact not only on individuals' WTP but also on
their WTA.
Another important finding is that win-lovers in SPA tend to be more
competitive in the social comparison context as well. This indicates
that win-loving in SPA may reflect the competitive characteristic of
individuals in other aspects as well. Moreover, win-loving gamblers can
be satisfied when they win some games, even though overall they
experienced a monetary loss. Therefore, we believe that win-loving
behavior can explain participation in auctions and Internet auctions.
Furthermore, win-loving may explain deal-prone behavior that can lead to
buying goods that are beyond an individual's optimal level.
Nevertheless, more work is needed to justify these intuitive claims.
Finally, we conclude that decision-makers' bidding patterns
can be better explained if we take into account an individual's
risk attitude and win-loving behavior, as well as the individual's
position with respect to the asset (buying or selling). Considering all
these elements together can give us greater insight into an
individual's bidding pattern. Researchers who use experimental
auctions, such as the second price auction, to test behavioral
hypotheses should take also take participants' competitiveness into
consideration and not only their risk attitude.
Appendix 1--Sample Questions for Group 1
Group 2's problems were multiplied by 10.
The Problems:
(1) Buying Lottery A (Stock)
Your initial balance is 200 N.I.S.
What is the maximum price you are willing to pay for buying the
following lottery ticket:
Probability Payoff
40% 120
40% 80
20% 25
Price --.
(2) Selling Lottery A (Stock)
Your initial balance is 100 N.I.S. In addition, you own the
following lottery ticket:
Probability Payoff
40% 120
40% 80
20% 25
What is the minimum price you are willing to receive for selling
this lottery ticket.
Price --.
Appendix 2--Instructions
The instructions for Group 2 were the same as for Group 1, except
for the following details:
(1) All the values were multiplied by 10.
(2) In the payment calculation we promised participants 1% of the
final balance in the chosen question (and not 10%).
The Instructions:
Welcome to an experiment concerned with decision-making in
lotteries.
General Explanation:
* In the experiment, you will be asked to answer questions about
lotteries.
* You should answer all the questions.
* You will be asked to bid a price for two types of lotteries: (1)
buying lotteries (2) selling lotteries. You will participate in auctions
for the buying and selling of lotteries.
* All participants will be randomly divided (by the computer) into
groups of five participants. Each group will participate in auctions for
buying and selling lotteries.
* In the case of buying a lottery, the highest price in the group
will win the auction.
* In the case of selling a lottery, the lowest price in the group
will win the auction.
* In each question you will receive an initial balance, which you
can use in the auctions. The initial balance can differ from one
question to another.
* The Auctions
(1) Buying a Lottery
In some of the questions, you will participate in an auction for
buying a lottery ticket. In these questions, you will be asked to state
the maximum price you are willing to pay for the lottery.
Example
Your initial balance is 150 N.I.S.
What is the maximum price you are willing to pay for buying the
following lottery ticket:
Probability Payoff
20% 150
70% 100
10% 50
Price --.
(2) Selling a Lottery You Own
In some of the questions, you will participate in an auction for
selling a lottery ticket you own. In these questions, you will be asked
to state the minimum price you are willing to receive for this lottery
ticket.
An Example
Your initial balance is 150 N.I.S. In addition, you own the
following lottery ticket:
Probability Payoff
20% 150
70% 100
10% 50
What is the minimum price you are willing to receive for selling
this lottery ticket?
Price --.
* Rules of the Auctions
Participants will be randomly divided into groups of five
participants.
* For Buying a Lottery
The highest bidder in the group will receive the lottery and pay
the second price in the group.
For example: Let's say the bidding prices in a group are 112,
73, 135, 80, and 140. The bidder with the price of 140 will receive the
lottery and pay 135 (the second price in the group).
* For Selling the Lottery You Own
The lowest bidder in the group will receive the second price in the
group and will relinquish the lottery he owns.
For example: Let's say the bidding prices in a group are 112,
73, 135, 80, and 140. The bidder with the price of 73 will receive 80
(the second lowest in the group) and relinquish the lottery he owns.
* Payment Calculations
At the end of the experiment, one of the questions will be randomly
chosen (by the computer). We will pay you 10% of the final balance in
the chosen question.
For Example:
If the final balance in the chosen question is 200, you will get 20
N.I.S. for participating in the experiment (10%*200 = 20).
* You should relate to each question separately. The amounts are
not accumulated from one question to another.
Appendix 3--Description of the Problems
TABLE A.1.
Description of the Problems
Problem Symbol Description
1 R Control for risk attitude
2 WTP-A WTP for the basic lottery
3 WTA-A WTA for the basic lottery
4 WTP-B WTP for call option on
the basic lottery
5 WTA-B WTA for call option on
the basic lottery
6 WTP-C WTP for put option (90)
on the basic lottery
7 WTA-C WTA for put option (90)
on the basic lottery
8 WTP-D WTP for put option (120)
on the basic lottery
9 WTA-D WTA for put option (120)
on the basic lottery
Appendix 4--Win-Loving Questionnaire
TABLE A.2.
Win-Loving Questionnaire
1 I try harder when I'm competing with other people.
2 I enjoy competing with others.
3 It annoys me when other people perform
better than I do.
4 It is not so important to me to become the
"top dog" when I am competing with others.
5 I feel disappointed if I do not win a competition.
6 I define myself as a competitive person.
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Notes
(1.) The expected utility is calculated by taking the weighted
average of all possible outcomes under certain circumstances, with the
weights assigned according to the likelihood, or probability, that any
particular event will occur.
(2.) We could have reduced the initial balance in these problems by
the lottery's expected value, but to simplify the questionnaire we
preferred rounded amounts. Hence we reduced the initial balance from 200
to 100, even though the expected value was 85.
(3.) Although we used Lottery A to identify the win-lovers, we
could have used any other lottery for the same purpose, since there is
consistency across lotteries in terms of participant responses.
Tal Shavit, * Shosh Shahrabani, ** and Uri Benzion ***
* Tal Shavit, Ph.D., is a senior lecturer and Head of Department of
Finance, The School of Business Administration, College of Management, 7
Yitzhak Rabin Blvd., Rishon LeZion 75190, Israel, shavittal@gmail.com
** Shosh Shahrabani, D.Sc., is a senior lecturer in the Economics
and Management Department, The Max Stern Academic College of Emek
Yezreel, Emek Yezreel 19300, Israel, shoshs@yvc.ac.il
*** Uri Benzion is a professor in the Department of Economics,
Ben-Gurion University, Beer-Sheva 84105, Israel, and the Western Galilee
College, P.O.B. 2125 Akko, Israel, uriusa2@gmail.com.
Corresponding author: Shosh Shahrabani, D.Sc., Economics and
Management Department, The Max Stern Academic College of Emek Yezreel,
Emek Yezreel 19300, Israel, shoshs@yvc.ac.il Tel: 972-49533686, Fax:
97246423522
TABLE 1.
Main Assets Description
Probabilities
and Values
Probabilities Expected
Assets 40% 40% 20% Value
Lottery A 120 80 25 85
(Stock)
Lottery B Call 50 10 0 24
Option (70)
Lottery C Put 0 10 65 17
Option (90)
Lottery D Put 0 40 95 35
Option (120)
TABLE 2.
Average WTP and WTA, and difference between them according to
risk attitude groups and win-loving groups
Average ratio of the bid to the
expected value of the lottery
Risk-Averse Risk-Seekers Win-Lovers
Asset Position (N=29) (N=15) (N=14)
Lottery B Buy (WTP) 0.67 (0.43) 1.24 (0.64) 1.65 (0.82)
Sell (WTA) 1.02 (0.53) 1.17 (0.38) 1.22 (0.67)
WTA-WTP 0.35 ** -0.07 -0.43 *
Lottery C Buy (WTP) 0.67 (0.39) 1.35(l 2.16(l
Sell (WTA) 1.14 (0.76) 1.26 (0.6) 1.08 (0.72)
WTA-WTP 0.47 ** -0.09 -1.08 **
Lottery D Buy (WTP) 0.65 (0.3) 1.23 (0.51) 1.33 (0.62)
Sell (WTA) 0.89 (0.44) 0.96 (0.17) 1.08 (0.46)
WTA-WTP 0.24 ** -0.27 ** -0.25 *
Average ratio of the bid to the
expected value of the lottery
All
All Participants
Participants excluding
Asset Position
(N=86) Win-Lovers
Lottery B Buy (WTP) 1.04 (0.65) 0.92 (0.54)
Sell (WTA) 1.14 (0.61) 1.12 (0.6)
WTA-WTP 0.1 0.21 **
Lottery C Buy (WTP) 1.2 (1.04) 1.0 (0.78)
Sell (WTA) 1.13 (0.71) 1.14 (0.71)
WTA-WTP -0.07 0.14 **
Lottery D Buy (WTP) 0.95 (0.56) 0.88 (0.52)
Sell (WTA) 1.0 (0.42) 0.98 (0.41)
WTA-WTP 0.05 0.1 *
(+) Standard deviations are presented in parentheses.
* and ** denote significance at the 5% and 10% levels (of the
Wilcoxon Signed Ranks Test) for the hypothesis that the average
ratio of the bid to the expected value of the lottery is equal
for the buying position and for the selling position.
TABLE 3.
Statistical tests comparing WTP and WTA between Sub-Groups
All participants
Risk-Averse versus excluding
Risk-Seeking Win-Lovers versus
[Z.sup.+] value Win-Lovers Z
Position Asset (p value) * value (p value) *
BUY (WTP) Lottery B -3.76 (0.00) -3.5 (0.00)
Lottery C -3.63 (0.00) -2.38 (0.01)
Lottery D -3.95 (0.00) -2.53 (0.01)
Sell (WTA) Lottery B -1.18 (0.12) -0.3 (0.38)
Lottery C -0.86 (0.2) -0.81 (0.21)
Lottery D -0.1 (0.46) -0.61 (0.27)
* Z-value and significance (p value) in parentheses of one-
tailed Mann-Whitney U-Test for hypothesis that the average ratio
of the bid to the expected value of the lottery is equal for the
two sub groups.
TABLE 4.
Bidding pattern of win-lovers and non-win-lovers in SPA and their
competitiveness index
Non-Win- Mann-Whitney
Win-Lovers Lovers Test Z value
(n = 28) (n = 37) (p value)
WTP-WTA 0.72 -0.16 2.96 (0.00)
Competitiveness 3.65 3.2 6.9 (0.00)
Index *
WTP 1.38 0.77 2.12 (0.01)
WTA 0.66 0.93 5.02 (0.00)
* Average score for six competitive questions. Higher score
indicates higher level of competitiveness (5 = very competitive,
1 = not competitive at all).
(+) Z-value and significance (p value) in the parentheses of
one-tailed Mann-Whitney U-Test for hypothesis that average
variable is equal for the two sub-groups.
TABLE 5.
Bidding Patterns of Competitive group versus
Non-Competitive group
Mann-Whitney
Competitive Non-Competitive Test Z value
Index * group (p value)
Competitiveness 4.45 2.32 5.74 (0.00)
Index *
WTP 1.19 0.98 1.33 (0.09)
WTA 0.71 0.79 0.93 (0.17)
WTP-WTA 0.48 0.19 1.54 (0.05)
* Average score for 6 competitive questions. Higher score
indicates higher level of competitiveness (5 = very competitive,
1 = not competitive at all).
(+) Indicates Z-value and significance (in parentheses) of
one-tailed Mann-Whitney U-Test for hypothesis that average
variable is equal for the two sub-groups.
