Disappointment Aversion in
Internet Vickrey Auctions*
Doron Sonsino
School of Business Administration
College of Management
Rishon Lezion, Israel
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* This document summarizes the study. The paper will be available at the conference.
Disappointment Aversion in
Internet Vickrey Auctions*
Alternative Titles:
*Fear of regret in Internet Vickrey auctions?
(Intuition behind results; but I do not employ
regret theory)
*Pessimism in Internet Vickrey auctions?
(actually what I document)
2
Preliminary Description of experiment
•Run a Vickrey auction experiment on the
Internet (strategic equivalence to “English
auctions with proxy bidding”)
•Subjects bid for basic gift certificates and
short sequences of binary lotteries over these
gifts (actual payoff determined by random
auction selection)
3
•Bids for lotteries and underlying gifts are
used to derive the risk-weighting patterns of
subjects and check dependence on the level
of prizes employed
Main Results
•Value-uncertainty has a two-fold aversive
effect on bidding
1. Bids for binary lotteries are close to the
bids for the worst prizes that the lotteries may
pay, even when the probability of obtaining
the better prize is larger than 50% (Uniform
pessimism)
2. Pessimism becomes stronger as payoff
variability increases
•Results appear for 3 groups of subjects, from
2 different universities, in 2 different versions
of the experiment (N=107 in total)
4
Motivation: Internet Auctions (1)
Empirical research:
Significant decrease in bids and prices when
auctions (auctioneers) seem risky
Kauffman and Wood (forthcoming):
description-length and picture
Bajari and Hortaçsu (2004):
reputation of seller
Melnik and Alm (2005):
Reputation effect strongest for non certified coins
without a “visual scan”
5
Motivation: Internet Auctions (2)
• Uncertainty regarding the value that winner
would collect significantly reduce bids and
prices
•
Actual complaint rates- very low
-140,000 complaints in 2005 when Ebay alone listed
1.9 billion auctions
-0.6% negative feedbacks on Ebay
• Empirical examination of the effect in the
field hindered by control problems
• Motivate a controlled experimental
examination
6
Motivation: Probability Weighting
Kahneman and Tversky (1979,1992)
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
p
w( p)  
( p  (1  p) )1 / 
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
•Careful (Non parametric) Elicitation studies (Wu
and Gonzales, 1999; Abdellaoui, 2000; Bleichrodt
and Pinto, 2000, recent literature on weighting of
uncertainty)
•Morivates the examination of weighting patterns
in (field) incentive-compatible Vickrey auctions
7
Why Study Vickrey Auctions?
• Most frequent auction format on the Web:
English auction with proxy bidding
Example:
•
•
•
•
•
Minimum bid: 600
Bidder A: proxy bid 1000
Bidder B: Proxy bid 800
Bidder C: proxy bid 1200
Closing price 1000 (+increment)
• Strategic equivalence to Vickrey auctions
• Equilibrium bid (iid):
maximal willingness to pay
8
Method – Subject’ recruiting
• Subjects recruited by distributing ads calling for
participation in auction-experiment
• real valuable prizes (luxurious weekend vacation..)
• Personal usernames and passwords
• No restrictions on location and length of participation
• Four-phase (screen) experiment
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Basic Gift Certificates
• 3 certificates of different valuation
• Certificate A: weekend vacation in 4 stars hotel
for the winner and her spouse (bed & breakfast)
• Certificate B: Dinner for the winner and her
friend in a one of 3 gourmand restaurants
• Certificate C: Choice between a fine bottle of
wine and box of gourmand chocolate
• 3 versions of A; 3 versions of B and 2 versions
of C
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Lotteries on Gift Certificates
3 treatments X 5 (same) win-probabilities
Version I of the experiment
AC (HL)
0.1
0.3
0.5
0.7
0.9
AB (HM)
0.1
0.3
0.5
0.7
0.9
BC (ML)
0.1
0.3
0.5
0.7
0.9
Version II of the experiment
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AC (HL)
0.2
0.4
0.5
0.6 0.8
AB (HM)
0.2
0.4
0.5
0.6 0.8
BC (ML)
0.2
0.4
0.5
0.6 0.8
The Lottery-auctions: Method
• 3 treatments (AB/AC/BC) presented in random
order
• Separate page for each treatment
•Descending/ascending p-order (fixed across
treatments)
• Subjects filled in their bids for the 5 lotteries and
than clicked a submit bids button. Bids were
represented for reconfirmation
• Returning to preceding pages was impossible
• Additional lottery (for checking reliability)
12
Methodological Concerns (1)
1. Subjects suspicion
Subjects invited in advance to take active part in the
lottery drawing process; list of winners and prizes;
2. Collusion
-6-bidders auctions
-“The experiment would be run on more than 120
subjects from several academic institutes; chances that
you will be matched with colleagues are slim”
3. High noise rates (casual participation)
Attempts to facilitate participation and minimize noise
within experimental strategy (bids for gifts represented in
lottery screens; pie charts; reconfirmation of bids)
13
Method: Special Concerns (2)
4. Strategic bidding (common value considerations)
-Gifts restricted to personal use of winners.
-“values may strongly depend on individual tastes”
-Rules of auctions and dominance of bidding the
“maximal willingness to pay” demonstrated in examples
-3 test problems
_______________
Actual payoff: by random selection of one auction
14
Sample
3 main groups of subjects (N=107)
• MBAs (age 31). College of Management. (N=38)
• Business etc Undergraduates (age 24). Mostly from
College of Management (N=34)
• Engineering and exact sciences students (age 24). TelAviv University (N=35)
Distributions across Versions
• Version I (N=55)
• Version II (N=52)
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Results: Preliminaries
• Average participation time: 21 minutes
• Only 16 subjects took more than 30 minutes
Reliability
• Coefficient of correlation 0.9167
• Ratio of deviation = (repeated-original)/original
• Median = 10.56%
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Results: Bids for Basic Gift Certificates
• Bids of 6 subjects did not follow the market-
value ordering
• Redefine the 3 prizes H/M/L and 3 treatments:
HL/HM/ML
N=107
Median
Std
17
Vh
550
420
Vm
160
88
Vl
35
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Weighting of Basic Gift Certificates -Example
•Consider the case where subject x bids:
500 –for certificate A
200 – for certificate B
275- for the lottery L paying A and B with
probability 50%
Solve 275=a*500+(1-a)*200, to derive the
“decision weight” of prize A: 0.25
Using probability weighting notation, write
w(0.5)=0.25 for this case
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Weighting of Basic Gift Certificates
• In general, consider a lottery L paying X with probability
p and Y with probability (1-p) where VX>VY
•Solve for the weight of prize X from the underlying bids
V ( L)  Vy
w( p) 
Vx  Vy
• V(L)=w(p)*VX+(1-w(p))*VY (RDU equation)
• w(p) also represents the normalized bid for the lottery
• w(p)=p in EU
• w(p)=f(p) in each treatment in RDU
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Revealed Weights
Table 4.1: Median Decision Weights
p=
(N)
0.1
(55)
0.2
(52)
0.3
(55)
0.4
(52)
0.5
(107)
0.6
(52)
0.7
(55)
0.8
(52)
0.9
(55)
HL
0.00
0.00
0.02
0.04
0.10
0.16
0.27
0.31
0.56
HM
0.00
0.00
0.00
0.06
0.12
0.20
0.31
0.50
0.60
ML
0.00
0.00
0.05
0.014
0.19
0.42
0.38
0.71
0.67
•1392 of 1604 weights (87%) satisfy w(p)<p
•Pessimism (Quiggin, 1982) w(p)<p
• Uniformly pessimistic bidding
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Revealed Weights
• Pessimism (Quiggin, 1982) w(p)<p
• Weight of the win-probability is decreased while weight
of loss-probability is accordingly increased
• Intuition: subjects are reluctant to pay for a lottery more
than the value of the worst prize that the lottery may pay
• Fear of regret (Bell; Loomes and Sugden 1982)
(although we do not follow regret theory approach)
• Disappointment-Aversion (Gul 1991) (estimated later)
• Small win-probabilities are not always (not at least, in
Vickrey auctions) overweighed.
•10%-30% win probabilities do not affect subjects bids for
the low-valued certificate
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Probability Weighting (median data)
0.9
Max
0.7
Med
0.5
Min
w(p)=p
0.3
KT (gamma=0.6)
0.1
0.1
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0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Lottery Dependent Weighting
p=
(N)
0.1
(55)
0.2
(52)
0.3
(55)
0.4
(52)
0.5
(107)
0.6
(52)
0.7
(55)
0.8
(52)
0.9
(55)
HL
0.00
0.00
0.02
0.04
0.10
0.16
0.27
0.31
0.56
HM
0.00
0.00
0.00
0.06
0.12
0.20
0.31
0.50
0.60
ML
0.00
0.00
0.05
0.014
0.19
0.42
0.38
0.71
0.67
•Multivariate repeated measure Anova reveals a
significant treatment effect (Wilks’ Lambda for
Problem*Treatment effect 0.8183 p<0.001)
• Possible explanation?
•Fear of regret/disappointment increases as the distance
in values of best and worst prizes decreases (intuitive)
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Distance Effect on Weighting
•
Hypothesis: w(p) decreases as the distance between
values of best and worst prizes increases
•
Treatments have to be ranked again for testing:
min(d); med(d); max(d)
•
Testing at the individual level – problematic
•
Methods of testing:
(1) Page tests for each problem
(2) Calculate for each subject the proportion of increase
and decrease in weights across treatments. Then apply
Wilcoxon signed-ranks test
24
Page Tests Results
25
p=0.9
p=0.8
p=0.7
p=0.6
p=0.5
p=0.4
p=0.3
p=0.2
p=0.1
N=107
z=2 (0.02)
z=4.4 (0.001)
z=1.4 (0.07)
z=4.3 (0.001)
z=2.4 (0.01)
z=1.5 (0.06)
z=1.2 (N.S)
z=-0.73 (N.S)
z=-0.38 (N.S)
N=78
z=3 (0.001)
z=4.3 (0.001)
z=2.7 (0.003)
z=4.3 (0.001)
z=3.5 (0.001)
z=2.4 (0.01)
z=2.9 (0.005)
z=0.39 (N.S)
z=1.31 (0.1)
Increase and Decrease proportions
For each subject, calculate the proportion of increase
(INC) and decrease (DEC) in weights across distanceranked treatments
Joint comparison of max(d) to med(d) & med(d) to min(d):
INC>DEC for 48% of the subjects
DEC>INC for 26% of the subjects
Magnitude of weights-increase stronger than decrease
Wilcoxon signed rank test p<0.01
•Significance improves when subjects that violated
internality are filter away
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Violations of Internality (1)
•Gneezy, List and Wu (2006)
The internality Axiom: Vy ≤ V(L) ≤ Vx
Uncertainty Effect: violations of LHS (between subject)
•11.9% of the bids violated the LHS inequality
(within subject!)
•29 subjects (27%) violated the internality condition at
least in 1 of 15 problems. 21 subjects (20%) violated the
condition in more than 3 problems.
• Violation-rates for p=0.1 to 0.3 treatments about 20% vs
violations-rate of about 4% for p=0.8 to 0.9
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Violations of Internality (2)
Possible explanations:
1. Subjects dislike lotteries (lotteries aversion)
2. Noise
Post experimental survey (N=63)
*34 subjects (54%) admit violations are possible
*65%: lotteries aversion. 18% - noise
*Average participation time of violating subjects (16
Minutes) lower than average time for non violating
subjects (24 minutes) (z=2.88 p<0.002)
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Convexity of Revealed Weights (1)
0.8
0.6
Max
0.4
Med
0.2
Min
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
• Median data reflects a convex weighting pattern (kinksbetween versions)
• Direct tests for convexity of revealed weights; e.g.
w(0.2)<1-w(0.8)
• Proportion of compliance with convex weighting
71.4% compared to 14.3% compliance with concave
weighting and 14.3% compliance with linear weighting
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Convexity of Revealed Weights (2)
Tversky and Kahneman (1992)
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
*law of diminishing sensitivity
*with respect to 0 and 1 end points
*lower and upper subadditivity
*In current study, only the probability 1 end-point
acts as relevant reference point (pessimism)
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Estimation of a Convex Weighting Function
• Nonlinear least squares estimation of the convex
weighting function
w( p)  p
• Estimation on complete sample (N=1605) gives =3.69
(0.08) (MSE=11,836)
• Estimation on individual subjects (N=15) gives >1 for
94.4% of the subjects. Median =3.65 (MSE=1,387)
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Distance-Dependent Convex Weighting
• Separate estimation for each subject and distance
ranked treatment (N=5) gives median  values of 3.79,
3.48 and 2.32 (MSE=280)
• To generalize the convex weighting function for cases
where weights may depend on prize-distance assume
w( p, x, y)  p ( x, y ) where
Vx  Vy
 ( x, y )     
Vh  Vl
•Median =2.33 =1.49 reflect the dependency of
weighting on distance (MSE=1,042)
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Estimation of Disappointment Aversion Theory
• Nonlinear
least squares estimation of the weighting
function
w(p)=p/(1+(1-p)*)
• Estimation on complete sample (N=1605) gives =5.5
(0.22) (MSE=11,360)
• Estimation on individual subjects (N=15) gives >0 for
103 of 107 subjects. Median =5.65 (MSE=1,280)
33
Estimation of Lattimore et al (1992)
Weighting Function
• Nonlinear least squares estimation of the possibly non
additive value function
V ( pxy)  w( p) Vx  w(1  p) Vy
w( p) 
  p
  p  (1  p)
• =0.2889 (0.0084) =0.8321 (0.0295)
• <1 for 65% of the subjects (>1 for 32%)
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Discussion
• Preceding evidence on domain dependent weighting
Lattimore et al (1992), Abdellaoui (2000) – loss vs. gain
Etchart Vincent (2004) – loss-level dependence
Rottenstreich et al (2001) – Affect-rich outcomes induce stronger weighting
•Measures to avoid hidden risks, increase experimenter
reliability and prohibit collusion
•Implications: strong discounting of prices for risk in Web
auctions. Sellers should attempt to minimize perceived
risk
35