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Disappointment Aversion in Internet Vickrey Auctions*

Doron Sonsino

School of Business AdministrationCollege of Management

Rishon Lezion, Israel

*This document summarizes the study. The paper will be available at the conference .

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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 (

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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) •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

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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)

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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 coinswithout a “visual scan”

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Motivation: Internet Auctions (2)

• Uncertainty regarding the value that winnerwould 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

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Motivation: Probability Weighting

Kahneman and Tversky (1979,1992)

•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

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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

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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-probabilitiesVersion I of the experiment

Version II of the experiment

AC (HL)0.10.30.50.70.9

AB (HM)0.10.30.50.70.9

BC (ML)0.10.30.50.70.9

AC (HL)0.20.40.50.60.8

AB (HM)0.20.40.50.60.8

BC (ML)0.20.40.50.60.8

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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)

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Methodological Concerns (1)

1. Subjects suspicionSubjects 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)

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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

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Actual payoff: by random selection of one auction

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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). Tel-Aviv 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=107VhVmVl

Median 55016035

Std4208827

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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)=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

VyVx

VyLVpw

)(

)(

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Revealed Weights

Table 4.1: Median Decision Weights

•1392 of 1604 weights (87%) satisfy w(p)<p •Pessimism (Quiggin, 1982) w(p)<p• Uniformly pessimistic bidding

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 (

HL0.000.000.020.040.100.160.270.310.56

HM0.000.000.000.060.120.200.310.500.60

ML0.000.000.050.0140.190.420.380.710.67

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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)

0.1

0.3

0.5

0.7

0.9

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Max

Med

Min

w(p)=p

KT (gamma=0.6)

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Lottery Dependent Weighting

•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)

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 (

HL0.000.000.020.040.100.160.270.310.56

HM0.000.000.000.060.120.200.310.500.60

ML0.000.000.050.0140.190.420.380.710.67

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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 increaseand decrease in weights across treatments. Then applyWilcoxon signed-ranks test

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Page Tests Results

N=107N=78

p=0.9z=2 (0.02)z=3 (0.001)

p=0.8z=4.4 (0.001)z=4.3 (0.001)

p=0.7z=1.4 (0.07)z=2.7 (0.003)

p=0.6z=4.3 (0.001)z=4.3 (0.001)

p=0.5z=2.4 (0.01)z=3.5 (0.001)

p=0.4z=1.5 (0.06)z=2.4 (0.01)

p=0.3z=1.2 (N.S)z=2.9 (0.005)

p=0.2z=-0.73 (N.S)z=0.39 (N.S)

p=0.1z=-0.38 (N.S)z=1.31 (0.1)

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Increase and Decrease proportions

For each subject, calculate the proportion of increase (INC) and decrease (DEC) in weights across distance- ranked 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 decreaseWilcoxon 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) ≤ VxUncertainty 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)

• Median data reflects a convex weighting pattern (kinks- between versions) • Direct tests for convexity of revealed weights; e.g.w(0.2)<1-w(0.8)

• Proportion of compliance with convex weighting71.4% compared to 14.3% compliance with concave weighting and 14.3% compliance with linear weighting

0.0

0.2

0.4

0.6

0.8

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Max

Med

Min

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Convexity of Revealed Weights (2)

Tversky and Kahneman (1992)

*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

• 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

•Median =2.33 =1.49 reflect the dependency of weighting on distance (MSE=1,042)

),(),,( yxpyxpw VlVh

VyVxyxwhere

),(

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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)

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Estimation of Lattimore et al (1992)Weighting Function

• Nonlinear least squares estimation of the possibly non additive value function

• =0.2889 (0.0084) =0.8321 (0.0295)• <1 for 65% of the subjects (>1 for 32%)

VypwVxpwpxyV )1()()(

)1()(

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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