Disappointment Aversion in Internet Vickrey Auctions

1
Disappointment Aversion in Internet Vickrey
Auctions

• Doron Sonsino
• School of Business Administration
• College of Management
• Rishon Lezion, Israel
• This document summarizes the study. The paper
  will be available at the conference.

2
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)

3
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

4
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 (N107 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
  coins
• without a visual scan

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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

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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-probabilities
• Version I of the experiment
• Version II of the experiment

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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 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)

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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
• _______________
• Actual payoff by random selection of one auction
  

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Sample

• 3 main groups of subjects (N107)
• MBAs (age 31). College of Management. (N38)
• Business etc Undergraduates (age 24). Mostly
  from College of Management (N34)
• Engineering and exact sciences students (age
  24). Tel-Aviv University (N35)
• Distributions across Versions
• Version I (N55)
• Version II (N52)

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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

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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 275a500(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
  VXgtVY
• 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

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Revealed Weights

• Table 4.1 Median Decision Weights
• 1392 of 1604 weights (87) satisfy w(p)ltp
• Pessimism (Quiggin, 1982) w(p)ltp
• Uniformly pessimistic bidding

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Revealed Weights

• Pessimism (Quiggin, 1982) w(p)ltp
• 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)
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Lottery Dependent Weighting

• Multivariate repeated measure Anova reveals a
  significant treatment effect (Wilks Lambda for
  ProblemTreatment effect 0.8183 plt0.001)
• 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

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Page Tests Results
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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)
• INCgtDEC for 48 of the subjects
• DECgtINC for 26 of the subjects
• Magnitude of weights-increase stronger than
  decrease
• Wilcoxon signed rank test plt0.01
• 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 p0.1 to 0.3 treatments
  about 20 vs violations-rate of about 4 for
  p0.8 to 0.9

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Violations of Internality (2)

• Possible explanations
• Subjects dislike lotteries (lotteries aversion)
  
• Noise
• Post experimental survey (N63)
• 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) (z2.88 plt0.002)

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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)lt1-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)
• 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 (N1605) gives
  ?3.69 (0.08) (MSE11,836)
• Estimation on individual subjects (N15) gives
  ?gt1 for 94.4 of the subjects. Median ?3.65
  (MSE1,387)

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Distance-Dependent Convex Weighting

• Separate estimation for each subject and
  distance ranked treatment (N5) gives median ?
  values of 3.79, 3.48 and 2.32 (MSE280)
• 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 (MSE1,042)

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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 (N1605) gives
  ?5.5 (0.22) (MSE11,360)
• Estimation on individual subjects (N15) gives
  ?gt0 for 103 of 107 subjects. Median ?5.65
  (MSE1,280)

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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)
• ?lt1 for 65 of the subjects (gt1 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