when do bidders anticipate regret during auctions? empirical evidence from ebay

When Do Bidders Anticipate Regret During Auctions?Empirical Evidence From eBay

Meisam Hejazi Nia, Ozalp Ozer, Ahmet Serdar Simsek

Naveen Jindal School of Management, The University of Texas at Dallas

April 23, 2016

Hejazi Nia, Ozer, Simsek (UTD) When Do Bidders Anticipate Regret in Auctions? April 23, 2016 1 / 34

Auction Platforms

“The company typically holds 10 Petabytes of raw datain its Hadoop clusters and Teradata installations. ”(eBay’s vice-president of experience, search, andplatforms2012)

eBay Inc. Reports First Quarter Results Global commerceplatform and payments leader eBay (Nasdaq: EBAY) todayreported that revenue for the first quarter ended March 31,2015 increased to $4.45 billion (ecommercebytes.com)

Platform revenue sources:

Complex system of fees for servicesListing product featuresFinal Value Fee for sales proceeds by sellers (10%)

Significant Heterogeneity in:

Auctions (Millions of collectibles, decor, appliances, computers,furnishings, equipment)Bidders (Hundreds of Millions)

Platform Policies and Implication Requirements:

Target different bidders based on their behaviorEstimate the impact of each of the policies on the revenue(Counterfactual Analysis)


Structural Model of Emotionally Rational bidders

Consumore Forum: “I won an auction but regret:What can I do?”

eBay page: “Buy-and-Sell-Without-Regrets”

Winner and Loser Regret:

Regretting for paying too much in case of winning anauctionRegretting for not bidding high enough in case of losing

Intractability of Forward Looking approaches(Zeithammer 2006)

Auctions are emotionally laden (Chakarvarti et al 2002)

Naive bidders and incremental bidding to learn thevalue (Zeithammer and Adams 2010; Hossain 2008;Okenfels and Roth 2002)

Common value auctions and Winner Curse (Bajari andHortacsu 2003)

Bidder do not search across auctions(Ariely andSimonson 2003; Haruvy and Leszcyc 2010)

Bidder’s Choice of Bid:

Auction bid surplusAnticipated Winner and Loser RegretBounded Rationality, Learning (updating belief) andAffiliated Values


Research Questions

Can we design a computationally tractable system to estimate bidders’bidding behaviors in an online auction platform?

To what extent do bidders anticipate winner and loser regret and how dothey vary in bidders’ experience and learning behavior?

What is the effect of intervening bidders’ regret by notification policies onthe auction platform’s revenue?


Overview

Data: We Scraped in May 2014 from eBay Website

Individual 58,285 bids of 12,247 bidders over 1646 auctions indifferent categories

The auction categories include:

(1) The jewelries (rings, bracelets, ..) (8) The tickets and experiences (15) The health and beauty products(2) The clothing and the accessories (9) The gift cards and coupons (16) The video game and consoles(3) The potteries and glasses (10) The antiques (17) The dolls and bears(4) The crafts (11) The art works (18) The entertainment goods(5) The toys and hobbies (12) The music record (19) The books(7) The watches (14) The collectibles (20) The consumer electronics(6) The stamps (13) The DVD and movies


Overview

Methodology

Bayesian Learning Structural Model of bid amount choice: KalmanFilter Theory (Noisy Bidding process)

Model of the belief of evolution of auction bids and the number ofbidders, by assuming first order Markov processes

Model of bidders’ affiliated valuations, by first order condition

Monte Carlo Expectation Maximization (MC-EM)

Control Unobserved heterogeneity by Bayesian shrinkage of bidderswith the same level of experience

Empirical Bayesian Estimation: Optimized Maximum A Posteriori(MAP) of parameters by Simulated Annealing Optimization method

Latent Dirichlet Allocation (LDA) to incorporate text description data


Overview

Results

In all auction categories, both winner and loser regrets are significant

A positive relationship between winner and loser regret.

Those who are more regretful stick to status quo, i.e., they updatetheir valuations less frequently and learn less from others

Experience can explain the heterogeneity in the bidders’ learning,updating, and regretting behavior

Counterfactual analysis shows that if an auction platform can shutdown winner regret of bidders by its notification policies, it canincrease its revenue by 24%


Data: Scraped and Collected from eBay Auction Platform

Position of This Research in Literature


In summary in this Study....

Emotionally Rational Consumers(Regret)

Bounded Rationality (Learning,Experience, Belief Updating)

Affiliated Value Auction

Bayesian Updating Structural Model


Auction categories in the eBay data

Auction category Number of auction Items

Jewelry and Watches 149Collectibles 103Crafts 78Pottery and Glass 74Antiques 68Art 70Entertainment Memorabilia 88Tickets and Experiences 91Stamps 72Toys and Hobbies 93Books 84Clothing, Shoes and Accessories 84Gift Cards and Coupons 85Music 86Consumer Electronics 83DVDs and Movies 87Dolls and Bears 84Health and Beauty 74Video Games and Consoles 93


Sample auctions in the eBay data

Auction Item Title Auction Category Winning Bid Number ofBids

Number ofBidders

Ended

Vintage Original Co-op porcelain sign Collectibles $1,000.00 92 12 May 18, 2014 ,2:15PM

$3/1 Pantene Product CouponsShampoo Conditioner Styler

Gift Cards &Coupons

$17.50 30 5 May 19, 2014 ,6:30PM

Genesis Breyer P-Orridge ”NakedEye” Autographed Camera w/ Orig-inal Negatives

EntertainmentMemorabilia

$900.00 75 9 May 22, 2014 ,2:00AM


Summary statistics of the average bidder characteristicswithin each of 19 auction categories

Characteristic Min Max Mean SD

size 453 1550 644.53 238.21

avg. feedback score 342 1301 714.53 260.39sd feedback score 745 8033 2763.37 1897.84

avg. Number of bids on this item 3 7 4.84 0.74sd Number of bids on this item 4 13 8.05 1.93

avg. total number of bids in 30 days 56 504 195.16 100.57sd total number of bids in 30 days 110 1065 493.74 260.94

avg. Number of items bided on in 30 days 30 264 93.63 57.41sd Number of items bided on in 30 days 53 1001 251.42 197.83

avg. Bidding Activity with current Seller 17 50 28.63 8.51sd Bidding Activity with current Seller 24 40 31.11 4.05

avg. Number of categories bided on 1 3 2.05 0.39sd Number of categories bided on 1 1 1 0


Summary statistics of the average bidder characteristicswithin each of 47 bidder segments

Characteristic Min Max Mean SD

size 3 992 260.55 275.02

avg. feedback score 48 84027 3471.21 12399.8sd feedback score 5 45365 3635.04 8480.39

avg. Number of bids on this item 1 35 8.57 7.67sd Number of bids on this item 0 26 6.79 6.77

avg. total number of bids in 30 days 3 4530 680.32 1072.73sd total number of bids in 30 days 0 5814 630.98 1066.22

avg. Number of items bided on in 30 days 1 1631 257.57 412.59sd Number of items bided on in 30 days 1 2099 266.91 449.57

avg. Bidding Activity with current Seller 1 100 24.47 20.19sd Bidding Activity with current Seller 0 40 19.34 11.72

avg. Number of categories bided on 1 4 2.19 0.57sd Number of categories bided on 0 3 1.13 0.64


The Evolution of bids across various Auctions


The evolution of the number of bidders


Auction Platform: Bidder’s Utility


The utility of the bidder

The bidder’s utility

uit = (vit − bit)Gt−1(bit)

−∫zt≤bit

αi (bit − zt)dGt−1(zt)

−∫bit≤zt≤vit

βi (vit − zt)dG (zt)

t:Time index of the bid entry

uit :Utility of bidder i at time t

vit :the valuation of consumer i attime t

bit :The bid value of consumer i attime t

Gt−1(zt):Cumulative Distribution Functionof Maximum Bid

(vit − bit)Gt−1(bit):Expected profit of winning

−∫zt≤bit

αi (bit − zt)dGt−1(zt):Winner Regret

−∫bit≤zt≤vit

βi (vit − zt)dG (zt):Loser Regret

{αi}: Winner regret parameter of indiv. i{βi}: Loser regret parameter of indiv. i


Auction bids and the number of bidders evolution models

Bidders’ Linear approximationBelief

bjt = θjt + εjt , εjt ∼ N(0, σjν)

θjt = τjθjt−1 + γj + ωjt , ωjt ∼ N(0, σjω)

Gt(θt) = Ft(θt)nt−1

gt(θt) = (nt − 1)Ft(θt)nt−2ft(θt)

njt = κjt + ς1jt , ς1

jt ∼ N(0, σ1jς)

κjt = κjt−1 + ιj + ηjτjt + ξ1jt , ξ1

jt ∼ N(0, σ1jξ)

bjt :Observed bid in auction j at timet

θjt :Latent bid in auction j

njt :The actual number of bidders inauction j at time t

κjt :The latent number of bidders inauction j at time t

τj , γj : Growth factor, and drift parameterstj : Average rate of bidder entrance in

each periodηj : Increase rate of bidder entrance late

at the periodεjt :

The measurement error for bids inauction j at time t

ωjt :The system error for evolution of la-tent bid in auction j at time t

ςjt :The measurement error for number ofbidders in auction j at time t

ξjt :The system error for evolution of la-tent number of bidders in auction j attime t


The Maximum Utility of the Bidder Problem and Affiliatedvaluation and learning approach

Invert observed bid to find valuation

∂uit∂bit

= −Gt−1(bit) + (vit − bit)gt−1(bit)−

αGt−1(bit)− αbitgt−1(bit) + αbitgt−1(bit) + β(vit − bit)gt−1(bit) = 0

vit = Gt−1(bit)+bitgt−1(bit)+αiGt−1(bit)−αibitgt−1(bit)+(αi+βi )bitgt−1(bit)gt−1(bit)+βigt−1(bit)

vit = Eθ

[Gt−1(θit)+θitgt−1(θit)+αiGt−1(θit)−αiθitgt−1(θit)+(αi+βi )θitgt−1(θit)

gt−1(θit)+βigt−1(θit)

]

vit = ρib−i(t−1) + ϕit(Hossain 2008; Zeithammer and Adams 2010; Okenfels and Roth 2002)

log(ϕit) = log(ϑjt) + log(δi ) + ς2jt , ς2

jt ∼ N(0, σ2jς)

log(ϑjt) = log(ϑjt−1) + ξ2jt , ξ2

jt ∼ N(0, σ2jξ)


Identification of loser and winner regret

Identification of loser and winner regret

log

[Eθ

[Gt−1(θit)+θitgt−1(θit)+αiGt−1(θit)−αiθitgt−1(θit)+(αi+βi )θitgt−1(θit)

gt−1(θit)+βigt−1(θit)

]− ρib−it

]=

log(ϑjt) + log(δi ) + ς2jt , ς2

jt ∼ N(0, σ2jς)

log(ϑjt) = log(ϑjt−1) + ξ2jt , ξ2

jt ∼ N(0, σ2jξ)

Θi = (αi , βi , ρi ),Θi ∼ MVN(.|indi , di )

Ψj = (γj , τj , ιj , ηj),Ψj ∼ MVN(.|clustj ,Dj)∏Ii=1 PNorm(di |m, v , πi ) =

∏Ii=1

∑Kc=1 πicPNorm(di |mc , vc)

Θi = µindidi + χi , χi ∼ N(0, σindi )

Ψj = µclustjDj + Ξj , Ξj ∼ N(0, σclustj )


Estimation: Maximum A Posteriori (Empirical Bayes)

Estimation: Maximum A Posteriori (Empirical Bayes)

P(τj , γj , ιj , αi , βi , ρi , δi ,Σ|bjt , b−jt , njt , dj ,Dj) =∏Jj=1

∏Ii=1

∏Tj

t=1

[ ∫PNorm(bjt |θjt , σjv )× PNorm(θjt |θjt−1, σjv , τj , γj)dθj

]×[ ∫

PNorm(njt |κjt , σ1jς)× PNorm(κjt |κjt−1, σ

1jξ, ιj , ηj)dκj

]×[ ∫

PNorm(bjt |b−jt , αi , βi , ρi , δi , σ2jς , ϑjt , κjt)× PNorm(ϑjt |ϑjt−1, σ

2jξ)dϑj

]×PNorm(αi , βi , ρi , δi |µind(i), σind(i), di )

×PNorm(τj , γj , ιj , ηj |σclust(j), σclust(j),Dj)

×δΣ̂(Σ)× δµ̂clust(j)(µclust(j))× δσ̂clust(j)

(σclust(j))× δµ̂ind(i)(µind(i))× δσ̂ind(i)

(σind(i))


Summary statistics for the bidder specific parameterestimations

within each auction category (19) within each bidder segment (47)

Parameter Min Max Mean SD Min Max Mean SD

avg. winner regret -1.38 -1.24 -1.31 0.04 -1.67 -0.52 -1.28 0.19se winner regret 0.02 0.04 0.04 0.01 0.03 0.41 0.1 0.08

avg. loser regret -1.4 -1.28 -1.33 0.03 -1.7 -0.79 -1.34 0.13se loser regret 0.02 0.04 0.04 0.006 0.03 0.49 0.1 0.09

avg. valuation param. 1.17 1.28 1.23 0.03 0.79 1.42 1.22 0.1se valuation param. 0.02 0.04 0.03 0.004 0.02 0.27 0.08 0.06

avg. learning param. 0.18 0.32 0.25 0.03 0 0.81 0.27 0.12se learning param. 0.02 0.04 0.03 0.01 0.03 0.26 0.09 0.06

• Significant heterogeneity in bidders’ parameters across bidder segments (not category specific).• Winner (resp. loser) regret parameter is significant in 44 (resp. 45) out of the 47 bidder segments atp < 0 : 01 and it is significant in two (resp. one) categories at p < 0 : 05 (consistent with Bajari andHortacsu(2003) prediction in common value)• Average loser regret is slightly higher (in magnitude) than winner regret, but same range (inconsistentwith Ariely and Simonson (2003) prediction that eBay decreases the probability of winner regret, while maxloser regret).


Correlation between bidder specific parameters acrossbidder segments

winner regret loser regret valuation revelation learning

Winner Regret 1Loser Regret 0.427 1Valuation revelation 0.662 0.589 1Learning 0.135 0.474 0.613 1

Regressand Regressor Estimate SE t-stat p-value

Winner regretIntercept -0.43 0.27 -1.61 0.110loser regret 0.63** 0.2 3.16 0.000

Winner RegretIntercept -0.78** 0.2 -3.901 0.000learning 0.94** 0.13 7.305 0.00valuation revelation -0.59** 0.17 -3.418 0.001

Loser RegretIntercept -1.64** 0.16 -10.118 0.000learning 0.33** 0.1 3.149 0.003valuation revelation 0.17 0.14 1.193 0.239

• Winner regret is positively correlated with loser regret (emotional bidder type)• negative relationship between learning less from others (status quo tendency) and feeling winner regret(consistent with Inman and Zeelenberg 2002)• Bidders who update their valuations based on the new auction board bid less, anticipate more winnerregret than others


Explaining Heterogeneity in Regret with Bidders’Experience


Winner Regret (Adjusted R2 = 0.64)Intercept -1.278* 0.017 -75.449 0.000Segment Size 0.000 0.000 0.564 0.576Bidders Feedback mean 0.001* 0.000 6.344 0.000Number of Bids on This item -0.004 0.003 -1.570 0.125total number of bids in 30 days 0.013* 0.004 3.574 0.001Number of items bid on in 30 days 0.000 0.000 -1.456 0.153Bid activity with current Seller 0.003* 0.001 2.430 0.020Number of categories Bid on Mean 0.044 0.046 0.964 0.341

Loser Regret (Adjusted R2 = 0.30)Intercept -1.341* 0.016 -83.916 0.000Segment Size 0.000 0.000 -0.737 0.466Bidders Feedback mean 0.001* 0.000 4.261 0.000Number of Bids on This item -0.004 0.003 -1.734 0.091total number of bids in 30 days -0.001 0.003 -0.311 0.758Number of items bid on in 30 days 0.000 0.000 -1.025 0.312Bid activity with current Seller 0.000 0.001 -0.455 0.651Number of categories Bid on Mean -0.027 0.043 -0.635 0.529

• Bidders with more feedback score (i.e., more experience) are less regretful, and learn more from the bidson the auction board• Bidding in several categories correlates with more loser regret


Explaining Heterogeneity in Learning and ValuationRevelation with Bidders’ Experience


Learning value from bids (Adjusted R2 = 0.0.64)Intercept 0.271* 0.017 16.326 0.000Segment Size 0.000 0.000 1.168 0.250Bidders Feedback mean 0.001* 0.000 9.030 0.000Number of Bids on This item 0.003 0.003 1.216 0.231total number of bids in 30 days 0.002 0.004 0.601 0.551Number of items bid on in 30 days 0.000 0.000 -0.208 0.836Bid activity with current Seller 0.001 0.001 0.590 0.559Number of categories Bid on Mean -0.023 0.045 -0.507 0.615

Valuation update (Adjusted R2 = 0.41)Intercept 1.269* 0.016 79.126 0.000Segment Size 0.000 0.000 -0.215 0.831Bidders Feedback mean 0.001* 0.000 4.782 0.000Number of Bids on This item 0.004 0.003 1.521 0.136total number of bids in 30 days -0.011* 0.003 -3.148 0.003Number of items bid on in 30 days 0.000 0.000 1.859 0.071Bid activity with current Seller 0.000 0.001 -0.213 0.833Number of categories Bid on Mean -0.01 0.043 -0.242 0.810

• The valuation update correlates positively with the bidders’ feedback score• Bidders with more experience reveal their value more (consistent with the dominant strategy of rationalbidders)


Widely available versus Luxury Goods Regret parametert-Test: Paired Two Sample for Means

For Winner Regret For Loser Regret

Widely Available Luxury Widely Available Luxury

Mean -1.334 -1.317 -1.319 -1.33Variance 0.934 0.982 0.946 0.957Observations 6024 6024 6024 6024Pearson Correlation 0.008 0.002Hypothesized Mean Difference 0 0df 6023 6023t Stat -1.002 0.609P(T¡=t) one-tail 0.158 0.271t Critical one-tail 1.645 1.645P(T¡=t) two-tail 0.316 0.542t Critical two-tail 1.96 1.96

• No significant difference in regret (not category specific, but individual specific)


Distribution of individual specific parameters


Counterfactual analysis of the impact of Shutting DownRegret on Bids

• (blue line the optimal bidding when regret is shut down, and red line the observed)


Counterfactual analysis of shutting down winner regret

Auction Category Number ofAuctions

avg improvementof Winner Regretshutdown

avg improvementof Loser Regretshutdown

Jewelry and Watches 149 28% 28%Collectibles 103 36% 32%Clothing, Shoes and Accessories 84 25% 16%Crafts 78 28% 31%Pottery and Glass 74 27% 22%Antiques 68 40% 49%Toys and Hobbies 93 29% 30%Stamps 72 61% 43%Books 84 28% 30%Tickets and Experiences 91 18% 5%Art 70 25% 21%Gift Cards and Coupons 85 40% 38%Music 86 44% 27%Consumer Electronics 83 19% 17%DVDs and Movies 87 53% 39%Dolls and Bears 84 27% 39%Entertainment Memorabilia 88 23% 13%Health and Beauty 74 37% 40%Video Games and Consoles 93 39% 38%

Total improvement 24% 24%Average improvement across all auctions 32% 29%

• By shutting down the bidders’ winner regret through a notification policy, on average, the auction platformcan improve its revenue of each item by 32%, and its total revenue by 24%.• Significant improvements by shutting down winner regret occur in widely available good categories suchas DVD’s and movies, music, health and beauty, books, and gift cards and coupons, in which usuallynon-expert bidders bid on (stamps and antiques are exceptions).• Smaller improvements occur in tickets and experiences, entertainment memorabilia, and art, which mostlikely attract more expert bidders.


Counterfactual revenue improvements explained by thecharacteristics of bidder on each auction

Shutting down winner regret:

Coefficients Standard Error t Stat P-value

Intercept 0.1559 0.0921 1.6935 0.0905Feedback 0.0000 0.0000 -0.9519 0.3413Bids on this item 0.0035 0.0020 1.7814 0.0750Total bids in 30 days 0.0000 0.0001 -0.3022 0.7625Number of items bided on 0.0009 0.0004 2.5731 0.0102Activity with the Seller 0.0006 0.0011 0.5675 0.5704Number of Categories bid on 0.0231 0.0303 0.7613 0.4466

Shutting down both types of regret:

Coefficients Standard Error t Stat P-value

Intercept 0.1660 0.0840 1.9870 0.0470Feedback 0.0000 0.0000 -0.6110 0.5420Bids on this item 0.0020 0.0020 1.3580 0.1750Total bids in 30 days 0.0000 0.0000 0.4040 0.6860Number of items bided on 0.0000 0.0000 0.7560 0.4500Activity with the Seller 0.0000 0.0010 0.0080 0.9940Number of Categories bid on 0.0350 0.0270 1.2660 0.2060 height

• Number of bid on a specific auction item and the total number of items bid on are positively correlated with the improvementin revenue• Explained by incremental bidders. i.e, those who bid a lot are naive incremental bidders, and shutting down winner regretimproves the revenue more, when bidders are naive• A high number of auction items bid on is a signal of the bidder’s not concentrating on one auction item to win, which isanother proxy for less experience of the bidder


Robustness Checks

Assumption: bidders use their own bids as a proxy for how much theyare going to pay

Bidders considering the fact that she would pay an amount between herbid and the currently displayed maximum bid (replacing bit withλibit + (1− λi )maxit) did not changed the results significantly.

eBay Category as auction Clusters

Common keywords such as ‘Shampoo”, “Conditioner”, and “Styler” in titlemight contain information about auction characteristic, so incorporatedtext data through Latent Dirichlet Allocation (LDA) for auction clustering,but the insights delivered from the model did not change.

Clustering bidders based on Mixed Normal method

Tested the model using a k-mean clustering results instead of mixturenormal fuzzy clustering results, but the main insights delivered from themodel did not change significantly.


Conclusion

Developed a structural model that accounts for bidders’ learning and theiranticipation of winner and loser regrets in an auction platform

Proposed an empirical Bayesian estimation method to calibrate theparameters of this model

Showed that bidders anticipate significant levels of regret in variousproduct categories

Found that experience can explain the heterogeneity in the bidders’learning, updating, and regretting behavior

Found that if eBay can shut down winner regret of bidders by appropriatenotification policies, it can increase its revenue by 24%


Thank You


when do bidders anticipate regret during auctions? empirical evidence from ebay

Data & Analytics