Emerging behavior in electronic bidding

4 Pages·0.1 MB·English

by  I. Yang

Emerging behaviorinelectronic bidding
I. Yang1, H. Jeong2, B. Kahng1, and A.-L. Baraba´si3
1SchoolofPhysicsandCenterforTheoreticalPhysics,SeoulNationalUniversity,Seoul151-747,Korea
2DepartmentofPhysics,KoreaAdvancedInstituteofScienceandTechnology,Taejon,305-701,Korea
3DepartmentofPhysics,UniversityofNotreDame,NotreDame,IN46556,USA
3
(Dated:February2,2008)
0
0
Wecharacterizethestatisticalpropertiesofalargenumberofagentsontwomajoronlineauctionsites. The
2
measurements indicate that the total number of bids placed in a single category and the number of distinct

n auctionsfrequentedbyagivenagentfollowpower-lawdistributions,implyingthatafewagentsareresponsible
a forasignificantfractionofthetotalbiddingactivityontheonlinemarket. Wefindthattheseagentsexertan
J un-proportional influenceonthefinalpriceoftheauctioneditems. Thisdominationofonlineauctionsbyan

7 unusuallyactiveminoritymaybeagenericfeatureofallonlinemercantileprocesses.
2
PACSnumbers:89.75.-k,89.75.Da.

]
h
c Electroniccommerce(E-commerce)isanytypeofbusiness distinctauctions.
e
m or commercial transaction that involves information transfer Tobespecific,wecollectedauctiondatafromtwodifferent
acrosstheInternet. Overthepastfiveyears,E-commercehas sources.First,wedownloadedallauctionsclosingonasingle
-
t expandedrapidly,takingtheadvantageoffaster,cheaperand dayoneBay,including264,073auctioneditems,groupedby
a
t more convenient transactions over traditional ways. A syn- theauctionsite in194subcategories. Thedatasetallowedus
.s ergetic combination of the Internet supported instantaneous toidentify384,058distinctagentsviatheiruniqueuserID.To
at interactions and traditional auction mechanisms, online auc- verifythevalidityofourfindingsindifferentmarketsandtime
m tionsrepresenta rapidlyexpandingsegmentofE-commerce. spans, we collected data overa one yearperiodfromeBay’s
- Indeed,withtheadventoftheInternetmostlimitationsoftra- Korean partner, auction.co.kr, involving 215,852 agents that
d ditional auctions, such as geographicaland time constraints, bidon287,018itemsin62subcategories.
n have virtually disappeared, making a significant fraction of
o Inatypicalonlineauctionasellerplacestheitem’sdescrip-
the population potential auction participants [1, 2]. For ex-
c tion on the auction site and sets the starting and the closing
[ ample eBay, the largest consumer-to-consumer auction site,
time for the auction. Agents (bidders) submit bids for the

boosts over 40 million registered consumers, and has grown
1 item. Each new bid has to exceed the last available bid by
in revenueover100,000percentin the past five years. With
v apresetincrement. Agentscanbidmanually,placingafixed
3 therapidlyincreasingnumberofagentstheroleofindividuals bid, or on some auction sites (such as eBay but not on their
1 diminishes and self-organizing processes increasingly dom-
Koreanpartner)theycantakeadvantageofproxybidding. In
5 inate the market’s behavior [3, 4]. On the other hand, re-
proxybiddinganagentindicatestotheauctionhousethemax-
1
cently the self-organizingfeatures of complex systems have
0 imumpricehe/sheiswillingtopayforthegivenitem(proxy
attracted the attention of the statistical physics community
3 bid),whichisnotdisclosedtootherbidders.Eachtimeabid-
because they contain diverse cooperations among numerous
0 derincreasesthebidprice,theauctionhousemakesautomatic
/ components of a system, resulting in patterns and behavior
t bidsfortheagentwithanactiveproxybid,outbiddingthelast
a which are more than the sum of the individualaction of the
bid with a fixed increment, until the proxy price is reached.
m components. While many systematic studies have been car-
In online consumer-to-consumerauctions the agent with the
- riedouttounderstandsuchemergingpatternsinvarioussys-
d highest bid wins and pays the amount of that bid; all other
tems, little attentionhas been paid to electronic auctions. In
n participantspaynothing.
this Letter, we collect auction data and show that the bid-
o
Most online auction sites keep a detailed, publicly avail-
c dingofhundredsofthousandsof agentsleadstounexpected
: emergingbehavior,impactingoneverythingfromthebidding ablerecordof allbidsandidentifythebiddingagentsvia an
v
uniqueloginname. Itisthistransparencyofthebiddinghis-
i patternsoftheparticipatingagentstothefinalpriceoftheauc-
X tory that allows us to characterize in quantitative terms the
tioneditem. Wefoundthatthetotalnumberofbidsplacedin
r asinglecategorybyagivenagentfollowsapower-lawdistri- auction process. Each completed auction can be character-
a
izedbytwoquantities: thenumberofdistinctagentsbidding
bution. The power-lawbehavioris rootedin the finding that
on the same item (n ) and the total number of recorded
an agent that makes frequentbids up to a certain momentis agent
bidsfortheitem(n ),wheren ≥n ,aseachagent
morelikelytobidinthenexttimeinterval.Moreover,wefind bids bids agent
canplacemultiplebids. InFig.1weshowthedistributionof
thatthenumberofdistinctitemsfrequentedbyagivenagent
n and n over all auctionsrecordedon eBay, finding
alsofollowsapower-lawdistribution. Thepower-lawbehav- agent bids
thattheybothfollowP(n) ∼ exp(−n/n ),wheren = 5.6
iorimpliesthatafewpowerfulagentsbidmorefrequentlyand 0 0
for n and n = 2.5 for n . We obtained similar re-
on more distinct items than others. We will show that such bids 0 agent
sults for the Korean market, with n = 10.8 for n and
powerful agents exert strong influence on the final prices in 0 bids
n = 7.4 for n . This simple exponentialform is unex-
0 agent
2
0 0
10 10
(a)
nnP( )P( ),agentbid 1100−−24 κ P( )bid10−2
−4
10
(a)
−6
10
0 20 40 60 80 100 0 1 2 3
nagent,nbid 10 10 κ 10 10
0 bid
10
(b) (c) 100
0
10
nP( )bid 10−2 nP( )bid 10−2
nP( ),agent nP( ),agent 10−2 nP( )auct10−4
−4
10
(b)
−4
10 −6
0 20nagen4t,0nbid60 80 0 n2a0gent,n4bi0d 60 10 100 101 102 103
nauct
FIG.1: BidandagentdistributiononeBay.(a)Distributionofnum-
ber ofagents(n ,(⋄))simultaneously bidding onacertainitem FIG.2: Frequencyofbidsplacedbyindividualagents. (a)Cumula-
andnumberofbiadgsen(tn ,(+))receivedforanitem,obtainedbycon- tivedistributionoftotalnumberofbids,κbid,placedbyagivenagent
bids
inauctionsinthesamecategory. Foreachofthe194categorieswe
sideringallitemscontainedinthe194categoriesonindividualbids
separatelydeterminedthecumulativedistributionsandaveragedthe
thatwerecollectedfromauctionsendingonJuly5,2001oneBay.(b)
obtained curves. (b) Cumulative distributionof thenumber of dis-
and(c)Agentandbiddistributioninthelargest(b)andthesecond
tinct auctions, n , frequented by agiven agent. Thedotted line
largest(c)categoryoneBay. Thelargestcategorybythenumberof auct
on (a) has slope -2 while on (b) has slope -2.5, indicating that the
auctioneditemscontains21,461itemsrelatedtosporttradingcards
correspondingprobabilitydistributionfollowsP(κ ) ∼ κ−3 and
wprhinilteedthaendserceocnodrdleadrgmesutscica.teTgohreystirnacilguhdtelsin1e3s,6c1o0rreitsepmonsdretloateexdpoto- P(nauct)∼n−au3c.t5,respectively. bid bid
nentialfitsandthesymbolsarethesameasin(a).
ofκ followsapowerlaw
bid
pected,asoneexpectsthatthebiddingdistributionistheresult P(κ )∼κ−γ, (1)
bid bid
of many independent events, and therefore follows a Gaus-
sian,peakedaroundtheaveragenumberofbidsanddecreas- whereγ =3(Fig.2a)onbotheBayandtheKoreanauction.A
ing as ∼ exp(−an2) with a constant a. The deviation from similarpowerlawcharacterizesthedistributionofthenumber
aGaussiandistributioncouldcomefromthefactthatFig.1a of differentauctions, nauct, frequentedby individualagents,
collapses data from different categories, displaying different findingthat
biddingpatterns. InFig.1bandcweshowthedistributionin P(n )∼n−β , (2)
twosubcategories(sportstradingcardsandprinted,recorded auct auct
music), findingthat they follow the same functionalform as whereβ = 3.5(Fig.2b). Thepower-lawdistributionshown
the aggregateddata. Therefore,the exponentialformfor the in Fig. 2a implies that while most agents place only a small
activitydistributionappearstobeageneralfeatureofallauc- numberofbids,afewagentsbidveryfrequently,placingsev-
tions,indicatingthatthemajorityofauctionshaveonlyafew eralhundredbidsonthesameday.Similarly,Fig.2bindicates
biddersandauctionswithalargenumberofbidsorparticipat- thatwhilemostagentsparticipateinafewauctionsonly,afew
ingagentsareexponentiallyrare. agents bid very widely, some placing simultaneous bids on
To characterize the activity of individual agents we deter- overahundreddistinctitemsonthesameday.Therefore,un-
minedthenumberofbidsplacedbyeachagentoneachauc- knowntomostparticipants,theauctionprocessisdominated
tion. Asagentsplacesimultaneousbidsonitemsthatclosely by a small number of highly active agents, or power-agents,
resemble each other, we denote by κ the total number of thatpursuea veryaggressivebiddingpattern, placingsimul-
bid
bidsplacedbythesameagentinauctionsinthesamecategory. taneously a large number of bids on a wide range of items.
Forexample,ifseveralsimilarcomputersaresoldonseparate Thesepower-agentsareresponsibleforthepower-lawtailof
auctions, agentslookingfora computeroftenbid simultane- the distributionshownin Fig. 2. Our measurementsindicate
ouslyforseveralorallofthem. We findthatthedistribution thatthereis a strongcorrelationbetweenthe numberof bids
3
1
0.6
0.9
nt
e
ag 0.8
0.4 n
a
f 0.7
o
e
0.2 at 0.6
r
s
(a) es 0.5
c
0 c
1 3 rank 5 7 Su 0.4
0.8 n a g e n t =2 0.6 n a g e n t =3 0.3
0.6 0 10 20 30 40
0.4 Number of auctions
0.4
0.2 (b) 0.2 (c)
FIG.4: Thedependenceofanagentssuccessrateonthenumberof
0 0
1 rank 2 1 ra2nk 3 auctionstheagentparticipates. Foreachproductsubcategory(con-
n =4 n =5 taininghighlysimilaritems)wecalculatedPiwin,theaverageofthe
0.4 agent 0.4 agent winning prices for items won by agent i. For the same agent we
alsocalculatedPilost,theaverageoverthewinningpriceoveritems
0.2 0.2 inwhichagentiparticipatedbutlost. Asuccessfulagentcangeta
(d) (e) lowerpricefortheitemsitwonthanotheragentsbiddingonsimilar
01 2 3 4 01 2 3 4 5 itemsonparallelauctions,i.e. forasuccessfulagentPiwin<Pilost.
rank rank Wefindthatthesuccessrateofanagent,measuredasthefunctionof
auctionswonatalowerthanaverageprice(i.e.thefractionofagents
FIG. 3: Frequent bidders more likely to win an auction. (a) The forwhichPiwin<Pilost)increaseswiththenumberofauctionsthese
probabilitythatanauctioniswonbyagentswithgivenactivityrank. agentsparticipatein.Ahorizontaldottedlinecorrespondstothecase
Using all completed auctions we calculated how many times the whenthereisnocorrelationbetween thefrequency of bidding and
most, thesecond, or then-thfrequent bidder winstheauction. (b) the chances of getting a better price. A numerical fittingindicates
The probability that the most frequent bidder wins the auction of thatthesuccessrateincreaseslogarithmically(dashedline).
twoparticipants. (c)-(e): theprobabilitythatanagentwinsanauc-
tion of n [(c) n=3; (d) n=4; (e) n=5] participants. (a) is based on
143,325auctions,while(b)-(e)arebasedon47,610,30,205,20,017, cate that frequentlybidding agentsplay a key role in setting
and13,762auctions,respectively. thefinalpriceofmostauctioneditems:inthevastmajorityof
thecasestheagentswhoplacethelargestnumberofbidsare
thewinnersoftheauctionprocess. Thisfindingindicatesthat
placed by an agent on an item and the number of items the despitethewidespreadpracticeofsnipingamongexperienced
same agent bids for, indicating that power agents simultane- users[5]whenbiddersplacebidsonlyinthelast60seconds
ouslybidfrequentlyandwidely. of the auction hoping to win the auctioned item, on average
Agentswithanaggressivebiddingpatternsignificantlyal- frequentbiddersaremoresuccessful.
terthenatureofthebiddingprocess,potentiallydistortingthe Asthepowerlawdistribution(Fig.2b)indicatesthatsome
chanceofatypicalagenttowinanauction.Toinspecttheef- agentsbidratherwidely,thequestionis,doessuchwidebid-
fectofthebiddingpatternonthesuccessrateofagivenagent, ding result in economic advantage for power bidders? Our
we determinedthe fractionof auctionswonby the most, the results indicate that power agents not only are the frequent
second, or the k-th most frequentlybidding agents. We find winners of the auctions in which they participate, but they
thatin61%ofallauctionsthewinneristheagentthatmakes also pay less than other agents on similar items. Indeed, in
themostbids,andin29%ofallauctionsthesecondmostfre- Fig.4weshowthefractionoftimesthemostfrequentlybid-
quently bidding agent wins the auction (Fig. 3a). Less than ding agent pays less for an item than other agents that win
0.3%oftheauctionsarewonbyagentswhoseactivityranks auctionofitemsinthesamecategory. We findthatthemore
fifthorhigher.Asmostauctionshaveonlyafewparticipating auctionsan agentparticipates, the largeris its chance to pay
agents(Fig.1a),itisusefultore-examinethewinningpatterns lessforthesameitemthanthelesswidelybiddingagents.
in auctions with the same number of agents. We find that if The observed power law distribution is rooted in the dy-
onlytwoagentsparticipateinanauction,andeachplacemul- namics of the bidding process. Indeed, two processes con-
tiplebids,in85%ofthecasestheagentwithmorebidswins tributetothefinalnumberofbidsplacedonagivenitem:new
theauction(Fig.3b). Thesituationissimilarforthreeagents agents entering the bidding process and agents that already
as well (Fig. 3c): in 64% of the cases the more active agent placed a bid increase their bid. We find that this pattern is
wins,followedbythesecondmostactive,whichwinsin32% governedbyaprocessoftenreferredtoaspreferentialattach-
of the cases. In auctions with larger number of participants ment,similar tothoseresponsiblefortheemergenceofscal-
(Fig. 3d-e) we observe a similar pattern. These results indi- ingincomplexnetworks[6]: morebidsanagentplacesona
4
10 In conclusion, we have collected online auction data
and analyzed the statistical properties of emerging patterns
createdbya largenumberofagents. We foundthatthetotal
number of bids placed in a single category and the number
1
of distinct auctions frequented by a given agent follow
k power-law distributions. Such power-law behaviors imply
∆
that the online auction system is driven by self-organized
0.1 processes,involvingallagentsparticipatedinagivenauction
activity. We also uncoveredthe empiricalfact that the more
bids an agent places up to a givenmoment, more likely it is
thatitwill place anotherbid in the nexttime interval, which
0.01 playsanimportantroleingeneratingthepower-lawbehavior
0.1 1 10
inthebiddingfrequencydistributionbyagivenagent.
k
FIG.5: Theoriginoftheobservedpowerlawisinpreferentialat-
tachment.Thefigureshowsthechangeinthenumberofbidsplaced
byanagentithatpreviouslyplacedk bids,averagedoverallitems This work is supported by the KOSEF Grant No. R14-
andalltimes. Thelinearbehaviorinthelog-logplotindicatesthat 2002-059-01000-0intheABRLprogram.
themorebidsanagentplacesuptoagivenmoment,themorelikely
itisthatitwillplaceanotherbidinthenexttimeinterval.Suchpref-
erentialbiddingisknowntoleadtoapowerlawbiddingdistribution
[7,9].Thedottedlinewithslope1isshownforvisualreference.
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