Analyzing the Economic Efficiency of ebay-like Online Reputation Reporting Mechanisms Chrysanthos Dellarocas

Transcription

1 Anlyzing th Economic Efficincy of By-lik Onlin Rputtion Rpoting Mchnisms Chysnthos Dllocs Slon School of Mngmnt Msschustts Institut of Tchnology Cmbidg, MA 39, USA ABSTRACT This pp intoducs modl fo nlyzing mktplcs, such s By, which ly on biny puttion mchnisms fo qulity signling nd qulity contol. In ou modl slls kp thi ctul qulity pivt nd choos wht qulity to dvtis. Th puttion mchnism is pimily usd to dtmin whth slls dvtis tuthfully. Buys my xcis som lnincy whn ting slls, which nds to b compnstd by cosponding stictnss whn judging slls fdbck pofils. It is shown tht, th mo lnint buys whn ting slls, th mo likly it is tht slls will find it optiml to sttl down to stdy-stt qulity lvls, s opposd to oscillting btwn good qulity nd bd qulity. Futhmo, th finss of th mkt outcom is dtmind by th ltionship btwn ting lnincy nd stictnss whn ssssing sll s fdbck pofil. If buys judg slls too stictly (ltiv to how lnintly thy t) thn, t stdy stt, slls will b focd to undstt thi tu qulity. On th oth hnd, if buys judg too lnintly thn slls cn gt wy with consistntly ovstting thi tu qulity. An optiml judgmnt ul, which sults in outcoms wh t stdy stt buys ccutly stimt th tu qulity of slls, is nlyticlly divd. Howv, it is gud tht this optiml ul dpnds on svl systm pmts, which difficult to stimt fom th infomtion tht mktplcs, such s By, cuntly mk vilbl to thi mmbs. It is thfo qustionbl to wht xtnt unsophistictd buys cpbl of diving nd pplying it coctly in ctul sttings. Kywods Elctonic commc, puttion systms, tust in lctonic mkts.. ITRODUCTIO Onlin puttion poting systms mging s n impotnt qulity signling nd qulity contol mchnism in onlin tding communitis (Kollock 999; Rsnick t. l. ). Rputtion systms collct fdbck fom mmbs of n onlin community gding pst tnsctions with oth mmbs of tht Pmission to mk digitl o hd copis of ll o pt of this wok fo psonl o clssoom us is gntd without f povidd tht copis not md o distibutd fo pofit o commcil dvntg nd tht copis b this notic nd th full cittion on th fist pg. To copy othwis, o publish, to post on svs o to distibut to lists, quis pio spcific pmission nd/o f. EC, Octob 4-7,, Tmp, Floid, USA. Copyight ACM // $5.. community. Fdbck is nlyzd, gggtd nd md publicly vilbl to th community in th fom of mmb fdbck pofils. If on ccpts tht pst bhvio is ltivly libl pdicto of futu bhvio, thn ths pofils cn ct s powful qulity signling nd qulity contol mchnism, ssntilly cting s th digitl quivlnt of mmb s puttion. By lis on its puttion mchnism lmost xclusivly in od to both poduc tust nd induc good bhvio on th pt of its mmbs. By buys nd slls ncougd to t on noth t th nd of ch tnsction. A ting cn b dsigntion of pis, complint o nutl, togth with shot txt commnt. By mks th sums of pis, complint nd nutl tings submittd fo ch mmb, s wll s ll individul commnts, publicly vilbl to ll its uss. Ancdotl nd mpiicl sults sm to dmonstt tht By s puttion systm hs mngd to povid mkbl stbility in n othwis vy isky tding nvionmnt (Dwn nd Hsu ; Rsnick nd Zckhus ). Th ising pcticl impotnc of onlin puttion systms not only invits but th ncssitts igoous sch on thi functioning nd consquncs. A such mchnisms tuly libl? Do thy pomot fficint mkt outcoms? To wht xtnt thy mnipulbl by sttgic buys nd slls? Wht is th bst wy to dsign thm? How should buys (nd slls) us th infomtion povidd by such mchnisms in thi dcision-mking pocss? This is just smll subst of unnswd qustions, which invit xciting nd vlubl sch. Th study of puttion s mchnism fo inducing good bhvio in mkts with symmtic infomtion is ctinly not nw. Svl conomists hv publishd impotnt woks nlyzing its poptis (Rogson, 983; Schmlns, 978; Shpio, 98; Smllwood nd Conlisk, 979; Wilson, 985, just to nm fw). vthlss, lthough pst wok in conomics hs studid som of th ovll ffcts of puttion, it hs pid vy littl ttntion to th nlysis of spcific mchnisms fo foming nd communicting puttion, in pt bcus in tditionl bick nd mot socitis such mchnisms lgly infoml (thy oftn fd to s wod-of-mouth dvtising ) nd dfy dtild modling. Th fw publishd sults focusing on th ffcts of spcific poptis of puttion mchnisms clly mk th point tht such poptis cn hv significnt ffcts on th mkt outcom. Fo xmpl, Rogson (983) shows tht 7

2 puttion bsd on subjctiv biny tings (.g. good/bd, pis/complint) cts n xtnlity, which ffcts th nti mkt. Shpio (98) shows tht, unlss th mchnism by which puttion is fomd stisfis ctin poptis, slls my find it optiml to continuously oscillt in qulity, piodiclly building good puttion nd subsquntly milking it. On th oth hnd, th dsign nd implmnttion of onlin puttion systms hs so f bn th sch domin of comput scintists (s Bs t. l., 998; Sw t. l., ; Schf t. l. fo ovviws of pst wok). Th mphsis of pst wok in th hs bn on dvloping lgoithms nd systms fo collcting, gggting nd xtcting usful infomtion fom sts of us tings, dwing fom wok in infomtion tivl, dt mining nd collbotiv filting. Th nlysis nd vlution of th poposd lgoithms is typiclly don in tms of computtionl complxity nd sttisticl mtics, such s thi unning tim, mmoy quimnts, vg cll nd pcision, vg bis, tc. W bliv tht th is nd fo wok tht bidgs th two disciplins: sch, which tks into ccount th lgoithmic dtils of spcific puttion systms but lso modls how ths systms mbddd insid tding communitis nd invstigts thi ffctivnss nd impct, not only in tms of computtionl nd sttisticl poptis, but th in tms of thi ovll impct in th fficincy of th mkt nd th wlf of th vious clsss of mkt pticipnts. Givn tht puttion systms w concivd in od to ssist choic in nvionmnts of impfct infomtion, thi impct in thos ltt mkt dimnsions should b th ultimt dtminnt of succss of ny nw poposd nw lgoithm nd systm. This pp contibuts in this diction by poposing modl fo nlyzing th conomic fficincy of biny puttion systms, such s th on usd by By. Sction intoducs th modl nd its undlying ssumptions. Following tht, Sction 3 dfins numb of poptis tht puttion mchnisms should stisfy in such sttings, in od to b considd wll functioning. Sction 4 pplis ou modl in od to dtmin und wht cicumstncs biny puttion systms cn indd b wll functioning. Ou min conclusion is tht biny puttion mchnisms cn, in thoy, b wll functioning, povidd tht buys stik th ight blnc btwn ting lnincy nd sll ssssmnt stictnss. Howv, gtting this blnc ight is difficult without dditionl infomtion, which is not cuntly povidd by By. Sction 5 consids th implictions of lxing som of th simplifying ssumptions on which ou nlysis is bsd. Finlly, Sction 6 summizs th contibutions nd conclusions of th pp.. BIARY REPUTATIO MECHAISMS This sction intoducs modl fo nlyzing mktplcs, which ly xclusivly on biny puttion mchnism fo qulity signling nd qulity contol. A biny puttion mchnism is mchnism wh ts givn th oppotunity to t pst tnsctions using on of two vlus, commonly intptd s positiv (i.. stisfctoy) nd ngtiv (i.. unstisfctoy, poblmtic). Ou intntion is to us this modl in od to study th conomic impct of puttion mchnisms simil to th on usd by By (s Rsnick nd Zckhus fo dtild dsciption). In ou modl, qulitis non-ngtiv l-vlud quntitis, which subsum spcts of both poduct qulity nd svic qulity. W ssum tht ch sll poducs itms, whos l qulity q is unknown to buys nd cn only b dtmind with ccucy ft consumption. W futh ssum tht ll buys pf high qulity to low qulity, lthough thy might diff in th xtnt to which thy ppd to py fo n xt unit of qulity. Finlly, w ssum tht lthough th l qulity of itms is not communictd to buys, slls do infom buys by dvtising. On By, dvtising cosponds to th sllsupplid dsciption, which ccompnis ll itms. Th dvtisd qulity q of n itm is compltly contolld by th sll (i.. th is no vlidtion of ny kind by thid pty) nd my o my not cospond to its l qulity. Slls ims to mximiz th psnt vlu of thi pyoff function π ( x, q, q ) G( x, q, q ) c( x, q ) wh x is th volum of sls, G(.) is th goss vnu function nd c(.) is th cost function. W ssum tht c / q nd π / q fo ll slls. Und th bov ssumptions, slls hv n incntiv to ovdvtis qulity. Th mkt would thn dgnt to mkt fo lmons (Aklof 97). In od to void this fom hppning, buys givn th option to t ch tnsction using positiv o ngtiv ting. A puttion systm, optd by tustwothy thid pty, ccumults ll tings into fdbck pofil R (,, ) fo ch sll, wh no ting is th sum of ll positiv tings civd fo tht sll duing th most cnt tim window, is th sum of ll ngtiv tings civd duing th sm piod nd is th no ting numb of tnsctions fo which no ting ws submittd. Tim windowing is usd in od to ddss th possibility tht slls my impov o dtiot thi bhvio ov tim. Fo xmpl, on By, fdbck pofils disply th sums of tings civd duing th pst 6 months only. Buy utility fom puchs of singl itm is modld by U θ q p, wh p is th pic, θ is buy s qulity snsitivity nd q is th lvl of qulity pcivd by th buy ft consumption. Whn considing puchs, buys combin ll th infomtion tht is vilbl to thm, i.. n itm s In ddition to positiv (pis) nd ngtiv (complint) tings, By s puttion mchnism lso suppots nutl tings (which, howv, ly usd in ctul pctic). As will bcom ppnt blow, ou modl subsums ts who would submit nutl tings on By into th st of ts who don t submit ny ting t ll. By dos not cuntly publish. Th sults of this no ting pp mk stong cs tht thy should. 7

3 dvtisd qulity nd sll s fdbck pofil, in od to fom subjctiv ssssmnt of n itm s stimtd qulity q, wh: q f (, R) () q Amd with knowldg of pics nd stimtd qulitis, buys pocd to puchs on of th vilbl itms, psumbly th on which mximizs thi xpctd utility U θ q p. Following puchs, buys obsv th itm s pcivd qulity q q ε, wh ε is nomlly distibutd o tm with stndd dvition σ. Th intoduction of n o tm is intndd to collctivly modl numb of phnomn, which occu in ctul pctic. Fo xmpl: buys my misintpt sll s dvtisd qulity (this should b modld s q q ε, howv, ou nlysis is idnticl if w dd th o tm to q instd) slls my xhibit smll vitions in ctul qulity fom on tnsction to noth buys my hv smll diffncs in thi pcption of qulity bsd, sy, on thi moods tht dy som spcts of pcivd qulity dpnd on fctos byond sll s contol (.g. post-offic dlys) Finlly, buys dcid whth to t tnsction s wll s wht ting to giv. Ou modl ssums tht tings function of buy s stisfction ltiv to h xpcttions. W dfin buy s stisfction fom givn tnsction to b th diffnc btwn pcivd nd xpctd utility. Tht is, S U U θ ( q q ε). Und th bov ssumptions, S is nomlly distibutd ndom vibl with mn θ ( q q ) nd stndd dvition θ σ. On intsting popty of By, which hs bn potd on svl mpiicl studis, is tht most buys giv vy fw ngtiv tings to slls. Rsnick nd Zckhus () hv spcultd tht th svl sons fo this: By llows cipocl tings (tht is, slls lso t buys) nd buys oftn fid tht posting ngtiv ting fo sll will ld to tlitoy bd tings, hssing mils tc. By dos not povid mchnisms to pvnt o ssist such situtions. Futhmo, it hs bn potd tht slls oftn communict with buys vi mil nd ngotit sttlmnts to tnsction poblms, whil xplicitly plding with thm to not post ngtiv tings. Finlly, By hs ctd cultu of pis, wh th vst mjoity of tings nd commnts xtmly positiv. In such stting, most buys fl mol obligtion to confom to th pviling socil noms nd b nic nd ltivly fogiving to thi tding ptns. Ou modl uss ting function (S), which ttmpts to modl th bov mpiiclly obsvd bhvio. Mo spcificlly, w ssuming tht buys t tnsction s positiv if thi ctul utility fom th tnsction xcds thi xpctd utility (i.. if S>). On th oth hnd, buys only t tnsction s ngtiv if thi ctul utility flls shot of thi xpctd utility by mo thn lnincy fcto λ, tht is, if S < λ. Finlly, fo tnsctions, which nd up bing slightly bd but not too bd (i.. wh λ < S ), w ssuming tht buys pf to simply fin fom ting t ll 3. To summiz: " " if S > ( S) " " if S λ () no ting if λ < S wh S U U θ ( q q ε), ε ~ (, σ ), To simplify th initil nlysis, w mking th ssumption tht θ, σ nd λ constnt coss th nti popultion of buys nd slls. In Sction 5, w will lx thos ssumptions nd study how thy impct th sults divd in Sctions 3 nd WELL FUCTIOIG REPUTATIO MECHAISMS Th following sctions will us th modl dvlopd in Sction, in od to xplo und wht cicumstncs biny puttion mchnisms cn b wll functioning. Bfo doing tht, howv, in this sction w will discuss wht it mns fo puttion mchnism to b wll functioning in mktplcs with pivt qulity infomtion. W dfin wll-functioning puttion mchnism to b on, which stisfis th following two poptis: WF: If th xists n quilibium of pics nd qulitis und pfct infomtion (i.. in sttings wh q q q ) thn, in nvionmnts wh q is pivt to slls, th xistnc of th puttion mchnism mks it optiml fo slls to sttl down to stdy-stt pi of l nd dvtisd qulitis, th thn to oscillt, succssivly building up nd milking thi puttion. WF: Assuming WF holds, und ll stdy-stt sll sttgis ( q, q ) th qulity of slls s stimtd by buys bfo tnsctions tk plc, is qul to thi tu qulity (i.. q ). q Bfo w pocd, lt us justify th bov dfinition by poviding bif tionl fo th dsibility of poptis WF nd WF. Fist, th vlu of puttion mchnisms in gnl lis on th ssumption tht pst bhvio is libl pdicto of futu bhvio (Wilson 985). If oscilltions w optiml, th pdictiv vlu of cumultiv functions of pst tings, such s,, would b gtly diminishd. In nvionmnts wh th pimy (o only) mchnism fo ctifying nd contolling sll qulity is bsd on puttion, it is, thfo, dsibl tht slls find it optiml to sttl down to stdy-stt bhvio th thn to oscillt. Scond, ccoding to ou modl, buys mk puchs dcisions bsd on knowldg of pics nd stimtd qulitis. If it w possibl fo slls to sttl down into stdy-stt sttgy tht would consistntly dciv buys into stimting q > q, thn 3 On By, som buys would post nutl ting in this cs. 73

4 this would llow slls to n dditionl pofits t th xpns of buys. In th psnc of comptitiv mktplcs, buys would thn vntully lv th mktplc in fvo of oth mkts with btt infomtion. On th oth hnd, if, und ll possibl stdy-stt sll sttgis th ffct of th puttion mchnism ws such, so tht buys stimtd q < q, thn th opposit ffct would tk plc: buys would liz xt suplus t th xpns of slls. Onc gin, w would thn xpct tht slls would dst th mktplc in fvo of oth, mo tnspnt mkts. Th only fi stdy-stt sttgy, thfo, is on wh q q. 4. CA BIARY REPUTATIO MECHAISMS BE WELL FUCTIOIG? This sction will dmonstt tht, givn ting function, which hs th gnl fom givn by (), whth n By-lik biny puttion systm stisfis popty WF dpnds on th ltionship btwn () nd th qulity stimtion function q f (, R). Futhmo, w will show tht, if buys q lnint nough whn thy t nd cospondingly stict whn thy judg sll pofils, slls will find it optiml to sttl down to stdy-stt tu nd dvtisd qulity lvls if such n quilibium xists und pfct infomtion. 4. Estimtd vs. l qulitis in stdy stt Lt us fist focus ou ttntion on th cicumstncs und which biny puttion mchnism stisfis condition WF. W ssuming tht WF holds. Thfo, th xists t lst on stdy-stt sttgy q, q ) fo ch sll 4. A stdy-stt ( sttgy is sttgy tht optimizs sll s pyoff function, whil t th sm tim sulting in n stimtd qulity q f ( q, R), which is stbl ov tim. Dnot q ξ q, wh ξ is th dcption fcto, tht is, th distotion btwn stimtd nd l qulity t stdy stt. If ξ > thn buys ovstimt sll s tu qulity, whs if ξ < thn buys undstimt tu qulity. Lt b th totl numb of sls tnsctions of givn sll in th most cnt tim window. It is sy to s tht. Assuming tht buys no ting t ccoding to (), fo lg t stdy stt th following will hold: P [ > ] Φ[( ) / σ ] Φ[ ξ / σ ob S q q ] P ob[ S λ] Φ[( q q ) / σ λ Φ[ ξ / σ λ wh Φ (.) is th stndd noml CDF. Givn tht q f ( q, R), stisfction of condition WF dpnds on th qulity ssssmnt function f. Mo spcificlly, f 4 Sction 4. will xplo th conditions und which slls will indd find it optiml to sttl down to stdy stt sttgy. (3) must b chosn so tht, fo ll stdy-stt sttgis ( q, q ) th qution: q q ξ f ( q, R( ξ )) (4) hs uniqu solution t ξ. By dos not spcify, o vn commnd, spcific qulity ssssmnt function f. It simply publishs th quntitis nd fo ch sll nd llows buys to us ny ssssmnt ul thy s fit. It is impotnt to not t this point tht By dos not cuntly publish th quntity (nd thfo ) fo sll. As w will show blow, no ting knowldg of is ssntil fo constucting libl qulity ssssmnt functions. Th sults of this pp, thfo, mk stong gumnt tht th numb of tnsctions tht hv civd no ting should b ddd to th pofil infomtion publishd by By nd simil systms. Ou objctiv in this pp is to xplo whth in pincipl, biny puttion systms cn b wll functioning. Thfo, ou im is to xplo th xistnc of qulity ssssmnt function f which, whn usd in conjunction with ting ul (), stisfis WF. In th st of th pp, w will xplo th suitbility of th following fmily of qulity ssssmnt functions: q if ξˆ( R) q f ( q, R) (5) if ξˆ( R) > wh ξ ˆ( R ) is som stimt of th sll s dcption fcto bsd on infomtion contind in th sll s fdbck pofil. Though function (5), buys ssss th qulity of n itm to b qul to tht dvtisd by th sll, if, bsd on th sll s pofil, thy conclud tht th sll dos not ov-dvtis. Othwis, buys ssum tht th sll lis nd ssss minimum qulity. Function (5) thfo uss th infomtion povidd by th puttion mchnism in od to div (biny) ssssmnt of tuthfulnss in dvtising. It is sy to s tht, if buys hv wy of libly stimting th sign of ξ fom fdbck pofil infomtion nd ssss sll qulity though function (5), slls who ov-dvtis thi qulity will quickly s thi stimtd qulity fll to zo. Thfo, if f is givn by (5), qution (4) hs no solution fo ξ >. ot tht function (5) dos not pvnt slls fom unddvtising thi qulity bcus fo q q ξ, ll ξ lso solutions of qution (4). Howv, givn tht w hv ssumd tht π / q, w would not xpct ny pofitmximizing sll to und-dvtis. Thfo, th only stdy- stt sll sttgy fo slls would b to tuthfully dvtis thi l qulity. In tht cs, buys would stimt q q q, dsibl outcom, which stisfis WF. 74

5 In conclusion, biny puttion systm wh buys t ccoding to () ssss itm qulity ccoding to (5) nd hv libl ul fo clculting ξ ˆ( R ) fo givn sll stisfis WF. Lt us now xplo th diffnt wys in which buys cn us, nd in od to stimt th sign of ξ. Estimtion bsd on th numb of positivs On wy to stimt sll honsty is to qui tht th fction of positiv tings of good slls xcd thshold. Fom (3) w cn s tht η ˆ / cn b intptd s point stimto of Φ [ ξ / σ ]. Givn tht Φ[ ξ / σ ] <. 5 fo llξ >, ssssmnt of th sign of ξ ducs to tsting th sttisticl hypothsis H : η. 5 givn ηˆ. Th cosponding qulity ssssmnt function thn bcoms: q if H ccptd q if H jctd (6) wh H : η.5 givn ηˆ / Hypothsis H cn b tstd using on of th known tchniqus fo computing confidnc intvls of popotions following binomil distibutions (.g. Blyth nd Still 983). Function (6) is n ppling mthod fo ssssing sll qulity bcus of its ltiv simplicity. ot tht its computtion dos not qui knowldg of th modl pmts λ, θ nd σ. Howv, (6) is difficult to comput libly without knowldg of, th totl numb of td plus untd tnsctions of sll. As ws mntiond, By dos not mk known to its mmbs. Tking η ˆ /( - ) would sult in lg ovstimtion of Φ [ ξ / σ ], spcilly bcus of th ting lnincy fcto. Fo tht son, on would inf tht qulity ssssmnt bsd on th numb of positiv tings is not (nd should not b) widly usd on By. This hypothsis is consistnt with mpiicl obsvtions (Dwn nd Hsu ). Sction 4. will discuss noth disdvntg of function (6), which is tht it mks it si fo slls to oscillt btwn piods wh thy milk thi good puttion by ovstting thi qulity nd dciving buys nd piods wh thy sto thi puttion by offing btt qulity thn wht buys xpct. Estimtion bsd on th numb of ngtivs In n nlogous mnn, w xpct good slls to hv fw ngtiv tings. Thfo, noth wy to stimt sll honsty is to qui tht th fction of ngtiv tings of good slls sty blow thshold. Fom (3) w cn s tht ζˆ / cn b intptd s point stimto of Φ [ ξ / σ λ. Givn tht Φ [ ξ / σ λ > Φ[ λ fo llξ >, ssssmnt of th sign of ξ ducs to tsting th sttisticl hypothsis H : ζ Φ [ λ /( θ givn σ ζˆ. Th cosponding qulity ssssmnt function thn bcoms: q if H ccptd q if H jctd wh H : ζ k Φ[ λ givn ζˆ - / Lt us cll k Φ[ λ th optimum tustwothinss thshold. k is monotoniclly dcsing function of th lnincy fcto λ. Thfo, th mo lnint buys whn thy t, th low th thshold of ngtiv tings to tnsctions bov which thy should not tust slls, nd vic vs. This is sult tht cosponds wll to documntd mpiicl findings: most By buys wigh ngtiv tings much mo hvily thn positiv tings whn ssssing th tustwothinss of pospctiv sll (Dwn nd Hsu ). Givn tht thy sm to b th lnint whn thy t thos slls, ccoding to (7), w would xpct thm to b stict whn ssssing th qulity of slls, nd thfo to b ltivly intolnt of ngtiv tings. Fom qution (7) w cn lso s tht, in thoy, buys will complt knowldg of th systm pmts λ, θ nd σ cn div n optimum k fo vy λ 5. On wy of intpting this sult is tht stisfction of WF is lwys possibl no mtt how lnint (o stict) buys whn thy t, povidd tht thy stik th ight blnc btwn ting lnincy nd qulity ssssmnt stictnss. In th nxt sction, w shll pov tht, mo lnint ting (nd cospondingly stict ssssmnt) incss th liklihood tht slls will find it optiml to sttl down to stdy-stt bhvio. Som dg of lnincy, thfo, cn b bnficil to th stbility of th mktplc. It is lso impotnt to point out tht, unlss buys us th ight thshold k whn vluting th numb of ngtiv tings of sll, WF will not b stisfid. If buys us thshold k > k thn th will b somξ > fo which H will b stisfid nd slls will b bl to consistntly dciv buys by ovdvtising thi qulity. In contst, if k < k, th will b ξ < such tht H will b jctd fo ll ξ > ξ. In th ltt cs, to pvnt thi stimtd qulity fom dopping to zo, slls will b focd to und-dvtis nd, thfo, b consistntly und-ppcitd by ξ. W s, thfo, tht th choic of th ight k is cucil to th wll functioning of th puttion mchnism, nd of th mktplc in gnl. It is impotnt to sk whth buys cn 5 Although this conclusion stblishs th thoticl wll functioning of biny puttion mchnisms, in pctic, typicl buys will not hv knowldg of th pmts ndd to stimt k. Pls d on fo discussion of th implictions of this. (7) 75

6 b sonbly xpctd to b bl to coctly div it. Fom qution (7), clcultion of k quis knowldg of th modl pmts λ, θ nd σ. It is unlikly tht buys would hv ccut undstnding nd knowldg of thos pmts (spcilly σ, which ptly flcts poptis of th sll). vthlss, vn if th modl pmts not known, it is possibl to stimt th vlu of Φ [ λ fom nd. Fom (3):, ξ / σ Φ λ ) ξ / σ Φ k ( ( Φ[ λ Φ[ Φ / ) / ) ( / ) Φ ( / If is smll thn confidnc intvl should b constuctd fo k. Evn with th hlp of qution (8), buys still nd to know in od to poply comput function (7). Ovll, function (7) dfins th fgil ul fo ssssing sll qulity fficintly. Givn tht lot of By buys hvily bsing thi sll qulity ssssmnts on th numb of ngtiv tings on th slls fdbck pofil, it is vy intsting to sk wht mthods thy us to comput thi tustwothinss thsholds nd, vn mo impotnt, whth thi tustwothinss thsholds do indd com clos to stisfying WF. Clly, ths impotnt qustions, which invit futh mpiicl nd xpimntl sults to complmnt th sults of this wok. Estimtion bsd on th tio btwn ngtivs nd positivs In both pvious css, coct implmnttion of th qulity ssssmnt function quid knowldg of. On might think tht, by bsing qulity ssssmnt on th tio btwn ngtiv nd positiv on my b bl to div n optiml ssssmnt function fom nd only. W will show tht this is not possibl. Fom (3) w gt: ρ( ξ ) ( ξ) Φ[ ξ / σ λ ( ξ ) Φ[ ξ / σ ] Function ρ(ξ ) is non-ngtiv nd monotoniclly incsing in ξ. Futhmo ρ( ) Φ[ λ. Sinc ρ ( ξ ) > ρ() fo ll ξ >, ssssmnt of th sign of ξ ducs to tsting th sttisticl hypothsis H : ρ Φ[ λ /( θ givn σ ˆρ /. Th cosponding qulity ssssmnt function thn bcoms: q if H ccptd q if H jctd () wh H : ρ Φ[ λ givn ˆ ρ / Unlss buys hv knowldg of th modl pmts λ, θ nd σ, clcultion of Φ[ λ fom (8) quis knowldg of. Thfo, using th tio of ngtivs to positivs is vy simil to using th fction of ngtivs nd is qully ticky to gt ight without knowldg of. - (8) (9) 4. Existnc of stdy-stt bhvio Th nlysis of Sction 4. hs bn bsd on th ssumption tht slls sttl down to stdy-stt l nd dvtisd qulity lvls. This sction will invstigt th conditions und which slls will indd find it optiml to do so. Th ltntiv is to oscillt btwn building good puttion nd thn milking it by ov-dvtising l qulity. As w gud in Sction 3, puttion-mditd mktplcs should b dsignd in od to induc slls to sttl down to stdy stt bhvio (othwis infomtion bout pst bhvio will not b vy hlpful s wy of pdicting th futu). Th pincipl sult of this sction is tht whn qulity ssssmnt is bsd on functions (7) o (), which involv ngtiv tings, thn, if th ting lnincy fcto λ is lg nough, slls will find it optiml to sttl down to stdy stt bhvio. In contst, th is no such gunt whn qulity ssssmnt is bsd on function (6), which only involvs positiv tings. This sult shows tht mo lnint ting (coupld with mo stict qulity ssssmnt) suppots stbility in th systm. Fo th sm son, lthough mo fgil nd difficult to gt ight, functions (7) nd (), i.. functions which bs sll qulity ssssmnt on th numb of ngtiv tings, pfd to function (6), which only looks t th sll s positiv tings. In od to div ou sult, lt us consid wys in which slls my ttmpt to liz dditionl pofits though oscillting bhvio. Assum tht sll is bl to pfom tnsctions bfo tings of thos tnsctions postd to h fdbck pofil. This numb dpnds on th fquncy of tnsctions nd th dly btwn tnsctions nd th posting of tings by buys (on By, this dly is typiclly -3 wks). Lt us consid sll who, t th nd of piod, hs compltd tnsctions in th cunt tim window nd hs ccumultd good puttion, by poducing nd dvtising itms of qulity q, th qulity tht optimizs pofits ssuming stdy-stt bhvio. Lt us futh ssum tht buys ssss qulity bsd on function (7). At th nd of piod : ( ξ ) Φ[ λ k () P At th bginning of piod th sll dcids to milk h puttion by choosing l qulity q nd thn ov-dvtising h qulity by ξ so tht h pofit is mximizd ltiv to th stdy stt cs. Givn th sll s good pst puttion, initilly buys will b dcivd. Howv, ft thy puchs th sll s itms, thy will liz thi infio qulity nd will post popotionlly mo ngtiv tings. Thfo, t th nd of piod (ft dciving tnsctions): Φ[ λ Φ[ ξ / σ λ > k P () nd th sll s subsqunt stimtd qulity will fll to zo. Assuming tht som buys willing to buy fom sombody with zo qulity if th pic is low nough, ou sll will sty in businss. In od to incs h puttion onc gin, sh nds 76

7 to duc th tio / to blow th thshold k. Th only wy sh cn chiv this is to go though piod wh sh poducs high qulity itms but civs low pics, supssing buys xpcttions (who now xpct q ) by ξ. Lt us ssum tht it would tk dming tnsctions bfo / k. At th nd of piod : - Φ[ λ /( θ σ Φ[ ξ / σ λ /( θ σ Φ[ ξ / σ λ /( θ σ P k Φ[ λ /( θ σ (3) A pofit-mximizing sll will choos to oscillt if th pofit fom th dciving tnsctions ltiv to th stdy-stt pofit xcds th loss fom th dming tnsctions ltiv to th stdy-stt pofit. If ths two quntitis hv finit tio, thn, povidd tht th numb of dming tnsctions tht ncssy in od to undo th puttion ffcts of dciving tnsctions is high nough, slls will not find it pofitbl to oscillt nd will sttl down to stdy-stt l nd dvtisd qulity lvls. Fom (3) ft som lgbic mnipultion, w gt: Φ[ ξ / σ λ Φ[ λ g( λ, ξ, ξ ) (4) Φ[ λ Φ[ ξ / σ λ Aft som mnipultion w gt g / λ > nd g/ λ >. In fct g(.) gows xponntilly with λ 6. Figu plots g(λ) fo θ σ nd som psnttiv vlus of ξ ξ ξ. Minimum tio / Lnincy fcto (lmbd) ksi ksi ksi3 ksi4 ksi5 Figu. Minimum tio of dming to dciving tnsctions ndd in od to sto on s good puttion following piod of qulity ov-poting. 6 Futhmo, fo givn λ, g(.) gows pidly withξ nd dcss vy slowly with ξ. This mns tht th minimum ncssy tio of dming to dciving tnsctions gows with th mount of initil dcption ( ξ ) nd cnnot b significntly bought down by incsing th mount of dmption ( ξ ). Fom Figu it is vidnt tht in mktplcs wh buys t lnintly (nd ssss qulity stictly), slls nd mny mo dming tnsctions in od to sto thi good puttion following fw dciving tnsctions. Th ltiv numb of dming tnsctions incss xponntilly with th lnincy fcto. Othwis sid, th lg th λ, th mo difficult it is fo slls to sto thi puttion onc thy los it. Consquntly, if λ is sufficintly lg, slls will find it optiml to sttl down to stdy-stt l nd dvtisd qulity lvls. Q.E.D. A simil sult cn b divd if buys bs qulity ssssmnt on th tio /. In contst, if buys bs qulity ssssmnt on function (7), ou nlysis givs: Φ[ ξ / σ ] (5) Φ[ ξ / σ ] Eqution (5) givs ξ ξ nd slightly lss thn fo fo ξ <. Othwis ξ sid, following st of dciving tnsctions, it tks th sm numb of (o fw) dming tnsctions in od to sto on s good puttion. In such stting, it is mo likly tht som slls will hv pofit functions fo which it will b optiml to oscillt. Thfo, on xpcts tht in puttion-mditd mktplcs wh buys us (6) to ssss sll qulity, th will b lss stbility thn in mktplcs wh slls us (7) o (). Th sults of this sction povid som intsting gumnts fo both ting lnincy s wll s fo bsing th qulity ssssmnt of slls on thi ngtiv, th thn thi positiv tings. 5. REALITY CHECKS AD SOME RECOMMEDATIOS Th sults of th pvious sctions hv bn divd by mking numb of simplifying ssumptions bout buy bhvio. Mo spcificlly, w hv ssumd tht ll buys hv th sm qulity snsitivity θ nd lnincy fcto λ. Futhmo, w hv ssumd tht buys lwys submit tings whnv thi stisfction iss bov zo o flls blow λ. Both ssumptions not likly to hold in l mktplc. Buys hv diffnt psonlitis, nd thfo, xpctd to hv diffnt qulity snsitivitis, s wll s lnincy pmts. Futhmo, tings do incu cost (tim to log on nd submit thm) nd som buys do not both ting, vn whn tnsctions tun out lly good o vy bd. In this sction, w will injct bit of lity to ou modl nd will xplo how ou sults chng if w tk into ccount th bov considtions. Rlity Chck #: Som buys nv t W nd to modify ou ting function (S) in (), so tht whn S >, ( S) " " with pobbility β nd (S) no ting with pobbility ( β ). Similly, whn S λ, ( S) " " with pobbility γ nd (S) no ting with pobbility ( γ ). Und this nw ting function, th sttisticl hypothsis in (6) bcoms H : η β. 5, whil th hypothsis in (7) bcoms H : ζ γ Φ[ λ /( θ. W s σ 77

8 tht ou nw ssumption intoducs two dditionl pmts to ou modl. Th pmts nd to b libly stimtd in od fo popty WF to b stisfid. Rlity Chck #: Buys diff in qulity snsitivity nd lnincy Lt s dfin ω λ / θ nd lt s cll p (ω ) th pobbility distibution of ω mong buys. Thn (3) must b modifid s: P ob[ S > ] Φ[ ξ / σ ] (6) P ob[ S λ] Φ[( ξ ω) / σ ] p( ω) dω If qulity ssssmnt is bsd on th fction of positiv tings using (5), thn lity chck # dos not intoduc dditionl complictions. Howv, if qulity ssssmnt is bsd on th fction of ngtiv tings, which, in th psnc of lnint tings is th ul most likly to sult in stbl sll bhvio, thn things do bcom considbly mo complictd. Mo spcificlly, it is sy to s tht th sttisticl hypothsis to b tstd in (6) must bcom H : ζ k Φ[ ω / σ ] p( ω) dω. In od to clcult th ight k, on nds knowldg of p (ω ). Things bcom vn mo complictd if w combin lity chcks # nd #, which would b th sitution tht most closly cosponds to ctul lity. Of cous, on cn bgin to think of wys in which individul buys might b bl to stimt, myb with som dg of o, th dditionl modl pmts β, γ nd p( ω) fom, nd. Howv, instd of mbking in this diction, t this stg w bliv tht w povidd nough gumnts to mk on of th min points of this pp: Biny puttion mchnisms cn in thoy b wll functioning und th ssumption of simpl ting nd ssssmnt uls, but only if buys us th ight thsholds whn judging sll tustwothinss. Clculting th ight thshold fom, lon, th only infomtion cuntly povidd by By, is vy difficult. Clculting th ight thshold fom, nd is possibl und th simplifying ssumptions of Sction but bcoms mo nd mo difficult s ou modls ppoch lity. In listic css, th coct ssssmnt ul dpnds not only on th fdbck pofil of sll but lso on poptis of th t popultion. Givn tht th fficincy of th mktplc cucilly dpnds on th slction of coct ssssmnt thsholds on th pt of th buy, th most snsibl cous of sch thfo should b to think of dditionl infomtion tht th puttion mchnism cn povid to ts, in od to mk this clcultion si. 6. COCLUSIOS Th objctiv of this pp ws to xplo to wht xtnt biny puttion mchnisms, such s th on usd t By, cpbl of inducing fficint mkt outcoms in mktplcs wh () tu qulity infomtion is unknown to buys, (b) dvtisd qulity is compltly und th contol of th sll nd (c) th only infomtion vilbl to buys is n itm s dvtisd qulity plus th sll s fdbck pofil. Th fist contibution of th pp is th dfinition of st of conditions fo vluting th wll functioning of puttion mchnism is such sttings. W consid puttion mchnism to b wll-functioning if it () inducs slls to sttl down to stdy-stt bhvio ssuming it is optiml fo thm to do so und pfct qulity infomtion nd (b) t stdy-stt, sll qulity s stimtd by buys bfo tnsctions tk plc is qul to thi tu qulity. Th scond contibution of th pp is n nlysis of whth biny puttion mchnisms cn b wll-functioning und th ssumptions tht () tings bsd on th diffnc btwn buys tu utility following tnsction nd thi xpcttions bfo th tnsction nd (b) buys ltivly lnint whn thy t nd cospondingly stict whn thy ssss sll s fdbck pofil. Th fist conclusion is tht if biny fdbck pofils usd to dcid whth sll dvtiss tuthfully (in which cs buys ssss qulity qul to th dvtisd qulity) o not (in which cs buys ssss qulity qul to th minimum qulity), thn, in thoy, biny puttion systms cn b wll functioning, povidd tht buys stik th ight blnc btwn ting lnincy nd qulity ssssmnt stictnss. Futhmo, ssuming tht buys bs thi judgmnt on th tio of ngtiv tings civd by sll, if buys lnint nough whn thy t nd cospondingly stict whn thy judg sll pofils, w hv shown tht slls will find it optiml to sttl down to stdy-stt qulity lvls if such n quilibium xists und pfct infomtion. This is n intsting wy in which () judging sll tustwothinss bsd on thi ngtiv tings is pfbl to bsing it on thi positiv tings nd (b) som dg of ting lnincy hlps bing stbility to th systm. Th scond conclusion is tht, unlss buys us th ight thshold pmts whn thy judg sll pofils, biny puttion mchnisms will not function wll nd th sulting mkt outcom will b unfi fo ith th buys o th slls. In tht sns, lthough biny puttion mchnism cn b wll functioning in thoy, thy xpctd to b quit fgil in pctic. Th cucil qustion thfo bcoms whth biny fdbck pofils povid slls (sp. ltivly unsophistictd ons) with nough infomtion to div th ight sll judgmnt uls. It ws shown tht th ight judgmnt ul is difficult to inf coctly fom knowldg of th sum of positiv nd ngtiv tings lon, which is th only infomtion cuntly povidd by By to its mmbs. If knowldg of th sum of untd tnsctions is ddd to fdbck pofils, thn, und numb of simplifying ssumptions, it is possibl to div non-obvious but ltivly simpl optiml judgmnt uls which sult in wll functioning puttion mchnisms. Howv, if th simplifying ssumptions doppd, clcultion of th ight judgmnt ul fom, nd onc gin bcoms difficult, s it quis knowldg not only of sll tings but of th t popultion s wll. Ths findings ld to th commndtion tht mo infomtion should b povidd to ssist ts of such mktplcs us fdbck pofils in th ight wy. Th thoticl sults of this pp is som intiguing qustions ltd to th fficincy, finss nd stbility of Bylik lctonic mktplcs. Th utho would wlcom 78

9 xpimntl nd mpiicl vidnc tht will shd mo light into th qustions isd nd would vlidt th conclusions dwn fom his modls. 7. ACKOWLEDGMETS This sch ws suppotd by SF CAREER GRAT IIS nd n MIT Businss Vision Fund Awd. 8. REFERECES Aklof, G. (97) Th mkt fo lmons : Qulity unctinty nd th mkt mchnism. Qutly Jounl of Economics 84, pp Blyth, C.R. nd Still H.A. (983) Binomil Confidnc Intvls. Jounl of th Amicn Sttisticl Assocition 78, pp Bs, J.S., Hckmn, D., nd Kdi, C. (998) Empiicl Anlysis of Pdictiv Algoithms fo Collbotiv Filting. In Pocdings of th 4 th Confnc on Unctinty in Atificil Intllignc (UAI-98), pp. 43-5, Sn Fncisco, July 4-6, 998. Dwn, S. nd Hsu, V. () Tust in Elctonic Mkts: Pic Discovy in Gnlist Vsus Spcilty Onlin Auctions. Woking Pp. Jnuy 3,. Kollock, P. (999) Th Poduction of Tust in Onlin Mkts. In Advncs in Goup Pocsss (Vol. 6), ds. E.J. Lwl, M. Mcy, S. Thyn, nd H.A. Wlk, Gnwich, CT: JAI Pss. Rsnick, P., Zckhus, R., Fidmn, E., Kuwb, K. () Rputtion Systms. Communictions of th ACM, Vol. 43, (), Dcmb, pp Rsnick, P. nd Zckhus, R. () Tust Among Stngs in Intnt Tnsctions: Empiicl Anlysis of By's Rputtion Systm. Woking Pp fo th BER wokshop on mpiicl studis of lctonic commc. Jnuy. Rogson, W.P. (983) Rputtion nd poduct qulity. Bll Jounl of Economics, Vol. 4 (), pp Sw, B. M., Kypis, G., Konstn, J. A., nd Ridl, J. (). Anlysis of Rcommnd Algoithms fo E-Commc. ACM E- Commc Confnc, Minnpolis, M, Oct. 7-,. Schmlns, R. (978). Advtising nd Poduct Qulity. Jounl of Politicl Economy, Vol. 86, pp Schf, J.B., Konstn, J., nd Ridl, J., () Elctonic Commc Rcommnd Applictions. Jounl of Dt Mining nd Knowldg Discovy. Jnuy,. Shpio, C. (98) Consum Infomtion, Poduct Qulity, nd Sll Rputtion. Bll Jounl of Economics 3 (), pp -35, Sping 98. Smllwood, D. nd Conlisk, J. (979). Poduct Qulity in Mkts Wh Consums A Impfctly Infomd. Qutly Jounl of Economics. Vol. 93, pp. -3. Wilson, Robt (985). Rputtions in Gms nd Mkts. In Gm-Thotic Modls of Bgining, ditd by Alvin Roth, Cmbidg Univsity Pss, pp