Fuzzy Logic Based Effective Bidding Range Computation and Bidder s Behavior Estimation in Keyword Auctions

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1 Fuzzy Log sed Effetve ddng Rnge Comutton nd dder s ehvor Estmton n eyword Autons Mdhu umr Shool of Comuter nd Systems Senes Jwhrll Nehru Unversty New Delh, Ind e-ml: mdhu.gln@gml.om ml. hrdw Shool of Comuter nd Systems Senes Jwhrll Nehru Unversty New Delh, INDIA e-ml: kbhrdw@gml.om Abstrt eyword utons re beng used to sell the ostons long the sde of orgn results shown by serh engne when user tyes keyword or query relted to keyword n serh engne. It hs been huge revenue genertng ren for serh engnes sne lst dede. Irresetve of the gret suess of these tyes of utons there re ertn reserh ssues whh re stll n nhote stte nd needs urgent ttenton of reserh ommuntes e.g. how muh nve bdder should bd wthout referrng to ny omlex gents, how muh he/she wll be mnmlly hrged for the rtton et. In ths er we roose novel sheme to omute effetve bddng rnge bsed on fuzzy log whh hs threefold dvntges. Frstly, t rovdes bdders wth the nformton of hs effetve rnge of bds whh n ensure hs hnes of rtton nd wnnng. Seondly, t rovdes utoneer wth the nformton bout bdders bddng behvor whh n hel n redtng ther revenues nd lstly t n enfore the mnmum reservton res n nturl wy. Exermentl results re resented to llustrte workng of the roosed sheme. eywords- keyword utons,bddng behvour,reservton res,sonsereds serh,fuzzy log. I. INTRODUCTION The Internet eonomy hs been lrgely ffeted by the ntroduton of uton bsed dvertsng n the form of sonsored lnks. Sonsored lnks re smll number of dvertsements (ds, heneforth tht the serh engne dslys n ddton to the stndrd serh results. These ds re rrnged n ostons to to bottom, tylly on the sde. Normlly, the dvertser ys only when the user lks on the lnk (known s y er lk (PPC. It s dffult tsk to set fxed re for eh oston beuse the serh queres vry wdely nd wth them the vlue of the ostons. Advertsers n ths knd of utons usully bd (PPC on vrous keyword relted to ther roduts so t s known s keyword utons A mor tsk for the serh engne s to determne the rules of the oston uton, nd to selet, rnk nd re the ds tht wll be dslyed to the user, ordng to tht uton.. Hene, tylly, utons re used to determne the res, nd ostons of the dvertsers. The key Auton Serve Provdes wth most ommerl nterest, Google, Yhoo! nd MSN Lve mke vlble to dvertsers u to three lnks bove the orgn results (these re the mnlne slots, u to eght lnks besdes the orgn results (sdebr slots nd, more reently, MSN Lve even sells lnks below the orgn results (bottom slots. Aordng to reort by Intertve Advertsng ureu nd PrewterhouseCooers, the keyword dvertsng revenue rehed $8.5 bllon n 27. emrketer estmtes tht keyword dvertsng wll onsstently ount for 4% of the totl onlne dvertsng revenue for yers to ome.art from the nterestng revenue sttsts there re number of fts bout keyword utons whh mkes ths tye of utons dfferent from other mult-unt utons.in y-er-lk utons, keyword dvertsng rovders often lern bout dvertsers' bltes to generte lks, e.g., by observng the lk-through rtes of the dvertsement n the st. Suh nformton hs been grdully ntegrted nto the keyword uton desgns. For exmle, n 23, Google strted rnkng dvertsers by the rodut of ther bd res nd ther hstorl lk-through rtes. In 25, Google doted more sohstted rnkng sheme tht weghs dvertsers' unt-re bds by qulty sores", whh re determned by severl ftors nludng dvertsers' hstorl lk-through rtes, the relevne of the dvertsement text, nd qulty of lndng ges. The vlblty of lk-through nformton lso enbles lterntve mnmum bd oles. For exmle, Google hs bndoned ther one-sze-fts-ll mnmum-bd oly n fvor of new oly tht moses hgher mnmum bds for dvertsements wth low qulty sore. ref out lne of ths er s follows, we hve resented relted work n seond seton In thrd seton we exlned the termnologes nd keywords relted to the roosed sheme. Thrd seton underns the des of effetve rnge omutton nd bdder s behvor estmton nd lst seton onludes the er wth some future extensons to the roosed sheme.. II. RELATED WOR There numerous reserh ssues ertnng to keyword uton vryng from mthng of rorte keyword to /1/$ IEEE 299

2 sonsored lnks [6], to omutton of otml revenue of for the Auton serve rovders. ut n ths er we foused mnly on the frst hse of the uton where bdders exress rough estmtes of ther wllngness to y (PPC rnge. Our work s bsed on growng lterture n the feld.s ([3],[11],[13] ll ontn versons of the result tht ndtes the need of smlfed nd lud mehnsm to hndle nformton unertntes relted to the bdders vluton s well s the soe for the utoneers to estmte nd tegorze bdders behvor for revenue redton n future senro. The relted reserh [13] lerly lms tht gents hs to rete look hed lns (omlexto bd nd strteglly n ther budgets n vrous erods. Lernng how muh to bd wthout muh of the omlexty would ertnly nreses the nentves dvertsers to rtte n the uton. s [11] exlns keyword uton n terms of GSP(Generlzed Seond Pre Autons. GSP evolved n the mrket for onlne dvertsng, ts rules reflet the envronment s unque hrtersts. GSP nssts tht for eh keyword, bdders submt sngle bd even though severl dfferent tems re for sle: oston 1 s very dfferent from oston 5. The unusul one bd requrement mkes sense n ths settng: the vlue of beng n eh oston s roortonl to the number of lks ssoted wth tht oston. Consequently, even though the envronment s mult-obet, buyer vlutons n be dequtely reresented by one-dmensonl tyes. However, one bd er keyword s robbly not suffently exressve to fully onvey the referenes of the bdders e.g., t does not llow for the ossblty tht the users who lk on oston 5 re somehow dfferent from those who lk on oston 2, t does not llow for the ossblty tht dvertsers re bout the lloton of other ostons, nd so on. Whle [3]. nd [13] tke good ntl frst ste to nlyze the sonsored serh utons, they fl to tke nto ount reserve res tht serh engnes usully set for mny of the queres oston sef reservton res[4] nd bdder sef reservton res. One mortnt suh feture s the use of dvertsersef ftors for settng mnmum res. eyond the stndrd use of dvertsers' bds nd ther qulty sore s n GSP, the serh engnes fore the bd nd re er lk of dvertser to be t lest mnmum re. mortntly for sonsored serh, beuse the hevy tl" of nfrequent keywords often hs only few dvertsers er query, the mnmum re determnes whether or not the d wll er for tht query. So, dvertser-sef mnmum res hve rofound effet on dvertsers, users nd serh engnes n rte. In the roosed sheme the roblem of enforement of mnmum bd s solved omutton of effetve rnge of bd whh gurntees the bdders stnd n the rtton of uton. [5] It gves Weghted UPC(Unt Pre er Clk utons mehnsm whh re eselly sutble for use on the Internet, whh n often rovde effent wys of trkng bdder s st erformne. Consders the mt of mt of dvertser st lk nformton (erformne on the revenue of the serh engnes but t does not nlude the mt of bdders sendng behvor long wth st lk nformton. An uton n be vewed s multle-erson nonooertve gme [9], n whh the best bddng strteges re lwys heved t the equlbrum stte of ll lyers. Therefore, the theoretl foundton for utons s bsed on the Nsh equlbrum [7,1]. Mlgrom nd Webers uton theory nd Myersons otml uton desgn re tyl of the gme theory bsed works n the 198s [8]. Durng tht dede, the models of utons most studed were symmetr models devoted to the bddng roess for one obet. In more reent yers, symmetr models nd mult-obet uton models hve reeved more ttenton. The nternet offers hgh degree of flexblty n utons. Ths mkes the study of otml utons n suh envronment eselly nterestng. Mny new roblems nd rohes hve been brought u. These nlude the resoure onstrned mult-obet utons, rtton onstrned mult-obet utons, wnner determnton method for ombntorl utons [12], multssue utons nd double utons for e-ommere. Gme theory rovdes n effent tool for nlyzng the vlue estmton nd bddng roesses between seller nd otentl buyers [2]. It s eselly lble to utons of sngle obet or one knd of good. However, for the more omlted utons nvolvng more thn one obet, wth dfferent knds of onstrnts, or bddng on ombntons of obets, the mn ssue beomes how to orgnze the utons rther thn the bddng roesses. In ths se, the gme theory roh s no longer so workble. Ths ft stmultes us to onsder usng other mthemtl methods for utons. Consderng the bove wrtten roblems we med dvertsers rnge of wllngness to y er lk to fuzzy sets bsed on [2] nd roosed novel sheme to fltte bdders n knowng ther vlutons.when bdder submts bd, utoneer omutes sore to tegorze the bdders behvor whh n turn n be used to redt the revenue. III. TERMINOLOGIES dder s fuzzy vluton of the utoned obet s [, ] defned by n ntervl number b. We ssume tht vlutons [, b ], =, 1, 2, n re not ommon knowledge,.e. one bdder knows only hs/her own bddng rnge. In norml stuton, buyer wll ertnly resond when the urrent bd re s lower thn whle the ossblty of hs resondng wll derese s the bd rses. One the re s hgher thnb, the uer bound of hs vluton, the bdder wll ese to rtte. In ths lght, we defne followng fuzzy sets. The ossble bd of buyer s defned s fuzzy set denoted by wth membersh funton: 3 21 IEEE 2nd Interntonl Advne Comutng Conferene

3 μ 1 ( = f ( f f f < > b b (1 f ( desrbes the nture of bdder s: f ( = 1 b r r < 1 r = 1 r > 1 re senstve re neutrl re robust (2 The re senstvty of eh bdder n be desrbed by f (. dder s re-robust f ( s onve.e. bdder hs rsk versve behvor nd wnts to send money f ( rudently, s re-neutrl f s lner.e. bdder s re neutrl, nd re-senstve f s onvex whh reresents rsk seekng behvor of the bdders.smlrly, f ( f denotes the ossble reservton re from seller. Its membersh funton s μ ( = f ( 1 f f f < > b < b (3 Non ddng Cblty of Comettors In ny knd of utons the resene of omettors moses some knd externlty on hnes of wnnng of bdder t beomes extremely vtl to ture ths effet n mult-obet uton where eh obet s dfferent from other n terms of vlue. Therefore the ossblty of wnnng of bdder s not deendent totlly on ts blty of bddng but lso on the non bddng blty of others. Ths s known to the utoneer only n the roosed frmework. A fuzzy set whh tures ths noton n be defned for ny bdder s n = k =1 k k where k (4 Effetve ddng Rnge In the oston utons dvertsers do not know ther vluton for the sef ostons eselly when the res they y s deendent on the lks generted by ny externl gents (serh engne users nd lmted or no nformton bout other dvertses mkes t even worse. To oe u wth ths knd of stuton we lulte rnge of bds where mnmum vlue mkes sure tht dvertser s n rtte n the uton even fter the yment of the reservton re mosed by the utoneer. mxmum vlue delres the t most blty of bdder to bd. Merhnt Sef Clks One dvertsement s been led on rtulr slot, t get C th gets lks (lks for dvertser on slot form serh engne users whh re not only deendent on the oston of the slot but lso on the severl ftors lke qulty of the relevne wth the keyword tyed n the serh engne, lndng ge s qulty,brndng ftors relted to the dvertsers et. C Hene n be onsdered s rodut of oston sef lks nd merhnt sef lks s: C = q sef lks. Sore (5 q s merhnt sef lks nd s oston In order to tegorze bdders on three bove wrtten tegores bsed on ther ttern of bddng we used quntttve mesure Sore whh the sgned mxmum dstne of bd urrent submtted by the dvertser to the urve reresentng the membersh of the bddng blty of the bdder. Sore wll hve ostve sgn f urrent bd s bove the urve nd negtve sgn f the urrent bd s below the urve. IV. PROPOSED SCHEME In ths er we tred to use the re bddng nformton n the sonsored serh utons to hel bdder to know ther rough rnge of bds whh n feth them roer results nd wthout gong beyond ther mxmum lmt of wllngness to y. Ths rerton hse n be helful to utoneer too n wy 21 IEEE 2nd Interntonl Advne Comutng Conferene 31

4 they n mke brod estmtons bout the bddng tterns. In the followng work we mde followng ssumtons s.. dders don t hve revous nformton bout ther vluton for eh lks(ppc b. dders do not hve knowledge bout other bdder vlutons or bddng rnge.. Autoneer mkes merhnt sef vlble to very bdder. d. Every dvertser knows hs\her sef lks only. Let there be n number of bdders nd every bdder submts n ntl rnge nd get n Effetve rnge from the utoneer before tul bddng tkes le. Comutton of of the effetve bddng rnge s s follows: Ste1: dder submts ny rndom rnge. Ste2:. Autoneer hs re omuted fuzzy set of reservton res where eh vlue s membersh n be omuted from bove wrtten formul. b. sed on the Intl rnge submtted by the dvertsers, utoneer omutes the fuzzy set for eh bdders whh b reresents the utlty of bdder nd membersh for eh re n be omuted from the formuls gven n seton II. If no revous nformton s resent bout Assume tht bdder s re neutrl, Else Autoneer looks for the ltest bddng blty fuzzy set of the bdder.. Autoneer omutes fuzzy set for non-bddng bltes of other bdder for every usng formul d. Fuzzy set reresentng the Effetve Rnge E E = membersh funton of μ E = μ μ μ (6 n be desrbed s: = μ μ (1 μ E sed on the Set mnmum nd mxmum lmt of the ERnge(Effetve rnge s omuted s: (7 ERnge _ Mn Mn = Mx = Mn + ε (1 (8 ( IRnge _ Mn, Mn Mn IRnge_Mn s mnmum vlue of ntl rnge, s mnmum vlue n nd ε s reservton re onstnt redefned by utoneer bsed on the stutons. ERnge _ Mx = Mx ( Mx E So ERnge=(ERnge_Mn, ERnge_Mx, IRnge (9, _ Mx Ste3. dders submt ther bds bsed on Effetve Rnge Ste4.Comutton of Sore s the sgned mxmum dstne of the urrent bd submtted to the ltest ddng blty membersh funton of bdder. some of the mortnt hrtersts of Sore re.. Postve devton from the bddng lne shows re robust behvor b.negtve devton from the bddng lne shows re senstve behvor. for re neutrl behvor V. RESULTS Some of the reresenttve results of the sheme desrbed n seton IV re gven n Tble1 below., IRnge- Intl rnge submtted by bdders, ERnge- Fnl rnge lulted by bove gven sheme, - merhnt sef lks nd Sorequntttve mesure of bdder s behvor. For the omutton of ERnge nd Sore we hve {5,7} hosenbbb =, ε =. 5 nd r =.5, 1, 1.5(usng formuls(7,(8,(9. 1 As Shown n Tble1. IRnge of 1 s smller thn 2, t ndtes tht 1 s more nformtve thn 2 whh s refleted n the ERnge_Mn vlue for 1 s 5.8 nd tht of 2 s 5.9 b. For bdders 3,,4,5nd 6 ERnge s the sme s IRnge beuse they lredy stsfy the rter of reservton re.. In the lst olumn for Sore, the Zero vlue for 9 nd 11 sgnfes rsk neutrl behvor,the ostve vlue for bdder 12 shows the rsk seekng or re robust behvor nd the rest of the bdders hve negtve Sore vlue whh shows tht they re rsk versve(re senstve bdders IEEE 2nd Interntonl Advne Comutng Conferene

5 dder No. TALE I. IRnge COMPUTATION OF ERANGE AND SCORE ERnge (Merhnt Sef lks d Sore VI. CONCLUSION Ths work s n effort to brdge the nformtonl g between bdders nd utoneers n the re bddng hse of the keyword utons where dvertsers re not well wre of ther vluton for dfferent ostonl slots. There re three mn ontrbutons of the roosed work: (t mkes bdders equed wth bd rnge whh exlns how muh he/she should bd to onform hs/her rtton wthout gong beyond hs/her blty to bd. (b t rovdes the utoneer wth nformton relted to the bddng ttern of dvertsers. ( s byrodut of effetve rnge omutton, t n mose bdder sef reservton res. The results s gven seton V lerly demonstrtes the vblty of the roosed sheme. Ths sheme n be nororted wth ny knd of stndrd keyword uton mehnsm e.g. GSP(Generlzed Seond Pre [11] nd truthful utons[3]et. One of the mortnt future reserh dreton would be to extended the urrent work by onsderng other sets of keyword utons suh s users referenes (e.g. referene for rtulr slot.furthermore, future work would nlude nlyss of the mt of the roosed sheme on llotve effeny under vrous rng shemes. REFERENCES [1] Ygl Engel nd Dvd Mxwell Chkerng Inorortng User Utlty Into Sonsored-Serh Autons (Short Per,, Pro. of 7 th Int. Conf. on Autonomous Agents nd Multgent Systems (AAMAS 28 [2] Shu-Cherng Fng, Henny W.L. Nuttle, Dngwe Wng, Fuzzy Formulton of Autons nd Otml Sequenng for Multle Autons, Fuzzy Sets nd Systems 142 ( [3] A. Goel G. Aggrwl nd R. Motwn. Truthful utons for rng serh keywords. In ACM Conferene on Eletron Commere, 26. [4] R. Gonen, S. Vsslvtsk, Sonsored Serh Autons Wth Reserve Pres: Gong eyond Serblty, LNCS Srnger erln Vol- 5385(28, [5] D. Lu nd J. Chen, Desgnng onlne utons wth st erformne nformton, Deson Suort Systems 42 ( [6] A. Meht, A. Sber, U. Vzrn, nd V. Vzrn. AdWords nd generlzed onlne mthng. In FOCS, 25. [7] P.R. Mlgrom, R.J. Weber, A theory of utons nd omettve bddng, Eonometr 5 (2 ( [8] R.. Myerson, Otml uton desgn, Mth. Oer. Res. 6 (1 ( [9] J.F. Nsh, Equlbrum onts n n-erson gme, Pro. Nt. Ad. S. 36 ( [1] J.F. Nsh, Non-ooertve gmes, Ann. Mth. 54 ( [11] M. Ostrovsky. Edelmn nd M. Shwrz. Internet dvertsng nd the generlzed seond re uton:sellng bllons of dollrs worth of keywords. In Seond worksho on sonsored serh utons, 26. [12] T. Sndholm, Arohes to wnner determnton n ombntorl utons, Deson Suort Systems 28 ( [13] Vrn, H. R. (27. Poston Autons. Interntonl Journl of Industrl Orgnzton, 25(6: [14] R. Wlson, Strteg nlyss of utons, n: R.J. Aumnn, S. Hrt (Eds., Hndbook of Gme Theory wth Eonom Alton, Elsever Sene, New York, 1992, IEEE 2nd Interntonl Advne Comutng Conferene 33