Impact of ROI on Bidding and Revenue in Sponsored Search Advertisement Auctions

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1 Impact of ROI on Bddng and Revenue n Sponsored Search Advertsement Auctons Boleslaw K. Szymansk and Juong-Sk Lee Optmaret Inc., Newtonvlle, NY, 228 Rensselaer Polytechnc Insttute, Computer Scence Department, Troy, NY 280 ABSTRACT In ths paper, we dscuss how advertsers, by consderng mnmum return on nvestment (ROI), change ther bddng and, consequently the auctoneer s revenue n sponsored search advertsement auctons. We analyze the Vckrey- Clarke-Groves (VCG), Generalzed Second Prce (GSP) and Generalzed Frst Prce (GFP) aucton mechansms n that respect. Analytcal results are presented for the domnant strategy bddng prces n the Vckrey-Clarke- Groves aucton and the ex-post equlbrum locally-envy free prces n the Generalzed Second Prce aucton. The smulaton results are presented for all three mechansms: VCG, GSP, and GFP auctons. We conclude that the mpact of consderng ROI durng bddng vares among dfferent aucton mechansms, changng the tradtonal assessment of ther merts for sponsored search advertsement. reach $4.9 bllon n the U.S. market alone n 2009 []. An mportant reason for so fast and wde-spread adopton of the sponsored search advertsement s ts hgh return on nvestment (ROI) for advertsers, compared to other marketng methods []. The search engne customers already pre-select themselves by ntatng a search for keywords relevant to the advertsement and then show further nterest n the advertsed products by clckng on the lnk to the specfc advertsement. Hence, as shown n Fgure, the average cost per leadng purchase s lower n sponsored search advertsement than n other marketng channels. Keywords Sponsored search advertsement aucton, return on nvestment, aucton mechansm, locally-envy free prce, ncentve compatble aucton. Fgure : Comparson of average cost per lead to purchase. INTRODUCTION Next to e-bay, sponsored search advertsement auctons are one of the most common and wdespread examples of an electronc aucton system n use today wth enormous economc mpact on advertsng and computer ndustres. The revenues from the sponsored search advertsement auctons have been ncreasng contnuously and have already exceeded bllons of dollars annually. They are projected to As n other aucton applcatons, the revenue of the sponsored search advertsement depends heavly on the value that t delvers to advertsers. That value dctates the advertsers wllngness to pay. In addton, the advertsers bd behavor s nfluenced by the desgn of the aucton mechansm tself. As a result, understandng the advertser s bd behavor and ablty to model t correctly are of utmost mportance n analyss of exstng and n desgn of novel aucton mechansms targetng sponsored search Ths work was partally supported by the Natonal Scence Foundaton through award NGS The content of ths paper does not necessarly reflect the poston or polcy of the U.S. Government no offcal endorsement should be nferred or mpled.

2 advertsement. In ths paper, we analyze the most representatve bd strateges n auctons for sponsored search advertsements modeled after the soluton used by Yahoo! []. The remnder of ths paper s organzed as follows. In Secton 2, we analyze the propertes of the sponsored search advertsement auctons and defne basc notons of such auctons. In Secton 3 we analyze the Vckrey-Clarke- Groves aucton and compare t to the Generalzed Second Prce aucton analytcally, assumng that bdders acheve expost equlbrum of the locally-envy free bd prces. In Secton 4, we analyze and create models of the bdder strateges that we then smulate under dfferent aucton mechansms. We dscuss the smulaton results n Secton 5. Fnally, n Secton 6, we provde conclusons and outlne the future work n ths area. 2. ANALYSIS OF SPONSORED SEARCH ADVERTISEMENT MARKET The dea of the sponsored search advertsement s smple. The search engne produces the search result pages wth postons for sponsored search advertsements assocated wth a partcular keyword used n the search query entered by a customer. These sponsored postons contan pad for advertsements wth embedded lnks pontng to the advertser s web pages. Advertsers pay the search engne for ther advertsng whenever the search engne customer clcks on the lnk embedded n a sponsored poston. Accordngly, ths form of advertsng s called Pay-Per- Clck (PPC) advertsement. From the aucton structure pont of vew, a search engne company s an auctoneer and advertsers are aucton partcpants who bd for the sponsored postons. Hence ths s one-to-many market structure. The resources traded n the sponsored search advertsement aucton are ranked advertsng postons n a web page produced n response to the user query. It s well known that dfferent postons yeld dfferent numbers of user clcks per tme perod, even when they dsplay the same advertsement [3, 4]. Hence, those postons are heterogeneous resources. They are also pershable, because f they are not used for a tme perod, they brng no value to the auctoneer ( are wasted ) for ths tme perod. Each search keyword or phrase entered by the user of the search engne trggers a new aucton round for all the postons avalable on the response web pages. Hence, sponsored search advertsement uses recurrent auctons for multple heterogeneous resources [5]. Partcpants can change ther bd prces at any tme, and these prces wll then apply to the very next aucton round. The partcpants can also specfy the maxmum daly budget for ther clcks, whch, when exceeded, would cause a removal of the correspondng bd from the subsequent aucton rounds. The recurrng nature of the sponsored search advertsement aucton s one of the most mportant features that dfferentate ths aucton mechansm from tradtonal ones. In our recent studes, we have dscussed problems that arse n recurrng auctons for pershable resources f tradtonal aucton mechansms are appled. We also proposed a novel aucton mechansm sutable for such envronments [6]. The unque sponsored search advertsement aucton propertes are reflected also n novel rules desgned for those auctons. For example, Google s AdWords system uses ClckThrough Rate (CTR) to rank bds for advertsng postons [7]. Another nnovaton s the prcng rule whch evolved from the Generalzed Frst Prce aucton to the Generalzed Second Prce aucton, both dfferent from the Vckrey-Clarke-Groves aucton, tself generalzaton of the Vckrey aucton [8]. In ths paper we focus on yet another unque property of the sponsored search advertsement auctons, namely the mportance of return of nvestment (ROI) to the advertsers. The advertsng over the search pages s naturally spread over tme durng whch the advertser needs to mantan a budget for payng for the clcks receved to the advertser s lnk. Usually, there are many potental search keywords and phrases wth whch the advertser may choose to assocate ts lnks. Lkewse, there are also alternatve outlets for advertsement campagns competng wth sponsored search advertsement for advertsng money. Hence, the advertsers are not only nterested n maxmzng ther utlty from the aucton but also n mantanng ther mnmum return on nvestment (ROI) for each clck receved. As a result, the classcal aucton theory that assumes that bdders maxmze ther utlty from the aucton no longer apples. Consequently, we analyze here how consderng the mnmum return on nvestment changes the bddng behavor and auctoneer s revenue n dfferent aucton mechansms. To llustrate the man dea, consder for example a bdder enterng an aucton n whch there are only two postons yeldng clcks, p, and p 2. Assume that the frst poston s expected to yeld a =00 clcks n a tme unt whle the second poston yelds only a 2 =50 clcks. Two bdders, bdder one and bdder two, bd b =$5.00 and b 2 =$4.00, 2

3 respectvely. The thrd bdder has prvate true valuaton of each clck t 3 =$5.06 and sets ts mnmum requred ROI at f=0%. In VCG aucton, accordng to the classcal aucton theory, the optmal bddng strategy for the thrd bdder s to bd ts prvate true valuaton, that s to enter the bd b 3 =$5.06. As a result, the thrd bdder wll receve the frst poston and wll pay $5.00 for each of the frst 50 clcks and $4.00 for each of the remanng 50 clcks of 00 clcks receved. Ths bd ndeed wll maxmze the thrd bdder utlty at 50*$ *$.06 = $56. But what about ROI? The $250 nvested n the hghly prced 50 clcks brngs only $3 proft, a return of merely.2%. The bdder then cannot bd more than the prce that when pad would yeld at least the requred mnmum ROI on each clck, that s the prce equal to bdder s prvate true valuaton dvded by the sum of and that mnmum requred ROI. In our case, ths would be b 3 =$5.06/.=$4.60. Wth such a bd, the thrd bdder would wn the second poston and 50 clcks for whch she would pay $200 and reap $53 proft. The saved $250 (that otherwse would be spent on hghly prced clcks wth the hgher bd) can then be used to bd for example for another keyword or for the same keyword n another search engne aucton. The queston that we answer n ths paper s how does the bd lmt mposed by the mnmum requred ROI mpact bdders behavor and aucton revenues. We wll consder ths queston n the context of the followng three aucton mechansms that mplement dfferent prcng rules n a sponsored search advertsement aucton.. Generalzed Frst Prce (GFP) Aucton. In GFP, a bdder who receves an advertsng poston pays for each clck the prce that he bd n the aucton. 2. Generalzed Second Prce (GSP) Aucton. The GSP aucton charges a wnner the smaller of hs bd prce and the bd prce of the next hghest bdder plus the mnmum bd prce ncrement (n case of Yahoo! t s $0.0, but to smplfy reasonng, we wll gnore ths ncrement n analytcal soluton and consder t only n smulatons). For example, the bdder wth the unque hghest bd pays the bd prce of the second hghest bd plus the ncrement. 3. Vckrey-Clarke-Groves (VCG) Aucton, also known as Generalzed Vckrey Aucton. In VCG, each wnner of the aucton pays for clcks the externaltes that the wnner mposes on other bdders [9]. Hence, n a sponsored search advertsement aucton, VCG wll charge the wnner the sum of dsplacement costs computed for each bdder dsplaced by the wnner presence. The dsplacement cost of a bdder at poston j wth bddng prce b j s equal to the bd prce b j multpled the dfference between the number of clcks expected to be receved at poston j- and the actual number of clcks receved at the current poston j. Addtonally, we assume that the bdders have full knowledge of the other bdders (ths s true for Yahoo!/Overture sponsored search advertsement auctons because Yahoo! provdes a tool for obtanng the bd prces of current bdders and ther correspondng ranks for the gven keyword aucton). Regardless of avalablty of such a tool, wthout loss of generalty, we can assume that a bdder can learn bd prces of other bdders because the aucton s performed recurrently. 3. ANALYTICAL ANALYSIS OF ADVERTISERS BIDDING BEHAVIOR In ths secton, we present an analytcal analyss of the mpact of ROI consderaton on bdders behavor and auctoneer revenue n sponsored search advertsement auctons under VCG and GSP mechansms. Consder a VCG aucton wth n wnnng postons and m>n bdders. Let a, where =, 2,, n denote the number of clcks expected to be receved n a tme unt at poston and c j =a j+ /a j for j=, 2,, n-. We assume that a n+ =0 (so c n- +=0) for all =, 2,, m-n and 0< c j < for all j=, 2,, n-. Snce the VCG aucton s ncentve compatble, then for each bdder j=, 2,, m we have b j =t j where t j denotes prvate true valuaton of a clck by bdder j and b j denotes bdder j bd. Hence, accordng to the prcng rules of VCG aucton, the auctoneer revenue R VCG s R vcg = n n n a p a p+ ) t p+ = a ( c ) t+ = p= = (. () Consder now VCG aucton n whch bdders not only seek to maxmze ther utlty but also want to assure that every clck receved provdes them wth the mnmum return on nvestment, ROI, denoted as the fracton f of the prce pad. Ratonale for ths strategy s smple. If the purchase of a clck does not brng enough proft, the budget for 3

4 advertsement to buy ths clck can be redrected to other keywords or even to dfferent advertsement channels n whch such a ROI could be guaranteed. In VCG aucton, the prce for a clck depends on the poston of the dsplaced bdder. The hghest prced clcks are those that come from the hghest dsplaced bdder (the bdder ranked mmedately behnd the bdder whose prce s beng establshed). Hence, the bdder must be prepared to pay the prce bd for the hghest prced clcks, those at hs poston. Consequently the prce bd s lmted by ROI as t follows: ( t b ) / b f so b. Denotng + f d =, we get + f b =dt. Indeed, ncreasng the bddng prce (up to the prvate true valuaton) ncreases the bdder s utlty, so the domnant strategy for each bdder s to bd the hghest prce satsfyng the ROI lmtaton, that s b =dt. Hence, the VCG aucton wth ROI, denoted here VCG- ROI, wll yeld the revenue by factor d lower than the orgnal VCG aucton: R = dr vcg ro vcg. Let s consder now GSP aucton nstead and assume that each of n hghest bddng bdders bds ts locally-envy free prce [9] that for bdder s the maxmum prce satsfyng an nequalty: ( b ) a ( t b+ t ) a. (2) Inequalty (2) can be rewrtten as b ( c ) t + c b. For + =n we know that c n =0, hence b n+ =t n+. By recurson we get that the locally-envy free prce b for bdder s: Hence, b * * * n = j j+ k j= k= b t ( t t ) j c. < t for all 0<<n+ and such that t >t +. It s easy to show that R vcg =R gsp. Indeed, rewrtng formula (2) as an equaton for the locally-envy free prce, we get, for all > t ( a a ) = a b ab from whch t follows + that t (3) ( a a ) = a b ab + Addng Equaltes (3) together, the left hand sde wll reduce, accordng to equaton (), to R vcg whereas the rght n hand sde wll reduce to a b = R. gsp = 2 It s easy to show that n case of GSP-ROI, the envy free ' * prce s b = mn( dt, b ), snce n addton to beng bounded by the maxmum utlty, t s also bounded by the requred mnmum ROI. It mmedately follows that b ' * * < d b for all 0<<n and such that t >t +, therefore R gsp ro drgsp = drvgc = > R. (4) vgc ro Fnal concluson s that the GSP-ROI aucton brngs hgher revenue than the VCG-ROI aucton does as long as not all bdders have the same prvate true valuaton of clcks and they bd ther locally-envy free prces. 4. MODELING AND SIMULATION OF DYNAMIC BIDDER STRATEGIES In ths secton, we expand the analyzed bddng behavor to model and smulate the dynamc bdder strateges under dfferent sponsored search advertsement aucton mechansms. We start wth the descrpton of the smulated scenaros. There are 20 bdders (.e., advertsers) and one auctoneer (.e., the search engne company). All bdders bd for the same search keyword. We assume that the bdders are rsk neutral and symmetrc [5]. There are 0 postons avalable for sponsored search advertsements that are traded n the smulated aucton. Hence, only 0 bdders wll receve a poston for advertsement n each aucton round. The upper bound of each bdder s bd prce s restrcted by hs prvate true valuaton of each clck receved. In addton to consderng the prvate true valuaton, the bdders also take nto account return on nvestment (ROI) when decdng ther bds. In all smulatons, the prvate true valuatons of bdders are ndependently dstrbuted. We smulate three types of the standard dstrbutons of prvate true valuatons: () the exponental dstrbuton wth the mean of $3.00, () the unform dstrbuton over the range of [$0.00, $6.00], and () the Gaussan dstrbuton wth the mean $3.00 and standard devaton of. For the sake of smplcty, we assume that prvate true valuatons do not change durng the smulated auctons. Our smulatons model an aucton mechansm used n Yahoo!/Overture soluton. Hence, the ClckThrough Rate (CTR) or factors other than the bd prce are not consdered 4

5 n rankng of bdders n the aucton 2. Hence, a rank of a bdder s defned entrely by hs bd prce. The bdders wth the hgher bds occupy hgher ranked advertsng postons. As shown n Table, frequency of recevng clcks at any poston s dependent on the poston rank. To smulate ths phenomenon correctly, we use relatve frequency of expected number of clcks receved for each rank of the advertsng postons. The frequences that we selected for each poston were computed on the bass of Yahoo!/Overture sponsored search advertsement results provded n the Atlas reports [4, 0]. We assume that the expected numbers of clcks are only dependent on the rank of the advertsng poston. Any other factors, such as dentty of advertser or relevance and attractveness of the presented advertsement are assumed to be the same for each bdder. Poston Rank Frequency of Number of Clck Poston Rank Frequency of Number of Clck 00.0 % % % % % % % % % % Source: Atlas Insttuton 2004 Table : Expected number of clcks at each poston of the sponsored search advertsement To mplement recurrng feature of auctons for sponsored search advertsement, the smulated aucton conssts of a seres of aucton rounds executed sequentally. In each aucton round, bdders select optmal bd prces for the next aucton round accordng to ther bd strategy. Snce n ths paper we assume that the bdders are rsk neutral, decdng the bd prce, each bdder attempts to maxmze the utlty (.e., payoff) U ( b r ) of aucton round partcpaton: r r U( b) = ( t p( b)) a r, (5) r ( b ) where p( b r ) represents the payment for each clck whch s decded by the prcng rules of the consdered aucton 2 We conjecture that CTR would not change the conclusons of ths paper and we are workng on a proof of t. mechansms and r ( b r ) denotes the rank of the advertsng poston that the bdder wll occupy wth bd vector r b = ( b,... b m ). Hence, a r r ( b ) represents the expected number of clcks receved at the advertng poston r ( b r ). To maxmze the expected utlty U ( b r ), each bdder consders r the trade-off between the proft factor ( t p( b)) and the expected number of clcks a r. If the bdder ncreases hs r ( b ) bd prce, the expected number of clck may ncrease by movng the bdder to the hgher ranked poston n the correspondng search web page. However, the resultng proft factor decreases. Reversely, f the bdder decreases hs bd prce, the proft factor ncreases at the expense of the number of expected clcks. Addtonally, bdders also consder the mnmum requred ROI n selectng ther bd prces. Based on utlty functon expressed by Equaton (5), we consder the followng three potental bd strateges for decdng optmal bd prce of each bdder durng recurrng aucton: Dynamcally Adjustng Bd strategy, Locally-Envy Free Bd strategy and Truthful Bd strategy. Dynamcally Adjustng Bd Strategy (DAB): Snce each bdder knows the bd prces entered by the other bdders n the prevous aucton round, the most obvous bddng strategy s to adjust the bd prce contnuously based on the known bd prces of other bdders n an attempt to maxmze the expected utlty. Executng ths strategy, after each aucton round every bdder probes bd prces that can maxmze hs utlty (accordng to Equaton (5)) usng as the bass the bd prces of the other bdders n the last aucton round. Each bdder selects the seres of probng bds, each slghtly hgher than the exstng bd by some other bdder but not hgher than hs prvate true valuaton adjusted, as dscussed above, by the mnmum requred ROI factor. Then, for each probng bd n the seres, the bdder computes expected utlty n the next aucton round to select the one wth the hghest utlty. If two probng bd prces produce equal utlty, then the probng bdder selects the lower of the two as hs next round bddng prce. Locally-Envy Free Bd Strategy (LEF): Based on defnton of LEF (Locally-Envy Free) equlbrum proposed by Edelman at el [9], the optmal bd prce of each bdder that leads to the LEF equlbrum and maxmzes each bdder s expected utlty s computed accordng to Inequalty (2). Then, the bd s set to smaller of ths optmal bd prce and the prvate true valuaton adjusted by the mnmum requred ROI. However, as reported n [7], ths 5

6 optmal bd prce s an ex-post equlbrum prce, so the advertsers do not follow ths strategy n practce. Truthful Bd Strategy (TB): Another bddng strategy s for each bdder to bd the prvate true valuaton adjusted by the mnmum requred ROI consderaton. TB strategy s the smplest bd strategy but t s only benefcal to advertser n ncentve compatble aucton mechansms, n whch bddng prvate true valuaton s a domnant strategy. aucton rounds. In our smulatons, we also observe that even f the aucton mechansm changes from GFP to GSP (.e., the prcng rule changes from the frst prce to the second prce), there stll exst unstable bd patterns when the dynamcally adjustng bd strategy s used. Such unstable bddng creates correspondng unstable revenue patterns n the GFP and GSP auctons wth the dynamcally adjustng bd strategy Regardless of the bddng strategy smulated, we assumed that the bdders who were not allocated advertsng postons n the current aucton round bd ther prvate true valuatons (adjusted by the mnmum requred ROI consderaton) attemptng to occupy an advertsng poston. We assume that such bdders never drop out of the sponsored search advertsement and partcpate n all aucton rounds. Fgure 2: Bd pattern n dynamcally adjustng bd strategy For GFP aucton, we used only the dynamcally adjustng bd strategy, as others were napproprate for ths aucton mechansm. Lkewse, for VCG aucton only truthful bd strategy was used because VCG s ncentve compatble. In GSP aucton both dynamcally adjustng bd strategy and locally-envy free bd strategy were appled. The latter s denoted as GSP-LEF. In all smulated bd strateges, each bdder consders hs mnmum requred ROI (Return On Investment) whle selectng the bddng prce. 5. ANALYSIS OF SIMULATION RESULTS For each smulated aucton mechansm, our experments focus on bddng strateges from the bdder (.e., advertsers) pont of vew and revenue from the auctoneer (.e., the search engne company) pont of vew. In revenue analyss, we focus on the mpact of ROI on revenue n dfferent aucton mechansms and under dfferent bdder strateges. As shown n Fgure 2, adjustng bd prce contnuously based on bd prces of other bdders durng recurrng aucton causes unstable bd pattern n the GFP aucton. Ths s the result of contnuously montorng and adjustng bd prces n an attempt to mnmze the payment for mantanng the desred rank of an advertsng poston, and thereby maxmzng expected utlty. By analyzng data collected by Yahoo!/Overture [3], Edelman and Ostrovsky verfed that such unstable bd patterns ndeed appeared n the GFP aucton for sponsored search advertsement. They called those patterns sawtooth because the bd prces frst gradually ncrease and then suddenly drop n a sequence of From the revenue pont of vew, our smulaton results demonstrate that, as shown n Fgure 3, wthout consderng ROI (.e., when the mnmum requred return on nvestment s 0%), the revenues of GFP and GSP auctons are lower than the revenues of GSP-LEF and VCG auctons. Ths s caused by the unstable bddng patterns that drectly mpact the revenue. The revenues of GFP and GSP auctons are almost the same for all prvate true valuaton dstrbutons. Addtonally, our smulaton results show that the revenues of GSP-LEF and VCG aucton are the same and hgher than the revenues of GFP and GSP aucton. Fgure 3: Comparson of revenue of auctons wth ROI=0% However, as shown n Fgure 4, once the mnmum requred ROI s non-zero, the revenues of GSP-LEF and VCG aucton mechansms dverge. As the mnmum requred ROI 6

7 ncreases, the revenue of GSP-LEF aucton becomes hgher than that of VCG aucton for all prvate true valuaton dstrbutons. Fgure 4: Comparson of revenue of auctons wth ROI=20% Increasng the mnmum requred ROI for all bdders decreases the resultng revenue n all aucton mechansms wth all bdder strateges but n each case to a dfferent degree. Ths s because ncreasng the mnmum requred ROI decreases the upper bound on bd prce of every bdder. The tghter lmtaton on the maxmum bd prce results n decreased revenue n each aucton mechansm. The most affected are of course ncentve compatble aucton mechansms n whch every bd prce decreases n such stuaton. These conclusons are confrmed by the smulaton results presented n Fgure 5. Fgure 5: Comparson of revenue wth varous ROI s for dfferent aucton mechansms Fgure 6 shows the percentage of lost revenues as a functon of the change of the mnmum requred ROI for the unform dstrbuton of bdders prvate true valuatons. We also smulated the Gaussan and exponental dstrbutons but snce the results were dentcal, we dd not nclude here the addtonal plots. Compared to other aucton mechansms, the GSP-LEF mechansm acheves the lowest percentage loss of revenue n response to the changes n the mnmum ROI requrement. Ths means that the GSP aucton wth the LEF bd strategy provdes the most stable soluton from the auctoneer pont of vew. On the other hand, n VCG aucton, any ncrease n the mnmum requred ROI results n the matchng percentage loss of the auctoneer s revenue. Hence, the VCG aucton mechansm s the most unstable n terms of ts senstvty to changes to the mnmum requred ROI. Fgure 6: Loss of revenue wth dfferent ROI s 7

8 In concluson, our smulatons verfed the analytcal result of comparng the VCG and GSP auctons expressed n Equaton (4): R gsp ro > drgsp = drvgc = R vgc ro In our current and future work, we have been workng on developng new aucton mechansms capable of stablzng bd patterns and ncreasng the revenue of the search engne auctoneer as well as on extendng the smulatons of bddng behavor to such novel aucton mechansms. 6. CONCLUSIONS AND FUTURE WORKS The followng are the conclusons of our study. Includng the mnmum return on nvestment requrement n bddng for sponsored search advertsement aucton lmts bdder s maxmum bddng prce from the advertser pont of vew and decreases the resultng revenue from the search engne company pont of vew. The Generalzed Second Prce aucton wth the locally-envy free bddng strategy produces the hghest revenue among all mechansms studed n ths paper. It s also the most stable mechansms n terms of revenue senstvty to changes n the mnmum return on nvestment requred by the advertsers. Even though the classcal Vckrey-Clarke-Groves aucton mechansm makes the domnant bddng strategy smple, because of ts ncentve compatblty, t suffers the largest loss of revenue resultng from the changes to the mnmum return on nvestment requrement among all the aucton mechansms consdered here. Hence, t s the most unstable mechansm n that respect. As a result the revenue of Vckrey-Clarke-Groves aucton s lower than the correspondng revenue of the Generalzed Second Prce aucton wth locally-envy free bddng strategy for all nonzero values of the mnmum requred return on nvestment. For the larger values of ths factor, even the Generalzed Second Prce and the Generalzed Frst Prce auctons wth the dynamcally adjustng bd strategy can delver hgher revenue than the Vckrey-Clarke-Groves aucton. Our smulatons confrm also that even after the change of aucton mechansm from the Generalzed Frst Prce aucton to the Generalzed Second Prce aucton, the unstable bd patterns have not entrely dsappeared. Ths s because the locally-envy free ex-post equlbrum prces cannot be reached by maxmzng the bdder s utlty n response to the bddng of other bdders. The dynamc bddng behavor n GSP and emergence of unstable bddng patterns have been also analyzed analytcally n [2]. Hence, there s room for mprovement n the basc aucton mechansm for sponsored search advertsement. REFERENCES [] M. Moran and B. Hunt, Advertsement Engne Marketng Inc.: Drvng Advertsement Traffc to Your Company s Web Ste, IBM Press, [2] M. Bchler, The Future of e-markets: Multdmensonal Market Mechansm, Cambrdge Unversty Press, 200. [3] B. Edelman and M. Ostrovsky, Strategc Bdder Behavor n Sponsored Advertsement Auctons, Proc. ACM Electronc Commerce Conference, EC05, Vancouver, CA, [4] N. Brooks, The Atlas rank report: How advertsement engne rank mpacts traffc, Techncal Report, Atlas Insttute, July [5] V. Krshna, Aucton Theory, Academc Press, [6] J. S. Lee and B. K. Szymansk, Novel Aucton Mechansm for Sellng Tme Senstve E-Servces, Proc. 7th Internatonal IEEE Conference on E- Commerce Technology (CEC'05), Munch, Germany, July 2004, pp [7] H. R. Varan, Poston Auctons, Techncal Report, poston.pdf [8] W. Vckrey, Counterspeculaton, Aucton, and Compettve Sealed Tenders, Journal of Fnance, Vol. 6, No., March 96, pp [9] B. Edelman, M. Ostrovsky, and M. Schwarz, Internet advertsng and the generalzed second prce aucton: sellng bllons of dollars worth of keywords, gsp05003.pdf. [0] N. Brooks, The Atlas rank report, part 2: How advertsement engne rank mpacts conversons, Techncal Report, Atlas Insttute, July [] J. Feng, H. K. Bhargava and D. M. Pennock, Implementng Sponsored Advertsement n Web Advertsement Engnes: Computatonal Evaluaton of Alternatve Mechansms, Journal of Computng, [2] K. Asdemr, Bddng Patterns n Search Engne Auctons, bddngwars.pdf. 8