To Sponsor or Not to Sponsor: Sponsored Search Auctions with Organic Links and Firm Dependent Click-Through Rates

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1 To Sponsor or No o Sponsor: Sponsored Search Aucions wih Organic Links and Firm Dependen Click-Through Raes Michael Arnold, Eric Darmon and Thierry Penard June 5, 00 Draf: Preliminary and Incomplee Absrac In 009 sponsored search adverisemens generaed over $ billion in revenue for search engines in he US marke. Mos of hese adverisemens were sold using an aucion mechanism. Several exising papers analyze he aucion mechanism currenly used under he assumpion ha cusomers are only accessed hrough sponsored links. We exend his lieraure o incorporae wo imporan marke feaures. In paricular, we consider he impac of a second access channel, organic search lisings which appear beneah he sponsored links, and we allow for he possibiliy ha boh relevance of he adverising firm as well as is posiion in he sponsored link lisings impac he clickhrough-rae. Our resuls demonsrae ha he exisence of an ouside alernaive leads o less aggressive bidding behavior. The ouside alernaive also creaes an imporan role for he minimum cos-per-click esablished by he search engine in maximizing aucion revenue. In conras o equilibrium resuls in he exising lieraure, he firm wih he highes value per click does no necessarily win he firs spo in he sponsored search lisings. Moreover, under cerain condiions, firms adop a mixed sraegy wih regard o paricipaion in he keyword aucion, bu have a pure bidding sragey when hey do ener he aucion. Deparmen of Economics, Alfred Lerner College of Business and Economics, Universiy of Delaware, Newark, DE 976, CREM, Universiy of Rennes, France, CREM, Universiy of Rennes, France,

2 Inroducion Many firms now have a presence in boh radiional and elecronic markes. In elecronic markes firms ypically rely on consumers accessing he firm hrough a commercial websie where cusomers can find produc informaion, order producs, and pay direcly. Key issues for firms wih a websie include visibiliy o he online audience of poenial cusomers and he abiliy o conver online invesmens ino revenue. Firms can use several sraegies for his purpose. Search engine opimizaion SEO can increase he visibiliy of a websie by improving is posiion among organic links on popular search engines. This sraegy requires building a dense nework of links and rackbacks hrough, for example, acive paricipaion in social neworks or beer inernal organizaion of he websie e.g. cross linking, URL normalizaion. Ye, SEO has inheren limis because websie designers are dependen on search engines regarding boh he algorihm used o rank websies and he frequency of search engine SE updaes. As a consequence, he final posiion of a websie in he organic links generaed by he SE could appear somewha random, and he effecs of any SEO sraegy should be evaluaed in he medium run only. Websies also may use online adverising as an acive sraegy o improve heir visibiliy. Since he end of he 990s, he online adverising marke has rapidly developed boh in erms of echnological possibiliies e.g. racking opporuniies and business models pay-per-click, pay-per-prin, pay-per-sale. The mos prominen segmen of he online adverising marke is sponsored search. Sponsored search enables firms o display sponsored ads alongside organic resuls produced by he SE. In 009 sponsored search adverisemens generaed over $ billion in revenue for search engines in he US marke and 6.7 billion in he European marke Source IAB. Mos of hese adverisemens were sold hrough keyword aucions. The keyword segmen is he larges segmen of he sponsored search marke in erms of revenues more han 45% and is he segmen wih he highes growh rae +0% compared o 008. One imporan facor explaining he success of sponsored search is he fac ha i provides a balanced compromise beween several concerns. Firs, sponsored links are displayed ogeher wih organic links. From a user s perspecive, hey appear o be See Evans007 for a complee survey on online adverising. See Taylor009 for an economic raionale of he curren paymen schemes in he online adverising indusry.

3 less inrusive han oher ypes of ads e.g. pop-up windows or adverising. From he adveriser s perspecive, hey provide he abiliy o beer arge differen cusomers based on heir search query. This resuls in more qualified raffi c viewing he sponsored ads. Finally, sponsored search is largely based on a pay-per-click principle which is less cosly for adverisers because hey only incur a charge if he sponsored ad is suffi cienly ineresing o induce a consumer o click on he adverised link. A growing body of economics and markeing lieraure is focused on keyword adverising and he response of firms and consumers o his adverising channel. A firs srand of his lieraure addresses keyword adverising from he poin of view of search engines SE. Based on aucions models, he seminal papers of Varian 007 and of Edelman e al. 007 examine he specificiy of keyword aucions as compared o radiional aucions and look for an opimal aucion design o maximize SE revenue. Several subsequen sudies have exended his analysis by considering more specific issues in he design of online aucions. Mos of hese exensions analyze keyword bidding sraegies under he assumpion ha cusomers are only accessed hrough sponsored links. Our paper conribues o his lieraure by incorporaing several specific aribues of keyword aucion markes. We consider he impac of a second access channel, organic search lisings which appear beneah he sponsored links. We allow for he possibiliy ha boh he relevance of he adverising firm as well as is posiion in he sponsored and organic link lisings impac he click-hrough-rae for each lising. Finally, we allow for he possibiliy ha a cusomer may click on more han one of he links presened in he search lisings. Our model enables us o examine how organic and sponsored links impac he keyword adverising sraegies of individual firms and he reservaion bids esablished by he search engines when websies differ according o heir populariy or relevance he probabiliy ha a searching cusomer will click on a given firms sponsored or organic link. We demonsrae ha sponsored links induce wo opposie effecs; a crowding ou effec sponsored links reduce raffi c o organic links and a marke expansion effec he use of sponsored links increases he overall click-hrough rae relaive o a marke wih no sponsored links. When he crowding ou effec for a paricular firm is large, hen ha firm has lile incenive o paricipae in he keyword aucion because creaing a sponsored link subsanially reduces he firms abiliy o arac cusomers hrough is organic link. As a resul, he exisence

4 of organic links leads o less aggressive bidding, and, in conras o equilibrium resuls in much of he exising lieraure, he firm which is mos relevan or has he highes value per click does no necessarily win he firs spo in he sponsored search lisings. The inerplay beween crowding ou and marke expansion effecs also creaes an imporan role for he reservaion price minimum cos-per-click esablished by he search engine ha has no been considered in previous lieraure. In paricular, he SE can minimize he effec of less compeiive bidding by increasing he minimum cos per click. Under cerain condiions, he SE esablishes a reservaion price causes a less popular firm o use a sponsored link o increase is raffi c while a more popular firm submis a relaively low bid or chooses no o paricipae o he keyword aucion a all. In such equilibria he more popular firm relies on organic links o arac cusomers. We also demonsrae ha for some parameerizaions of our model, firms may no paricipae sysemaically in he keyword aucion bu play mixed sraegies insead. In conras o previous papers, he mixed sraegies apply no o he bids submied by each websie bu o he decision regarding wheher or no o paricipae in he keyword aucion. Our approach is mos similar o Work by Xu e. al. 009 and Kaona and Sarvary 009 who also consider he role of organic lising in he sponsored search marke. One key disincion is ha in our model he firm s decision o paricipae in he keyword aucion is endogenous and depends upon he minimum cos per click cpc esablished by he SE. In boh Xu e. al. and Kaona and Sarvary he SE has a fixed number of sponsored lisings o sell, and hese lisings are allocaed o he highes bidders. The minimum cpc is se o zero so here is no reason for firms o refrain from paricipaion in he keyword aucion. Xu e al. 009 invesigae a framework in which wo firms compee a wo levels, boh he keyword adverising marke and he producs marke. 3 are endowed wih differen marginal producion coss. 4 Firms sell a homogeneous produc bu There are wo ypes of consumers; shoppers ha sample all firms, and non-shoppers ha only sample he firm lised firs in he search resuls. They find ha he disadvanaged firm higher producion cos always has an incenive o be ranked firs while he firm wih he lower producion cos has an incenive o bid aggressively only when he advanage from being ranked firs significan. The effec 3 Goldfarb and Tucker 007 provide an empirical sudy of his wo-level compeiion. 4 See also Ahey and Ellison 008 where he differeniaion beween firms is linked o produc characerisics. 3

5 of keyword adverising on he price of he produc is ambiguous. Kaona and Sarvary 009 consider a firs-price aucion and show ha a less popular sie can be ranked before a more popular firm in he lis of sponsored links. They also exend hese resuls by considering a dynamic seing o accoun for cusomer loyaly over ime. 5 A relaed srand of he lieraure emphasizes he role of sponsored links in reducing consumer search coss see Chen e al., 009. Taylor 009 presens a heoreical model in which consumers may choose beween organic and sponsored links. Wih wo compeing search engines, he shows how he qualiy of organic resuls may cannibalize he revenues of he search engine. Ye, in his paper, he behavior of websies in he aucion process is no explicily considered. Whie 009 focuses on he inerplay beween organic and sponsored resuls when sponsored links are sold a a fixed price and he SE can deermine he qualiy of he ads i acceps. Higher qualiy ads reduce consumer search coss bu may lead o increased compeiion in he final produc marke which ulimaely reduces SE profi. The las srand in his lieraure analyses sponsored search empirically o beer undersand user response o keyword search resuls and SE sraegies. Ghose and Yang 009 examine how keywords impac consumer behavior and find ha reailer-specific and brandspecific informaion in paid ads increases he effi ciency of online adverising; he former increases he click-hrough-rae he number of clicks over he number of imes he ad is displayed and he laer increases he conversion raes ino sales. Agarwal e al. 006 find ha while he click-hrough-rae decreases wih posiion, he conversion rae firs increases and hen decreases wih posiion for longer keywords. They conclude ha he op posiions in sponsored search adverisemens are no necessarily he revenue or profi maximizing posiions for adverisers. Complemenary o hese sudies, Ruz and Bucklin forh. invesigae he ineracions beween several ypes of keywords generic versus branded keywords, and find ha generic keywords may induce posiive spillovers on he effi ciency measured by click-hrough rae of branded keywords. Similarly, Jeziorski and Segal 009 show he prevalence of exernaliies across ads meaning ha he click-hrough-rae on a given ad in a given posiion depends on which ads are shown in oher posiions. Secion presens he model. Secion 3 analyzes equilibrium bidding sraegies. Secion 5 Chen e al. forh. also consider a dynamic aucion process in which adverisers and search engines may change heir sraegy according o he performance observed in previous sages. See also Agarwal e al

6 4 discusses he resuls and concludes. The Model. Consumers behavior on he search engine We consider a duopoly marke wih search adverising in which firs firm, Firm has a higher probabiliy of being relevan o consumers han he second firm, Firm. In paricular, a randomly chosen consumer who conducs a search on a given keyword which produces only organic links will find he search resul lising of firm relevan wih probabiliy β, and he lising of firm relevan wih probabiliy β where β > β 0. Because Firm is more relevan, in he absence of any search adverising, he resuls of he search engine algorihm will always lis Firm firs and Firm second. To allow for he possibiliy ha sponsored search may expand he marke, we assume ha if sponsored links are presen, hen he probabiliy a consumer will find Firm i s sponsored link relevan is δ i β i. To accoun for he fac ha some consumers may no be willing o look hrough all sponsored links, we assume ha a fracion γ of consumers will consider all of he sponsored links, bu a fracion γ will only consider he firs sponsored link and will hen move on o he organic links if he firs sponsored link is no relevan These cusomers only consider he organic link of he firm lised second in he sponsored links i.e., hey do no consider he organic link of he firm whose sponsored link hey previously rejeced. If his organic link is relevan, hey click on i. Finally, o allow for he possibiliy ha some consumers are averse o uilizing sponsored links, we define α as he probabiliy ha a consumer firs considers he sponsored links if any sponsored links appear, and α as he probabiliy a consumer bypasses he sponsored links and goes direcly o he organic links. Given he above search behavior, he sponsored link-averse consumer will click on he firs relevan organic link she encouners. We are now able o deermine he click-hrough-rae for each firm as a funcion of he adverising sraegies adoped by each firm. Each firm has he opion o pay a fee o he search engine SE in order o have a sponsored link appear a he op of he search resuls. If only one of he wo firms sponsors a link, hen a link o ha firm will appear as he firs lising on he search resuls page. This sponsored link is followed by he organic resuls which always lis Firm firs and Firm 5

7 second. If boh firms choose o adverise a sponsored link, hen he SE mus deermine a rule deermining which of he wo firms is lised firs in he sponsored links area of he search resuls. The sraegy of he search engine is modeled in secion 3.. Click-hrough-raes Consider he expeced click hrough raes when neiher firm sponsors a link. The probabiliy ha a consumer clicks on Firm s link is β. We assume a consumer who clicks on Firm s link also considers clicking on he link o Firm wih probabiliy /, where. If =, i means ha a consumer only clicks on one link a mos ; afer visiing Firm or Firm s websie, she will never visi furher links on he resul page. So he probabiliy ha a consumer clicks on he link o Firm is β + β / β = β / β. The probabiliy calculaions are somewha more complex if one of he wo firms chooses o adverise. For example, if Firm sponsors a link and Firm does no, hen Firm s sponsored link appears a he op of he search resuls followed by he organic links o Firm and hen Firm. The probabiliy ha a consumer clicks on Firm s sponsored link is α, on Firm s organic link is α β / β, and on Firm s organic link is α / β + α β = α / β. The differences in click-hrough raes when neiher firm sponsors a link versus when Firm sponsors a link highligh boh a marke expansion effec and a crowding ou effec ha resul from sponsoring a link. Wih no sponsored links, he oal capure rae of consumers is β +β β β /. When Firm sponsors a link, his increases o β + β β β / + α β β / which is a ne increase of α β β /. There is also a crowding-ou effec in which some consumers who would have clicked on organic links in he absence of adverising, swich o he sponsored link insead. Firm s organic click hrough rae decreases from β o α / β, and firm s organic click-hrough rae decreases from β / β o α β / β. The overall crowding-ou effec is α β + β β /. If boh firms sponsor a link, hen he click-hrough raes depend upon which firm is lised firs in he sponsored links. If Firm s sponsored link appears firs, hen he click hrough rae for firm is α + α β, and he click hrough rae for firm is αγ / + α β / β. Click-hrough raes under each possible adverising combinaion are presened in he following able. 6

8 Click Through Raes by Firm and Link Type Firms wih a Sponsored Link Firm/Link Neiher Only Firm Only Firm Organic β α β α / β Sponsored 0 α 0 β α Organic β / β α+ αβ Sponsored 0 0 α Boh, Firm Appears Firs Boh, Firm Appears Firs α δ / γ Organic α β β + α Sponsored α α / γ α γ Organic + α β β α β / β Sponsored α / γ α.3 Firms revenues β β Firms are ineresed in maximizing profi generaed by he search channel. We assume ha revenues are direcly correlaed wih click hrough raes. In paricular, we le v i denoe he expeced value o firm i from a cusomer ha clicks on a link o firm i. 6 In addiion, le p i denoe he cos per click paid by he firm i o he search engine if firm i is he only firm wih a sponsored link, and le p i,k denoe he cos per click paid by firm i when boh firms sponsor links and firm i is lised in posiion k. Firms only incur he cos-per-click if a cusomer reaches he firm hrough he sponsored link. To deermine firm profi, we mus disinguish beween cusomers who reach he firm via he sponsored link and he organic link. Le π s i denoe he profi of firm i when only one of he firms adverises a sponsored link and Firm adops a sraegy s and Firm adops a sraegy, and s, {N, A}, where A is a sraegy of adverising a sponsored link and N is a sraegy of no adverising. Finally, le π AAk i denoe he profi for firm i when boh firms have sponsored links and firm i s sponsored link appears in posiion k. Using he above able, he expeced cos of aracing a cusomer can be calculaed and subraced from he click hrough rae o deermine he expeced profi 6 If he probabliy ha a click on a link o firm i is convered o a sale is ρ i i.e., he conversion rae is ρ i, and he average value of a sale a firm i is s i, hen v i = ρ i s i. For simpliciy, we assume ha ρ i is he same wheher he cusomer was encounered hrough a sponsored link as an organic link. However, he model does allow for differences in he probabiliy a cusomer clicks on a sponsored versus an organic link. 7

9 under each possible sraegy profile. If neiher firm adverises, hen If only Firm adverises, hen π NN = β v π NN = β β v. π AN If only Firm adverises, hen = α v p + α β v π AN = α α β β v. π NA = α δ β v π NA = α v p + α β β v. If boh firms adverise, hen each firm s click-hrough rae depends upon he placemen of is sponsored lising. If firm is lised firs, hen π AA = α v p, + α β v π AA = α δ γ v p, + α γ + α β β v. If firm is lised firs when boh firms adverise, hen π AA = α δ γ v p, + α γ + α β v π AA = α v p, + α β β v. In he nex secion, we deermine equilibrium bidding sraegies of firms and. They have firs o decide wheher hey wan o paricipae o he bidding process and hen how much hey bid. 3 Generalized Second Price Aucion 3. Cos per click and keyword aucion mechanism Consider a generalized second price aucion in which he firm s locaion in he sponsored links generaed by he search engine is deermined by a combinaion of he firm s bid and 8

10 is relevance his corresponds o he mechanism currenly used by Google. We le c denoe he minimum cos per click esablished by he search engine. 7 This defines he minimum bid o paricipae o he aucion. We assume ha he cos per click is c for a specific firm i if boh firms adverise and i is lised second or if i is he only firm ha adverises In choosing he locaion of each bidder, he search engine considers he expeced revenue generaed by he firm, where he expeced revenue per searching cusomer from lising firm firs is α p, + δ γ p, and he expeced revenue from lising firm firs is α p, + δ γ p, where p,j b, p,j b, and p i, = c for i =,. Recall ha firms are only considered for lising in he sponsored links if hey submi a bid b i c. Assuming bids exceed c, he search engine will lis firm firs if α p, + δ γ p, or α p, + δ γ p, p, p, + γ δ p, p, and will lis firm firs oherwise. Noing ha eiher firm pays a cpc of c if is is lised second, if bids are such ha firm is lised firs, hen firm pays a cos-per-click cpc of p, = b + γ / p, / p, = b + γc < b, where he inequaliy follows from he assumpion ha b > c, and firm pays a cpc of c. If bids are such ha firm is lised firs, hen firm pays a cpc of c and p, = b γ / p, / p, = b γc > b. 7 For example, esimaes provided by he Google AdWords keyword ool sugges ha Googles ses a minimum cos per click of $.05 for any keyword. 9

11 Given he assumpion ha >, firm may be lised firs even if i bids less han firm i.e. if firm bids beween p, and b and firm mus bid sricly more han firm in order o be lised firs. The premium ha firm mus pay in order o be lised firs p, b is increasing in and decreasing in. In he limiing case in which, he search engine will simply rank he firms according o heir bids. In addiion, he premium is decreasing in γ and c. This resul is inuiive. Recall ha γ represens he probabiliy ha a consumer considers all of he sponsored links while wih probabiliy γ a consumer only considers he firs sponsored link and hen moves on o he organic links. As γ increases, he cos o he search engine of lising he less relevan Firm firs in erms of revenue ha could have been gained by lising he sponsored link o he more relevan Firm firs insead decreases because a consumer who deermines ha Firm s sponsored link is no relevan is more likely o consider and poenially click on he sponsored link o firm, which generaes revenue of c for he SE. Similarly, he revenue generaed by a consumer who rejecs he sponsored link o Firm and hen clicks on he sponsored link o Firm is increasing in c. 3. Equilibrium bidding sraegies The profi funcions under each scenario can be used o creae a payoff marix for he game in which he firms simulaneously deermine heir adverising sraegies. There will be an equilibrium in which neiher firm chooses o adverise if π NN > π AN, and π NN > π NA. These resricions require β β v α v c + α β v, and β v α v c + α β β v. which imply ha firm will prefer no o adverise condiional on firm no adverising if c v β / c, and firm will prefer no o adverise condiional on firm no adverising if c v β β / c. An equilibrium in which neiher firm adverises exiss if c max {c, c }. If he search engine esablishes a minimum cos-per-click c < max {c, c }, hen a leas one firm will adverise wih sricly posiive probabiliy. Firm prefers o adverise and be lised firs over adverising and being lised second if α v p, + α β v > α δ γ v c + α γ + α β v 0

12 which implies p, < γ δ β γ / v + cγ δ p. Firm prefers o adverise and be lised firs over no adverising given firm does adverise if or α v p, + α β v > p, < v α δ β v δ β / ˆp. Firm prefers o adverise and be lised second over no adverising given firm adverises if or α δ γ v p, + α γ + α β v > α δ β v c < v β + γ p,. γ If c > p,, hen firm prefers no adverising over adverising and being lised second given firm adverises. Noe ha p = ˆp when c = p,. If c > p,, hen p > ˆp, and if c < p,, hen p < ˆp. Lemma ˆp > c > p, for all >, and v β / = p, for =. Proof. This follows direcly from ˆp c = β v > 0 and from c p, = β v γ γ. or Firm prefers o adverise and be lised firs over adverising and being lised second if α v p, + α β β v > α γ v c + α γ + α β β v p, < v γ / γ δ + γ β + cγ / = p. Firm prefers o adverise and be lised firs over no adverising given firm adverises if α v p, + α β β v > α α β β v

13 or p, < v δ / β ˆp. Noe ha ˆp = c. Finally, firm prefers o adverise and be lised second over no adverising given firm adverises if α δ γ v c + > α α β or Noe ha p > ˆp when c > p,. Lemma ˆp > c > p, for all. α γ + α β β v β v c < v β + γ p,. γ Proof. See Appendix. Proposiion 3 If c < min { p,, p, }, hen in equilibrium Firm bids p and Firm bids p. If p p + γc, hen firm is lised firs and pays a cpc of p + γc, and firm is lised second and pays a cpc of c. If p > p γc, hen firm is lised firs and pays a cpc of p γc and firm is lised second and pays a cpc of c. Proposiion 4 If c > max {c, c }, hen neiher firm bids on sponsored links. Proposiion 5 If p, c > p,, hen in equilibrium firm always bids p. If ˆp > p γc, hen firm bids ˆp and is lised firs and pays a cpc of p γc and firm is lised second and pays a cpc of c. If ˆp p γc, hen firm does no bid, and firm adverises and pays a cpc of c. Proof. Firm always bids because c p, implies firm is beer off adverising and being lised second han no adverising. Firm bids he maximum amoun p ha i is willing o pay o be lised firs. Noe ha p γc > c if and only if p c γ + γ / which always holds because p c for c p,. Therefore, if ˆp > p γc, hen ˆp > p γc > c γc = c δ γ+γ > c where he second inequaliy follows from p > c, and he final inequaliy follows from γ+γ >

14 because > by assumpion. Therefore, if ˆp > p γc, hen bidding ˆp is opimal for firm because i will be lised firs a his bid. However, because c > p, implies firm is beer off no adverising han adverising and being lised second and paying a cpc of c, firm does no bid if ˆp p γc. Proposiion 6 If p, > c > p,, hen in equilibrium firm always bids p. If ˆp > { } max c, p + γc, hen firm bids ˆp and is lised firs and pays a cpc of p + γc, and firm is lised second and pays a cpc of c. If ˆp max hen firm does no bid, and firm adverises and pays a cpc of c. { } c, p + γc, Proof. The proof is similar o he proof of proposiion 5. However, because c < p, does { } no ensure ha p + γc > c, he addiional condiion ha ˆp > max c, p + γc is needed o ensure ha bidding on a sponsored link is opimal for firm when he bidding would resul in firm being lised firs. Proposiion 7 Suppose min {c, c } > c > max { p,, p, }. If ˆp > ˆp γc, hen firm bids ˆp, firm does no bid, and firm pays a cpc of c. If ˆp ˆp γc, hen firm bids ˆp, firm does no bid, and firm pays a cpc of c. Proof. Because c > max { p,, p, }, firm i prefers adverising and being lised firs over no adverising, bu prefers no adverising over adverising and being lised second because he cpc from being lised second exceeds p i,. Also, c > max { p,, p, } implies ˆp i > p i, so ˆp i is he maximum firm i is willing o pay if i is lised firs. Finally, lemmas and imply ˆp i > c, so each firm is willing o pay he cpc c if i is lised firs, bu will no bid if i will be lised second. Proposiion 8 Suppose c > c > c and c > max { p,, p, }. If ˆp < ˆp γc, hen firm bids ˆp, firm does no bid, and firm pays a cpc of c. If ˆp ˆp γc, hen here is a mixed sraegy equilibrium in which firms decide o bid randomly and submi a bid of ˆp i when hey do bid. Proof. The proof ha firm bids and firm does no if ˆp < ˆp γc follows he proofs in he previous proposiions because c < c implies ˆp > c. If ˆp ˆp γc, hen firm is willing o pay he premium required o be lised firs. Bu if firm is lised 3

15 firs, hen firm prefers no o adverise. However, if firm adverises wih probabiliy 0, hen firm will choose no o adverise, bu hen firm prefers o adverise because c < c. Thus, here is no equilibrium in pure sraegies. Noe ha in an equilibrium wih mixed sraegies, if boh firms bid ˆp i, hen firm is lised firs. Leing σ i denoe he probabiliy ha firm i adverises, he equilibrium in mixed sraegies saisfies σ π AA + σ π AN = σ π NA + σ π NN and σ π AA + σ π NA = σ π AN + σ π NN. Proposiion 9 Suppose c > c > c and c > max { p,, p, }. If ˆp > ˆp γc, hen firm bids ˆp, firm does no bid, and firm pays a cpc of c. If ˆp ˆp γc, hen here is a mixed sraegy equilibrium in which firms decide o bid randomly and submi a bid of ˆp i when hey do bid. Proof. The proof is similar o he proof in proposiion 8. The above proposiions generae several insighs ino he role of he various parameers on he bids submied by each firm. Noe ha in equilibrium each firm will eiher bid p i or ˆp i. Comparaive saics resuls presened in he appendix demonsrae ha opimal bids are sricly decreasing in, non-increasing in β, and β, and sricly increasing in and. As a measure of consumers propensiy o visi muliple links increases, he premium required o be lised firs decreases because a consumer who clicks on he firs sponsored link is more likely o click on he second sponsored link as well. For he same reason, as increases he benefi o a given firm of being lised firs decreases. This causes bidding for sponsored links o become less compeiive and he opimal bids decrease. As β a measure of he naural relevance of firm increases, firm has less incenive o adverise because he value of is organic link increases in β. As a resul, he bids p and ˆp ha firm migh submi are boh decreasing in β. However, Firm has a greaer incenive o adverise because if Firm does no adverise, as β increases, here is a lower probabiliy ha Firm encouners a cusomer. Ineresingly, his does no impac he bid ha Firm submis. As he above proposiions demonsrae, if Firm submis a bid for a paricular 4

16 keyword, ha bid will be eiher p, or ˆp, and neiher of hese values depend upon β. This follows from wo facs. Firs, if Firm also adverises, hen an increase in β is irrelevan o Firm s bid because for he fracion α of cusomers who consider he sponsored links, he parameer, no β, impacs he probabiliy ha Firm encouners a given cusomer, and he behavior of he fracion α who do no consider sponsored links is no influenced by Firm s posiion in he sponsored lisings. Second, if Firm does no adverise, hen Firm is only ineresed in sponsoring a link if c c. However, because ˆp > c, i follows ha Firm will bid ˆp, and ˆp does no depend upon β. Similarly, an increase in β causes firm o bid less compeiively, bu has no impac on he bids of firm because any cusomer who considers he organic link o firm already will have considered he organic link o firm. Increases in and boh increase compeiion for sponsored links. The impac of changes in v and γ on opimal bidding sraegies is less clear. The opimal bids p and ˆp of firm are increasing in v if and only if β is suffi cienly small. In his case, he marke expansion effec dominaes he crowding ou effec so ha more compeiive bidding by firm for a sponsored link is opimal when v increases. An increase in v, on he oher hand, always leads o more compeiive bidding by firm. As he fracion γ of consumers who consider all sponsored links increases, bidding for sponsored links by firm i becomes more compeiive if and only if β i is suffi cienly large and c < p i,, so ha p i > ˆp i. 3.3 Opimal Search Engine Sraegy The Search Engine SE opimally chooses he minimum cos per click c in order o maximize expeced search engine revenue from he generalized second price aucion. As discussed in he previous secion, he order in which he firms are lised in he sponsored links when boh firms submi bids is no deermined solely by which firm submis he highes bid - he ordering also depends upon he probabiliies δ i ha consumers click on he sponsored links. As demonsraed in subsecion 3., he search engine s choice of he minimum cos per click c deermines he bidding sraegies of he wo firms. As proposiions 3 hrough 9 demonsrae, he choice of c is criical o deermining which proposiion applies and wha he resuling bidding sraegies for each firm will be. However, i is no obvious how changes in c will impac SE profi. For he bidding firms, an increase in c makes he alernaive of relying on organic links for which he firms incur no cos-per-click relaively more aracive which 5

17 suggess bidding for sponsored links would become less compeiive. However, because he firm lised second pays a cpc of c, if boh firms bid on sponsored links, hen an increase in c reduces he incremenal cos he firm lised second mus pay in order o be lised firs. A he margin, his makes a bid increase aracive o he firm lised second, and increases compeiion for he firs spo in he sponsored links. From proposiion 3 and he definiions of p and p, i is apparen ha he second effec dominaes when c is relaively low c < min { p,, p, }, so an increase in c leads o more compeiive bidding higher bids However, once c exceeds p i,, firm i is no longer willing o pay for a sponsored link ha is lised second because firm i s reurn from no adverising is greaer han is reurn from adverising and being lised second. In his case, firm i only bids if he maximum amoun ˆp i ha i is willing o pay o be lised firs is suffi cien o ensure ha firm i is lised firs in he sponsored links. The bid ˆp i does no depend upon c because for firm i he alernaive of relying only on organic links for which here is no cpc dominaes being lised second if c > p i,. In addiion, as he following lemma demonsraes, he acual paymens made by each firm in an equilibrium in which boh firms adop pure adverising sraegies are increasing in c. Lemma 0 When boh firms adverise, he cos per click paid by Firm, p + γc, and he cpc paid by firm, d dc p γc, are increasing in c. Proof. Subsiuing he expressions for p i yields d dc p γc = γ > 0. p + γc = γ > 0 and This lemma combined wih proposiions 3, 5, and 6 implies ha in any equilibrium in which boh firms bid wih probabiliy, he cpc paid by each firm is increasing in he minimum cos per click se by he search engine. This follows from he fac ha in any such equilibrium he paymen made by he firm lised firs in he sponsored lisings is one of he wo expressions in lemma 0, and he cpc for he firm lised second is c. This lemma implies ha if he SE maximizes profi under condiions saisfying proposiion 3, hen c = min { p,, p, } ; if i maximizes profi under condiions saisfying proposiion 5, hen c = p, ; and if i maximizes profi under condiions saisfying proposiion 7, hen c = min {c, c }. In each of hese cases, raising c increases he acual paymen made by all paricipans in he aucion wihou changing he firms ha paricipae. A similar saemen canno be made abou proposiions 6, 9 or 8 because in he condiions saisfying any of hese proposiions, 6

18 and increase in c may cause one of he wo firms o drop ou of he aucion. Thus, he SE mus compare profi wih boh firms bidding under a lower c wih profi achieved wih only one firm sponsoring a link a a price equal o he upper bound for c in he proposiion. Unforunaely, he general condiions under which he SE prefers o se c so ha boh firms bid, only one firm bids, or firms adop a mixed sraegy are quie complex and do no provide sraighforward inuiion. Therefore, o gain furher insigh ino he opimal SE sraegy, we consider several examples Numerical examples In he firs example, suppose γ = =,consumers consider all of he sponsored links, bu when hey click on a sponsored or organic link, hey never click on oher links laer and v = kv where k >. Under hese assumpions, p, = c, and p, = c, so he condiions of proposiions 6 hrough 9 canno apply. In addiion p, > p, if and only if k > β β. Suppose his condiion holds. If c = p,, hen proposiion 3 applies, so firms will bid p i, and firm is lised firs and pays v β + β, firm is lised second and pays β v and search engine profi is v + β + > 0. Noe ha his profi is increasing in boh and. If he SE increases c, hen proposiion 5 applies. Because ˆp < p γc firm will no bid on a sponsored link, and c = p, is opimal for he SE. In his case, SE profi is p, = β kv. Subracing profi when c = p, from profi when c = p, yields which is posiive if v + β + β k k < β + β β k. Noe ha > β implies β > 0, so k > β. Thus, if β k > k > β, hen i is opimal for he SE o se c = p β, and induce boh firm and firm o bid on sponsored links. However, if k > k, hen i is opimal for he SE o esablish a higher minimum cpc of c = p, even hough doing so will resul in only firm 7

19 bidding on a sponsored link. This example demonsraes ha seing c suffi cienly small o induce boh firms o adverise is opimal if v is no oo much larger han v. However, if v is subsanially larger han v i.e., if k is suffi cienly large, hen he SE should se a high cos per click ha excludes firm from he sponsored link compeiion. Anoher simple example considers he case in which v = v = v, and β = 0 so he less relevan firm is compleely excluded from he organic lisings. In his case ˆp = c = p, = v. I can be shown ha if β < /, hen he SE ses c = p,, boh firms bid on sponsored links, and firm is lised firs. In his case, even hough firm is willing o pay v o be lised firs in he sponsored links, a bid of v is no suffi cien for firm o be lised firs because firm submis a bid close o v and has a higher click hrough rae, so he SE liss firm firs in he sponsored links. For slighly larger values of β, he SE sill ses c = p,, boh firms bid, and firm is lised firs. Finally, as β, he SE ses c = v and exracs all possible surplus from firm, which is willing o pay v. This final oucome is also more likely as increases, because as increases firm is more willing o rely on aracing cusomers hrough is organic link. As a hird example, suppose ha v = v, and β > β +. Noe ha his implies p, > p,. Because p, > p,, if he SE ses ses c = p,, hen proposiion 3 applies. Furhermore, because p and p are boh increasing in c, if he SE chooses a value of c such ha proposiion 3 applies, i will se c = p,. If c = p,, and v = v = v, hen p p γc if and only if v γ β β + β + β > 0 which holds if and only if β > β + which is rue by assumpion. Because p p γc when c = p,, if he SE ses c = p,, hen firm bids p and wins and is lised firs wih a cpc of p γc, and firm is lised second wih a cpc of c. So seing c = p, generaes search engine profi of δ α p γc δ + δ γ p, = α p + γ c / = α v δ β + β + γβ γβ γ +γ + β β γβ + γβ +γ v β +γ γ δ / Alernaively, he SE could se c = p,. In his case, proposiion proposiion 5 implies ha firm will only bid on a sponsored link if ˆp > p γc. I can be shown ha 8

20 if c = p,, hen ˆp > p γc if β > β +. Thus, if he SE ses c = p,, hen proposiion 5 implies firm bids ˆp and is lised firs and pays a cpc of p γc, and firm bids p and is lised second and pays a cpc of p,. In his case SE profis are α ˆp + δ γ v β + γ γ Finally, i can be shown ha subracing he SE profi when c = p, from he SE profi when c = p, yields a sricly negaive value if β > β +. Thus, he SE maximizes expeced profi by seing low value of c o induce greaer compeiion beween he wo firms in heir bidding for a sponsored link. This resul is inuiive because if β is large, hen firm has relaively lile incenive o bid on a sponsored link paricularly if he cpc for cusomers who arrive hrough he sponsored link is large. The bes he SE can do is se c o exrac he maximum possible surplus from having firm lised second, and his occurs when c = p,. Furhermore, if β is suffi cienly large, hen c > c. Using his and proposiions 7 and 8 i can be shown ha furher increases in c resul in only firm sponsoring a link and reduce SE profi. This example shows ha when firms have an alernaive of relying on organic links o arac cusomers, i is possible ha he opimal bidding sraegies will resul in he less relevan firm firm being lised firs in he sponsored lisings. Furhermore, in his paricular example, he SE ses c suffi cienly high so ha firm is he only firm ha sponsors a link in equilibrium. This resul relies on β being suffi cienly large or, alernaively, on being suffi cienly small or being suffi cienly close o, so ha for firm, is organic link aracs enough cusomers relaive o he alernaive of a sponsored link. 4 Managerial implicaions and concluding remarks This paper invesigaes sraegic behavior of firms on a search engine. We develop a comprehensive framework o accoun for he exisence of asymmery beween hese firms. Firs, some firms may be more relevan for cusomers han ohers i.e. hey have a higher probabiliy o be clicked on heir organic link. Second, firms may differ in he value generaed by each consumer ha visis heir websies i.e. some firms can exrac more revenues from a consumer han ohers. Our model also inegraes several empirical feaures regarding consumers behavior on search engine. Firs, our model closely mimics consumer behavior 9

21 successive ieraions when considering a resul page. Second, i also explicily inegraes he possibiliy for some consumers o bypass sponsored links or o consider only he firs sponsored linked as documened in he lieraure on browsing behavior. Our framework allows us o deermine wha parameers are imporan for bidding sraegies and how hey affec he decision o bid and he amoun of bidding. Our resuls highligh hree kinds of equilibrium oucomes. In he firs equilibrium oucome boh firms bid on sponsored links. Under such an equilibrium, eiher firm can be lised firs in he sponsored links. In general, he more relevan firm, firm, is more likely o be lised firs as he difference in he relevance of each firm in he sponsored links increases, because his implies consumers are more likely o click on firm s sponsored link, so he SE prefers o lis firm firs. In addiion, as β decreases β increases, firm s bid becomes more compeiive relaive o firm, which also makes i more likely ha firm will be lised firs. The second ype of equilibrium oucome involves he search engine seing he minimum cpc suffi cienly high ha only one of he wo firms bids in he keyword aucion. This equilibrium occurs which here is a significanly large difference in he willingness o pay beween he wo firms. For example, if firm has a relaively high click hrough rae β on is organic links and firm does no, hen i may be opimal for he SE o se c high enough so ha firm chooses no o bid in he keyword aucion. Similarly, if he value v o firm of aracing cusomer is much higher han v, hen he SE will opimally se a high value of c which exracs surplus from firm while excluding firm. The analysis also demonsraes how he SE s abiliy o exrac surplus in his manner is consrained by each firm s abiliy o arac cusomers hrough is organic links. The final ype of equilibrium involved he firms adoping mixed sraegies o deermine wheher o paricipae in he aucion process. This equilibrium requires ha he SE se c suffi cienly large ha one of he wo firms, say firm, is beer off no adverising if firm also chooses no o adverise, bu firm is beer off adverising and paying c if firm does no adverise, and firm is beer off adverising and being lised firs if firm does adverise. The resuls and specific examples presened above demonsrae ha organic lisings can have a significan impac on equilibrium in sponsored search aucion boh in erms of he opimal bidding sraegies and decision o paricipae in he aucion by firms, and he 0

22 opimal reservaion price esablished by he SE. In paricular, he resuls are consisen wih oucomes in aucion sponsored search aucions in which less relevan firms are ofen lised ahead of more relevan firms in he sponsored links. The analysis also predics ha under cerain condiions, highly relevan firms will no appear a all in he sponsored links. The model can be exended in several direcions. Iniial analysis exending he model o include more han wo firms suggess ha i is possible ha a Vickrey aucion will generae more revenue for he SE han a generalized second price aucion under cerain condiions. This meris furher invesigaion. Anoher possible exension would endogenize parameers γ and δ i as pars of he search engine sraegy. Indeed, he SE has he possibiliy o improve he visibiliy of he firs sponsored link in conras o he oher sponsored and organic links. For insance, i may choose o display only one sponsored link a he op of a resul page, all he oher sponsored links being displayed a he lef-hand-side of he page which is a less favorable locaion. In ha case, he advanage given o he firs sponsored links is significanly increased. Secondly, one may empirically observe ha for valuable or popular keywords, he ranking and he ideniy of sponsored links may change for wo idenical and successive requess. The ads displayed in he sponsored links secion are he resuls of a random selecion process of ranking. Ye, his creaes some opporuniy for he SE o manipulae he probabiliy of clicking on a sponsored link δ i in our model so as o exrac more revenues from keywords adverising. 5 Appendix 5. Comparaive saics on opimal bids: p = v γ β γ / + cγ d p = γδ d c v < 0 d p dβ = v γ < 0 d p dγ = c c + β v v + v β v > 0 if and only if β > v c v. Sign here is unclear. If c = v, hen clearly his condiion on β is always saisfied and p is increasing in γ. If c = 0, hen 0 < v c v be saisfied. d p d = β v γ > 0 d p d = cγ β v γ v + γβ v > 0 <, so he condiion on β may or may no

23 d p dv = γ+γ. γ β + γβ γ + β + γ γβ > 0 if and only if β < d p dc = γ > 0 ˆp = v β / dˆp d = β v < 0 dˆp dβ = v < 0 dˆp d dˆp d = β = v > 0 β v > 0 dˆp dv = β + β > 0 if and only if β < /. p = v γ / γ +γ β + cγ / d p = γδ d c v < 0 d p = 0 dβ d p = γ +γ dβ < 0 d p = δ dγ c c + β v v + v β v > 0 if and only if β > v c v which may or may no hold. Always holds if c is suffi cienly close o v. Also always holds if β is suffi cienly close o because <. d p d = cγ β v γ v + γβ v > 0 if and only if v > c always holds. γ γ +β γ which d p d = β v γ > 0 d p dv = β + γβ γ + β + γ γβ > 0 if and only if β < γ+γ γ which always holds because γ+γ γ > δ, and β < by assumpion. d p = γ δ dc > 0 ˆp = v /β dˆp = δ β d v < 0 dˆp = 0 dβ dˆp dβ dˆp d dˆp d = / < 0 = β = dˆp dv = v > 0 β v > 0 β + β > 0 p, = v β +γ d p, d = γ γ β δ v γ < 0

24 d p, = v dβ γ d p, = β v dγ γ d p, d = β γ d p, d = β γ γ v + γ γ < 0 > 0 v + γ γ > 0 > 0 if and only if γ > /. d p, dv = β +γ γ > 0. p, = v β +γ d p, γ = β d γ v γ < 0 d p, = 0 dβ d p, = +γ dβ γ < 0 d p, = δ β v dγ γ d p, d = β γ γ v d p, d = β v γ d p, dv = > 0 < 0 γ + γ > 0.. β +γ γ c = v β / dc d = β v > 0 dc dβ = v < 0 dc dv = β / > 0 c = v β β / dc d dc dβ = β = v β > 0 β v > 0 dc dβ = v β < 0 dc = β β d v < 0 dc dv = v β β / > Proof of Lemma Proof of Lemma. This follows from ˆp c = β v β > 0, and from c p, = β v δ γβ γ γ + γβ + γ which is posiive when =. Furhermore, his expression equals 0 a he wo roos γβ ± δ + γ β + γ γ + 4γβ + γ β 4γ β γβ γ 3

25 which are boh less han. To see his noe ha he larger roo, γβ δ + γ β + γ γ + 4γβ + γ β 4γ β γβ, γ is less han if and only if γ > γβ + which always holds because + γ β + γ γ + 4γβ + γ β 4γ β γβ γ + γβ + γ β + γ γ + 4γβ + γ β 4γ β γβ = 4γβ γ > 0. 4

26 References Aggarwal G., Goel A. and Mowani,R. 006 Truhful aucions for pricing search keywords, Proceedings of he 7h ACM conference on Elecronic Commerce. Agarwal A.,Hosanagar K. and Smih, M.D. 008 Locaion, Locaion, Locaion: An Analysis of Profiabiliy of Posiion in Online Adverising Markes, SSRN Working Paper, available a hp://ssrn.com/absrac=5537 Ahey S. and Ellison G. 008 Posiion Aucions wih Consumer Search, working paper Chen J., De L. and Whinson A.B. 009 Aucioning Keywords in Online Search, Journal of Markeing, 73, 5-40 Chen J., Feng J. and Whinson A.B. forh., Keyword aucions, uni-price conracs and he Role of Commimen, forhcoming in Producion and operaions Managemen. Davenpor T. H. and Beck J.C. 00. The Aenion Economy: Undersanding he New Currency of Business, Harvard Business School Press. Edelman B., Osrovsky M. and Schwarz M. 007 Inerne Adverising and he Generalized Second Price Aucion: Selling Billions of Dollars Worh of Keywords, American Economic Review, 97, Evans D.S. 008, The Economics of he Online Adverising Indusry, Review of Nework Economics, 73. Ghose A. and Yang S. 009 An Empirical Analysis of Search Engine Adverising: Sponsored Search in Elecronic Markes, Managemen Science, 550, Goldfarb A. and Tucker C. 007 Search Engine Adverising: Pricing Ads o Conex, NET Insiue Working Paper No. 07-3, available a hp://ssrn.com/absrac=045. Jeziorski P. and Segal I. 009 Wha Makes hem Click: Empirical Analysis of Consumer Demand for Search Adverising, working paper. Kaona Z. and Sarvary M. forh. The Race for Sponsored Links: Bidding Paerns for Search Adverising, forhcoming in Markeing Science 5

27 Ruz O. and Bucklin R.E. forh., From Generic o Branded: A Model of Spillover in Paid Search Adverising, Journal of Markeing Research, forhcoming. Taylor G. 009 Search qualiy and Revenue Cannibalizaion by compeing search engines, working paper available a hp://users.ox.ac.uk/ ine08/aylor.pdf Taylor G. 00 The informaiveness of online adverising, working paper available a hp://users.ox.ac.uk/ ine08/obfuscaion.pdf Varian H. 007 Posiion aucions, Inernaional Journal of Indusrial Organizaion, 5, Whie A. 009 Search Engines : Lef Side qualiy versus Righ side profis, working paper Xu, L., Chen, J. and Whinson, A. Too Organic for Organic Lising? Inerplay beween Organic and Sponsored Lising in Search Adverising, McCombs Research Paper Series No. IROM

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