Jianqing Chen. Jan Stallaert

Transcription

1 RESEARCH ARTICLE AN ECONOMIC ANALYSIS OF ONLINE ADVERTISING USING EHAVIORAL TARGETING Jiaqig Che Jidal School of Maagemet, The Uiversity of Texas at Dallas, 8 West Campbell Road, Richardso, TX 758 U.S.A. {chejq@utdallas.edu} Ja Stallaert School of usiess, Uiversity of Coecticut, Hillside Road, Storrs, CT 669 U.S.A. {ja.stallaert@busiess.uco.edu} Appedix A. Summary of Notatios Notatio i j p i x ij q ij v i i Defiitio ad Commets Idex for advertisers Idex for users Number of advertisers Probability that advertiser i s most targeted user clicks o his advertisemet Distace betwee advertiser i ad user j alog the circle Decay factor, which also measures the heterogeeity of users prefereces Decay i the probability that user j clicks o advertiser i Uit value that advertiser i derives from each click Advertiser i s referece value, defied as i v i p i (i T The i th highest value amog all i The publisher s reveue uder traditioal advertisig The publisher s reveue uder behavioral targetig x i Margial user for allocatio uder behavioral targetig who has the same value to advertisers i ad i y i Margial user for paymet uder behavioral targetig who has the same value to advertisers i ad i Δ i H i A i Cross-border effect uder behavioral targetig Advertiser i s expected paymet for the users wo uder behavioral targetig Advertiser i s payoff uder behavioral targetig MIS Quarterly Vol. 38 No. Appedices/Jue A

2 Che & Stallaert/A Ecoomic Aalysis of Olie Advertisig Usig ehavioral Targetig A. Proof of Lemma Proof. We cosider ay advertiser i s biddig strategy b i. We suppose that amog the rest of advertisers, advertiser l has the highest proposed expected paymet b p l E[q]. If b p i E[q] > b p l E[q], advertiser i wis the auctio with total expected paymet b l p l E[q], ad his payoff is Otherwise, the advertiser loses the auctio ad his payoff is ero. v i p i E[q] b l p l E[q] (6 We first cosider biddig b i < v i. If b p i E[q] > b p l E[q], the advertiser wis the auctio ad derives the payoff i Equatio (6, just as if biddig v i. If b p l E[q] > v p i E[q], the advertiser loses the auctio ad derives ero payoff, just as if biddig v i. If b p i E[q] < b p l E[q] < v p i E[q], biddig b i causes the advertiser to lose the auctio ad receive ero payoff, whereas if he had bid v i, the advertiser would have wo the auctio ad derived positive payoff as i Equatio (6. Therefore, biddig b i < v i is (weakly domiated by biddig v i. We the cosider biddig b i > v i. If v p i E[q] > b p l E[q], the advertiser wis the auctio ad derives the payoff i Equatio (6, just as if biddig v i. If b p l E[q] > b p i E[q], the advertiser loses the auctio ad derives ero payoff, just as if biddig v i. If v p i E[q] < b p l E[q] < b p i E[q], biddig b i causes the advertiser to wi the auctio with egative payoff, whereas biddig v i leads to ero payoff. Therefore, biddig b i > v i is (weakly domiated by biddig v i. All together, biddig true value v i is advertiser i s (weakly domiat strategy. Uder behavioral targetig, the same argumet applies, simply replacig p i E[q] with p i q ij for user j. A.3 Proof of Lemma Proof. For ay advertiser k differet from advertisers i ad i, we first cosider the case where the shortest path from user j (located betwee advertiser i ad i to advertiser k passes advertiser i. If i > k, the k ( x kj < i ( x ij because x ij < x kj. If i < k, we have (assumig k < i i k k( xkj k xij i k xij i( xij < < where the first iequality follows from the comparable value assumptio ad the secod iequality is because i < k. Therefore, i this case, advertiser i derives higher value tha advertiser k from user j. Similarly, whe the shortest path from user j to advertiser k passes advertiser i, advertiser i derives higher value tha advertiser k from user j. All together, either advertiser i or advertiser i derives higher value tha ay other advertiser k from user j, ad thus user j must be assiged to either advertiser i or advertiser i i equilibrium. A. Proof of Lemma 3 Proof. We deote V ij / i q ij, the value that the advertiser i derives from user j, ad deote V (j ad V (j as the highest ad secod highest values amog all i s. Whe i is icreased to ' i (i.e., ' i > i, V ' ij > V ij ad thus V ' (j > V (j. I additio, for the additioal users that advertiser i wis uder ' i, the highest values uder i become the secod highest oes uder ' i, ad thus V ' (j V (j > V (j. ecause the publisher s reveue is the sum of the secod highest value from each user, ' >. A.5 Proof of Propositio Proof. (a y Lemma 3, M /M i >. Give ( ad the order costrait (i > (i,, to maximie, (3 ( ( (. For (, we have M /M ( > subject to (i.e., the comparable value assumptio. Noticig ( (, we coclude the ( that maximies is ( (whe the coditio bids. A MIS Quarterly Vol. 38 No. Appedices/Jue

3 Che & Stallaert/A Ecoomic Aalysis of Olie Advertisig Usig ehavioral Targetig (b Similarly, because M /M i >, to miimie subject to ( ad (i > (i, we have ( ( ad (3 ( (. ecause of the comparable value assumptio, the ( that miimies is. We ext determie how the relative locatio of the two advertisers with ( affects the reveue. Whe or 3, there is a uique relative distributio of these advertisers values. We ext focus o the case with >. We first examie the possible reveue for a user segmet i (i. For a user segmet with i ( ad i (, or for user segmet ( (, the reveue is from a base paymet (i Table A by Equatio (7 with xi. For user segmet ( (, if ( s other eighbor is of (, the reveue is from a base paymet (i Table A by Equatio (7 with x i /; if ( s other eighbor is of (, the reveue is the base paymet plus the cross-border effect. y Equatio (, the cross-border effect is ( ( (7 3 ( ( For user segmet ( (, if the eighbors are of (, the reveue is from a base paymet (i Table A by Equatio (7 with x i /(; if oe eighbor is of ( ad the other is of (, the reveue is the base paymet plus oe piece of the cross-border effect defied i (7. If both eighbors are of (, the reveue is the base paymet plus two pieces of the cross-border effect (with oe piece at each border. Table A. The ase Paymets for Possible User Segmets User Segmet ( ( ( ( ( ( ase Paymet 3 3 Notice the base paymet from each user segmet i (i is solely determied by the values i ad i (while the cross-border effect depeds o the eighbors values. Therefore, the reveue from base paymets (excludig the cross-border effect ca differ oly whe the two highestvalue advertisers are adjacet ad whe they are ot. I the former, the reveue cosists reveue from oe ( ( segmet, from two ( ( segmets, ad from ( 3 ( ( segmets; i the latter (the o-adjacet case, the reveue cosists of reveue from four ( ( segmets ad from ( ( ( segmets. The differece i these reveues is the reveue from oe ( ( ad from oe ( ( mius the reveue from two ( ( ; that is, > which idicates that the reveue from base paymets is greater whe the highest-value advertisers are adjacet. If the two highest-value advertisers are adjacet, the total reveue icludes four pieces of cross-border effects, i additio to the reveue from the base paymet. Whe, the four pieces cosist of two from the two ( ( segmets (because i each segmet ( eighbors the other ( ad two from the ( ( segmet (because both ( s eighbor (. Whe > 5, the four pieces cosist of two from the two ( ( segmets ad two from the two ( ( segmets with oe ( i each segmet eighbored by (. If the two highest-value advertisers are ot adjacet, the total reveue cotais o cross-border effect whe. Therefore, the total reveue (icludig the reveue from the base paymet ad the cross-border effect is lower whe the two highest-value advertisers are ot adjacet tha whe they are. Whe > 5, if the two highest-value advertisers are / distat to each other (i.e., there is oe lowest-value advertiser i betwee, the total reveue cotais two pieces of cross-border effect: either from the two ( ( segmets with oe ( eighbored by ( (if > 5 or from the ( ( segmet with both ( s eighbored by ( (if 5. If at least two lowest-value advertisers are located betwee the two highest-value advertisers, the total reveue cotais four pieces of cross-border effect. The reaso is that, aroud each arc coectig the two ( s, we should have either two ( ( segmets with oe ( eighbored by ( i each segmet or oe ( ( segmet with both ( s eighbored by (. Either case leads to two pieces of cross-border effect with oe arc, ad we have two differet arcs. Therefore, whe > 5, the structure with the two highest-value advertisers beig / distat from each other geerates the least total reveue (with the lowest reveue from the base paymet ad the least umber of cross-border effects. MIS Quarterly Vol. 38 No. Appedices/Jue A3

4 Che & Stallaert/A Ecoomic Aalysis of Olie Advertisig Usig ehavioral Targetig A.6 Proof of Propositio Proof. (a Whe, by Propositio, give (, the structure with ( ( /( / geerates the highest, i which the domiat advertiser wis all users (except the other advertiser s most targeted user, from which both advertisers derive the same value. I this case, by Equatio (7 with x i /,, which is the same as T by Equatio (3. Therefore, < T, ad the equality occurs oly if ( ( /( /. Whe > 3, > T is always possible. For example, whe ( ( (, cosists of the base paymets from the ( ( segmets. Accordig to Table A, 3. Noticig, we ca coclude > T whe > 3. Furthermore, a value structure T with ( > ( results i a higher reveue uder behavioral targetig (by Lemma 3 ad i the same reveue uder traditioal advertisig, which leads to > T. (b For < < 6, traditioal advertisig might geerate higher reveue tha behavioral targetig as well. For 5, see the proof i part (c. Whe, the least reveue uder behavioral advertisig is ( (from four ( ( segmets, which is less tha 8 T regardless of. Whe 3, the least reveue cosists of the base paymet (from two ( ( segmets ad oe ( ( segmet ad two pieces of cross-border effect: ( ( / which is less tha T regardless of because the term i the square bracket is egative. (c Whe > 5, accordig to the proof of Propositio, the least reveue cosists of the base paymet (from four ( ( segmets ad ( ( ( segmets ad two pieces of cross-border effect: The differece betwee this ad T i Equatio (3 is 3 ( ( 3 3 ( ( 3 3 ( ( ( ( The term i the secod square bracket is icreasig i by oticig the first-order derivative ( ( ( 3 8 ( > 3 8 > ad thus is greater tha its value at ero ²( (3 ( 6( (which is oegative if > 6. Therefore, the differece is positive, ad behavioral advertisig geerates higher reveue if > 6. If 5, the differece is egative for ay by otig that the value of the term i the square bracket at is 3.5. All together, we ca coclude that if < 6, the reveue uder behavioral targetig may be less tha the reveue uder traditioal advertisig. If > 6, the least amout of reveue uder behavioral targetig is still greater tha the reveue uder traditioal advertisig. Therefore, if ad oly if > 6, the publisher is better off usig behavioral targetig. A.7 Proof of Corollary Proof. Uder behavioral targetig, xi by Equatio (6. Accordig to Equatio (3, 3 by substitutig i x i ad otig Δ i. Accordig to Equatio (3, T. Therefore, whe 3, T, ad whe > 3, > T. A MIS Quarterly Vol. 38 No. Appedices/Jue

5 Che & Stallaert/A Ecoomic Aalysis of Olie Advertisig Usig ehavioral Targetig A.8 Proof of Propositio 3 Proof. (a Whe, accordig to Propositio, the publisher is (weakly better off uder traditioal advertisig. Meawhile, whe the lower-value advertiser gets o market share uder behavioral targetig, two advertisig strategies could lead to the same reveue for the publisher. Therefore, if, the maximum gai is ero. Whe >, without loss of geerality, we let ( ad ormalie (. is maximied whe ( (3 ( ad ( by Propositio. y substitutig ( ad x / ito (, we ca obtai the maximum ad thus calculate the maximum gai as T 3 3 ( ( 3 ( ( ( ( (8 (b We otice the first-order derivative of the term i the square bracket o the right-had side of (8 with respect to, 3 ( ( 3 ( ( ( ( 3 > 3 > 3 ( ( ( ( which idicates the maximum gai is icreasig i. We otice the first-order derivative of the right-had side of (8 with respect to, ( ( ( ( ( ( 8( ( 3 ( ( 3 ( Note that the term i the above square bracket is greater tha ( ( ( ( 8 3, which is positive. Therefore, the above first-order derivative is positive, ad the maximum gai is icreasig i. A.9 Proof of Propositio Proof. Part (a ca be foud to be true from the discussio i the body. (b We first derive advertiser i s payoff uder behavioral targetig: xi x i i( x i x dx i( x i x dx Δ i i i xi ( i i xi i i x x ( Δ i i i i i (9 x x Δ i i i i i i i where the first itegral is the expected value et the base paymet for the users i segmet i (i, the secod itegral is the expected value et the base paymet for the users i segmet (i i, Δ i is the cross-border effect, ad the last equality is because MIS Quarterly Vol. 38 No. Appedices/Jue A5

6 Che & Stallaert/A Ecoomic Aalysis of Olie Advertisig Usig ehavioral Targetig x i i i i i x i i i i i from Equatio (6. (b. Whe, the differece i the payoff uder behavioral targetig ad uder traditioal advertisig is where the first term (the advertiser s payoff uder behavioral targetig is from Equatio (9 (oticig Δ. (b. Advertiser s payoff uder behavioral targetig ca be formulated by lettig i i Equatio (9, ad the payoff uder traditioal advertisig is by Equatio (. The coditio for advertiser to be better off uder behavioral targetig specified i the propositio the follows. A. Proof of Corollary Proof. The differece i the payoff uder behavioral targetig ad uder traditioal advertisig is Δ Δ( has two roots: ad ' " with N < O. Notice that Δ( > because whe the advertiser s payoff uder behavioral targetig is positive ad his payoff uder traditioal advertisig is ero. Furthermore, because, we have N >. Uder the comparable value assumptio, ' " >. ecause, it follows that < O. Therefore, if < N, Δ( > ad thus the advertiser is < < " better off uder behavioral targetig; otherwise, it is worse off. Notice that. < N ca occur because N >. > N ca, occur because ' > A6 MIS Quarterly Vol. 38 No. Appedices/Jue

7 Che & Stallaert/A Ecoomic Aalysis of Olie Advertisig Usig ehavioral Targetig A. Proof of Propositio 5 Proof. We assume that advertiser is the domiat advertiser. The joit payoff of the publisher ad the advertisers uder traditioal advertisig ca be formulated as ( x xi x i dx. The joit payoff uder behavioral targetig is i( x dx i( x dx. i For ay user j i segmet i (i, if x ij [, x i ], by Lemma ad the defiitio of x i, advertiser i wis the user ad derives the highest value amog all advertisers, which implies ( x > ( x i ij j The left-had side of the iequality is also user j s cotributio to the joit payoff uder behavioral targetig, ad the right-had side is her cotributio to the joit payoff uder traditioal advertisig. Therefore, the joit payoff derived from user j is higher uder behavioral targetig tha uder traditioal advertisig. The same argumet applies if x ij [x i, /] (such that advertiser i wis the user ad derives the highest value. ecause the joit payoff is the sum of the joit payoff from each user, the joit payoff uder behavioral targetig is greater tha the joit payoff uder traditioal advertisig. A. Maximum Gai i the Geeral Case Proof. Without loss of geerality, we let ( ad ormalie (. y Lemma 3, is maximied whe ( (3 ( ad whe ( is large eough to wi all of the users. For each of the two segmets with oe ed at ( (i.e., segmets ad, the expected reveue is the lower-value advertiser s expected value of all the users i the segmet, which is. For each of the other segmets (e.g., i i, the expected reveue is advertiser i s expected value of the half of the users who are closer to him tha to advertiser i ad advertiser i s expected value of the other half, which is. We ca thus obtai the maximum ad calculate the maximum gai as ( ( T The maximum gai is clearly icreasig i. The gai is also icreasig i because its first-order derivative with respect to is positive; that is,. 3 > MIS Quarterly Vol. 38 No. Appedices/Jue A7