Competitive Targeted Advertising with Price Discrimination

Transcription

1 Compette Tageted Adetsng wth Pce Dscmnaton Rosa Banca Estees Unesdade do Mnho and NIPE Joana Resende Faculdade de Economa, Unesdade do Poto and CEF.UP Septembe 8, 205 Abstact Ths pape examnes how should ms allocate the adetsng budgets between consumes who hae a hgh pefeence fo the poducts (stong segment) and those who pefe competng poducts (weak segment). Tageted adetsng tansmts eleant nfomaton to othewse unnfomed consumes and t s used as a pce dscmnaton dece. Wth tageted adetsng and pce dscmnaton, we nd that, when the attacteness of the weak segment s low, each m adetses moe ntensely n ts stong segment than n ts weak segment. The same esult ases when the attacteness of the weak segment s hgh and adetsng s expense enough. Inteestngly, when the attacteness of the weak segment s hgh but adetsng costs ae su cently low, t s optmal fo each m to adetse moe ntensely n ts weak segment than n ts stong segment. The pape also nestgates how adetsng stateges and equlbum po ts ae a ected by pce dscmnaton. In compason to unfom pcng, ms can ncease o educe the ntensty of adetsng tageted to each segment when pce dscmnaton s allowed. Futhe, when the attacteness of The authos ae gateful to the Edto n Chef, Desa Peyas, to an anonymous Assocate Edto and to two anonymous efeees fo the ey constucte and detaled comments dung the eew pocess. We hae also bene ted fom useful comments and suggestons on eale esons of the pape fom Alexande de Conèe, Anthony Dukes, Dde Laussel, Emmanuel Petaks, Jean Gabszewcz, João Coea da Sla, José Moaga- Gonzalez, Lus Cabal, Rabah Am, Regs Renault, Santanu Roy. We also thank the patcpants of EARIE 202, EAIRE 203; IIOC 20; IIOC 203; NASM 203; Asan Meetng of the Econometc Socey 203; SAET 20; SAET 205; Meetngs of the PEJ 202; and the attendants of semnas at UAB and Unesty of Poto. Ths wok s funded by FEDER funds though the Opeatonal Pogam fo Competteness Factos - COMPETE and Natonal Funds though FCT - Foundaton fo Scence and Technology wthn the pojects PTDC/EGE- ECO/08784/2008 and EXPL/IIM-ECO/65/203. The usual dsclame apples.

2 the weak maket s hgh, pce dscmnaton boosts ms po ts poded that adetsng costs ae su cently low. The eese happens when adetsng costs ae hgh. Intoducton In many makets ms need to nest n adetsng to ceate awaeness fo new poducts, pces and specal o es (nfomate ew of adetsng). Untl ecently, the ms adetsng stateges wee mostly taloed to tadtonal meda and mass audences. Today, ms can explot new possbltes to dele ads tageted to spec c segments wthn a maket, usng fo nstance moble coupons, sophstcated foms of locaton-based adetsng, ncludng geo-fencng and geo-conquestng, 2 and poduct seach apps (see The New Retal: fom moble aspatons to busness esults, The Economst, Mach 204). The use of such adetsng technques dastcally nceases the scope fo tageted adetsng and pce dscmnaton. 3 In eal makets, not all consumes ae equally aluable to ms. Whle some consumes may hae a elate pefeence fo a m s poduct (stong segment) the emanng ones may hae a elate pefeence fo the compettos poduct (weak segment). Hence, ms n these makets need to choose the ntensty of adetsng and the pce to be taloed to each maket segment. The cental queston of ths pape s the followng. Should a m adetse moe ntensely n ts stong segment o athe n ts weak segment? Othe eleant questons ae: Whch custome segment should be ewaded? Is pce dscmnaton po table? Futhe, what changes n tems of pe-segment adetsng spendng and po ts when we depat fom a settng of tageted adetsng and unfom pcng to one of tageted adetsng and pce dscmnaton? We consde a model wth two ms A and B launchng a new poduct to consumes who may buy fom a m only f they ecee an adetsng message (hencefoth ad) fom t. Adetsng ceates awaeness (and also nfoms about pces). The set of potental buyes s composed of two emakete estmates that moble ad spendng wll ncease fom $8.4 bllon n 202 to $37 bllon n 206. See 2 Accodng to The Locaton Temnology Gude The Language of Locaton deeloped by a wokng goup of Moble Maketng Assocaton, geofencng dent es a pont of nteest on a map and establshes a adus aound t fo tagetng puposes. Geo-conquestng s used when ths pont of nteest s the competto s locaton. 3 Fo example, a Wall Steet Jounal nestgaton found that the Staples webste dsplays d eent pces to people afte tackng the locatons. Staples appeaed to consde the peson s dstance fom a competto s physcal stoe. If a competto had stoes wthn 20 mles o so, Staples.com usually showed a dscounted pce. See 2

3 dstnct segments of equal sze, half of consumes hae a elate pefeence fo poduct A, whle the emanng ones hae a elate pefeence fo poduct B. The desutlty of not buyng the most pefeed band s exogenously gen by > 0: In a locaton ntepetaton, ths means that consumes can puchase costlessly fom the m n the neghbohood but they ncu a tanspot cost f they go to the moe dstant m. Ths demand stuctue (à la Shlony, 977) suggests that, although ms may hae some adantage oe the compettos, all (nfomed) consumes may, n the end, be nduced to swtch. Wth tageted adetsng and pce dscmnaton, each m s stategy conssts n choosng an ntensty of adetsng and a d eent pce to be taloed to the stong and to the weak segments of the maket. By nestng n adetsng, ms endogenously segment the maket nto capte (patally nfomed), selecte (fully nfomed) and unnfomed customes. To motate ou model consde the followng example taken fom locaton-based adetsng a geo-fencng/conquestng, whch has become a hot topc n the adetsng and maketng wold. Suppose two ms e.g. McDonalds (Mc) and Bugue Kng (BK) ae unnng an awaeness moble adetsng campagn to a new menu tem. Both ae pefectly nfomed about the consumes locaton (.e., they know whethe a consume s nea the Mc stoe o the BK stoe) and they hae access to LBA tools that allow them to send ads wth d eent o es (pces) to customes n d eent locatons. Fo nstance, consde a potental custome standng n font of BK s doo. BK can send ths custome a eleant adetsng o e. The consume may also be tacked by Mc n the neghbohood, whch may send hm/he an ad wth a specal o e (dscounts o othe ewads). If the last ad s compellng enough, Mc can entce the consume to tael to the moe dstant stoe (ncung the cost ). The pactce of tagetng consumes located nea the competto has ecently been labelled as a geo-conquestng stategy. Today, geo-conquestng ads ae fequently used n makets n whch thee s a small wndow of thought befoe buyng (e.g. etal, estauants, hotels, tael,...) as well as n busnesses that sell bgge tems (e.g. automobles). 4 The model addessed n ths pape ts well adetsng and pcng polces that ae nowadays 4 Some well known geo-conquest campagns hae been used by Chysle, Lexus, Outback Steakhouse o Best Westen hotels. Tom MacIsaac, CEO of locaton-centc moble ad netwok Vee Moble says that The company looked at clck-though ates acoss 7 Mothe s Day campagns by etales usng the tactc, as well as geo-fencng the own locatons to pomote cads, owes, baked goods, and othe gft tems... The esults showed that geo-conquestng led to a 30% hghe clck-though ate than standad geo-fencng. See 3

4 possble though the use of moble deces, such as LBA and moble coupons. Ths knd of adetsng/pcng stateges hae aleady been employed by bands lke Stabucks, Bugue Kng, Taco Bell, Tast-D-Lte, Macy s and Peps. Fo example, the CEO of the New Yok Cty-based statup PlaceIQ sad ecently that PlaceIQ can be used to lue potental customes away fom a competto s locaton. Though the use of ths technology, Lexus could potentally dentfy moble phone uses at an Aud dealeshp and see them a moble ad dectng them to the neaest Lexus lot. In the peous examples, consumes physcal locaton s a key detemnant of ms adetsng stateges. Howee, ou stylzed model s also sutable to analyze othe foms of tagetng adetsng stateges n whch the geogaphcal element s not ntnscally pesent. Fo example, n the case of contextual adetsng though seach engnes, ms may engage on conquestng ads by tagetng them to consumes wth an ntnsc pefeence fo the al m. 5 Ths pape o es mpotant nsghts to the undestandng of ms adetsng decsons to the stong and weak maket segments. An mpotant contbuton s to clealy descbe what maket featues ae needed fo the two adetsng outcomes moe ntense adetsng n a m s stong maket, o n ts weak maket to ase n equlbum when ms ae able to engage n tageted nfomate adetsng. We show that the elate attacteness of the weak maket and the leel of adetsng costs ae key equlbum detemnants. When the attacteness of the weak segment s low, egadless of adetsng costs, the standad esult n the lteatue peals t s always optmal fo each m to adetse moe n ts stong segment than n ts weak segment. When the attacteness of the weak segment s hgh enough, the two equlbum outcomes ae possble: each m pefes to adetse moe ntensely n ts weak segment when adetsng costs ae su cently low; the eese happens when adetsng costs ae hgh (Poposton 3). Ths esult allows us to pode a theoetcal stategc atonale fo the nceasngly popula geo-conquestng adetsng stateges: by adetsng less ntensely n ts stong maket, each m ntes the al to play less aggessely n that maket. The pape also nestgates what changes n tems of tageted adetsng decsons and equlbum po ts when ms moe fom a wold of unfom pcng to one wth pce dscmnaton. In patcula, the esult of geate adetsng to the weak maket only ases n the equlbum 5 The Wall Steet Jounal efeed that seach engnes allow ms to bd on an adesay s tademaked seach tems. A ecent seach fo "Taco Bell" on Google, fo example, eealed a sponsoed lnk adetsng Wendy s new steakhouse double melt sandwch. See 4

5 wth pce dscmnaton. Wth unfom pcng, each ms always pefes to adetse moe ntensely n ts stong maket. Fnally, the pape also shows that pce dscmnaton by means of tageted adetsng can boost ms po ts and so t does not necessaly lead to the classc psone dlemma obtaned n the compette pce dscmnaton lteatue. Ths pape s manly elated to two stands of the lteatue, the lteatue on competton wth nfomate tageted adetsng and the lteatue on pce dscmnaton based on custome ecognton. We contbute to these stands of the lteatue by lookng at the ms tageted adetsng and pcng decsons egadng the stong and weak segment of consumes. Galeott and Moaga-Gonzalez (2008) and Bahm et al. (20) hae also looked at ths ssue n the wold of tageted adetsng and unfom pcng. In these papes, wthout adetsng consumes stay out of the maket. Galeott and Moaga-Gonzalez (2008) look at the ms adetsng and pcng stateges n a homogeneous poduct maket, whee one of the maket segments s exogenously moe po table than the othe. Bahm et al. (20) also nestgate the po t e ects of tageted adetsng n a Hotellng competton model wth no pce dscmnaton. Both papes show that ms adetse moe ntensely to the stong makets than to the weak makets. Ou analyss s moe closely elated to Iye et al. (2005). They chaacteze a d eentated maket n a Vaan (980) type set-up: the maket s exogenously segmented between capte consumes and compason shoppes. When ms decde to adetse to a spec c segment they nfom the whole segment. They show that, poded all consumes eman unnfomed wthout adetsng, ms wll always adetse moe healy to the hgh pefeence segment than to compason shoppes. 6 By dong so, ms stategcally aod Betand competton n ths weak maket. Fnally, Iye et al. (2005) also compae ms tageted adetsng decsons unde unfom pcng esus pce dscmnaton. In the settng pce dscmnaton does not a ect the adetsng ntensty tageted to each segment of the maket nethe the m s po ts. Thus, the pesent pape complements Iye et al. (2005) by studyng tageted adetsng and pcng wth a d eent demand stuctue. In dong so, new nsghts can be obtaned egadng 6 It s mpotant to stess that moe adetsng to compason shoppes (weak segment) can also ase n Iye et al. (2005) when a sgn cant popoton of consumes n the stong segment (who ae capte) ae aleady nfomed about the m s exstence. The hghe s the popoton of exogenous nfomed (stong) consumes the lowe s the ncente of ms to employ costly adetsng to the stong segment. Howee, n the set-up, as long as ths popoton s equal to zeo,.e., wthout adetsng consumes stay out of the maket (lke n ou settng), the esult of moe adetsng n a m s weak segment nee ases n equlbum. 5

6 the ms adetsng stateges and the mpact of pce dscmnaton on m s adetsng stateges and po ts. An mpotant d eence between ou wok and thes les on the behao of loyal consumes (those wth a stong pefeence fo a band). Whle Iye et al. (2005) assume that loyal consumes always buy fom the faote band (egadless of the pce of the al band), we assume that consumes n a cetan maket segment pefe the coespondng band by a cetan amount but they ae wllng to consde buyng the al band f the pce d eence s conduce. Ths assumpton s consstent wth empcal esults showng that consumes may swtch bands fo pcng easons (see, e.g., Keaeney, 995, Bolton and Lemon, 999). Kshnamuth and Raj (99) nd that loyals ae less pce senste than nonloyals n the choce decson but they stll eact to pce changes. Second, n ou set-up, ms adetsng decsons endogenously segment the maket nto capte (patally nfomed) consumes and selecte (fully nfomed) consumes. 7 In lght of ths, we nd that n makets whee consumes ae unnfomed wthout adetsng, the equlbum outcome may poduce moe adetsng to weak makets. Ou explanaton s a stategc one, gen the demand fomulaton à la Shlony, the ms ablty to engage n pce dscmnaton and the nteplay between adetsng costs and the attacteness of the weak maket segment. Fnally, ths pape s also elated to the lteatue on compette pce dscmnaton wth custome ecognton (e.g. Chen, 997, Vllas-Boas, 999, Fudenbeg and Tole, 2000, and Estees, 200). 8 In these models t s geneally the case that the maket exhbts best-esponse asymmety (Cots, 998): the stong maket segment of one m s the weak maket segment of the competto. A common ndng n such models (wth symmetc ms and full nfomed consumes) s that ms chage lowe pces to customes n weak makets and, n compason to unfom pcng, equlbum po ts fall wth pce dscmnaton. 9 The est of ths pape s oganzed as follows. Secton 2 descbes the man ngedents of the model. Secton 3 analyses the equlbum adetsng and pcng stateges when ms can 7 Anothe d eence between ou demand stuctue and the one used n Iye et al. (2005) les on the exstence of a goup of pue swtches that hae no loyalty o pefeences fo the bands n the model. We hae analyzed how the exstence of a segment of swtches would a ect ou model of taget adetsng wth pce dscmnaton and we nd that ths change would not qualtately a ect ou esul that ms may adetse moe ntensely to the weak maket than to the stong maket. Poofs can be obtaned fom the authos upon equest. 8 See Fudenbeg and Vllas-Boas (2007) fo a compehense suey on ths lteatue. 9 Moe ecently, Chen and Peacy (200) and Shn and Sudh (200) hae shown that po ts can ncease wth pce dscmnaton, bascally when consume pefeences ae weakly coelated acoss tme as well as n the case of hgh enough consume heteogenety. 6

7 pce dscmnate though the use of pefect tageted adetsng. Secton 4 dees the ms equlbum adetsng and pcng stateges n the context of tageted adetsng but unfom pcng and compaes the ms adetsng stateges and oeall equlbum po ts n the two pce egmes. Secton 5 concludes and an appendx collects the poofs that wee omtted fom the text. 2 The Model Two ms A and B ae each launchng a new good, poduced at a constant magnal cost, whch s assumed to be zeo wthout loss of genealty. Thee s a lage numbe of potental buyes, wth mass nomalzed to one, each of whom wshes to buy a sngle unt of ethe good A o B. The set of potental buyes s composed of two dstnct segments of equal sze, half of consumes hae a elate pefeence fo poduct A, whle the emanng ones hae a elate pefeence fo poduct B. The consumes hae a common eseaton pce fo the goods but consumes n segment pefe poduct oe poduct j by a degee equal to > 0. As n Shlony (977), Raju et al. (990) and Estees (200), can be de ned as a measue of the degee of a consume s pefeence towads hs faote poduct. In a locaton ntepetaton, ths means that consumes can puchase costlessly fom the m n the neghbohood but they ncu a tanspot cost f they go to the moe dstant m. Thus, s the mnmum d eence between the pces of the two competng poducts that nduces consumes to buy fom the least pefeed m. Although ms may hae some adantage oe the compettos, due fo nstance to band loyalty o tanspot costs, all consumes may, n the end, be nduced to swtch. 0 In othe wods, each m has a stong and a weak segment of consumes. Fo m, segment s ts stong segment, whle segment j s ts weak segment, ; j = A; B and 6= j. Although consumes ae endowed wth pefeences oe the poducts, t s assumed that consumes ae ntally unnfomed about the exstence and the pce of the goods. Lke n Buttes (977) and Stahl (994), a potental consume cannot be an actual buye unless ms nest n adetsng. We assume that each m can send two types of ads: ads tageted to the stong segment of consumes and ads tageted to the weak segment of consumes. Wthn each 0 Fo example, Bynjolfsson and Smth (2000) hae found that Amazon customes ae wllng to pay up to 5-8 pecent moe befoe they consde swtchng to anothe selle. Gen ou motatng example (n the Intoducton), Buge Kng can assume that almost eeyone standng at the entance of a McDonald s stoe s a potental BK custome. Wth a geo-conquestng campagn BK can 7

8 segment, we assume that ads ae andomly dstbuted. Moeoe, all ads contan tuthful and complete nfomaton about the exstence and the pce of the goods. The game s statc and poceeds as follows. Fms choose adetsng ntenstes and pces smultaneously and non-coopeately. Fm s stategy then conssts of choosng an optmal adetsng each and an optmal pcng stategy to each segment of the maket. The adetsng ntenstes o and espectely denote the adetsng ntensty of m tageted to ts own (stong) maket and to the al s maket ( m s weak maket). Ads tageted to each segment announce d eent pces, espectely p o and p. The ms tagetng ablty s assumed to be pefect,.e. P(fall n jtageted to ) = whle P(fall n jtageted to j) = 0. Pefect adetsng tagetng s also assumed n Bahm et al. (20) o Galeott and Moaga-Gonzaléz (2008) and t means that thee s no leakage of ads between goups. Thus, consumes n segment wll only be awae (as long as nfomed) of p o and p j : The emanng pces, namely p and po j ; ae quoted n ads tageted to consumes n segment j. Afte ms hae sent the ads ndependently, some consumes wll be eached by one of the ms, by both ms o by none of them. In each segment of the maket, consumes can then be dded nto capte, selecte and unnfomed consumes. Spec cally, n segment, a popoton o and j of customes s eached, espectely, by m and j s ads. Some consumes ae capte to m, namely o j ; whle othes ae capte to m j; namely j ( o ) : Capte consumes ae only awae of one of the ms. They puchase the poduct they know as long as they obtan a non-negate suplus. To guaantee that ms can always see consumes n both maket segments, we need to mpose that > : The goup of selecte customes n segment, o j; ecee ads fom both ms. Hence, consumes n ths goup buy fom the m o eng them the hghest suplus. Fnally, n segment, thee s a goup of ( o ) j consumes who ecee none of the ads and so they ae excluded fom the maket. Fo p o ; the expected demand of m n ts stong maket, D o ; wtes as follows: D o = 2 o j + 2 o j P(p o < p j + ) : () Analogously, fo p, m s expected demand n ts weak maket, D ; s equal to: D = 2 o j + 2 o j P(p + < p o j) : (2) dele tageted ads wth d eent content to moble deces of consumes who ae nea the Mc s stoe (compaed to ads sent to consumes who ae nea ts stoe). 8

9 Adetsng s a costly actty fo ms. The adetsng technology s exogenously gen and t s the same fo both ms. In lne wth Iye et al. (2005), Galeott and Moaga-Gonzalez (2008) and Bahm et al. (20), we assume that the adetsng cost functon s addte sepaable n o and. We denote by A( k ) m s total cost of adetsng n segment k = fo; g : Followng the standad lteatue, we mpose A k > 0 and A k k 0; whee the subscpts stand fo patal deates. In what follows, whenee a functonal fom s needed, we consde that the cost of eachng a facton k of consumes s gen by the quadatc adetsng functon: A( k ) = k 2 : Snce we assume that thee s a lage numbe of buyes, nomalzed to unt, can be dent ed wth the cost pe ad. 3 Tageted Adetsng wth Pce Dscmnaton Fms make the adetsng and pcng choces smultaneously. To begn the analyss, we need to dee the expected po t of each m. Because thee s no leakage between segments, they ae completely ndependent. Fo a gen stategy of the al m, m s expected po t condtonal on ads and pces tageted to segment k = o; s denoted by E k whch s equal to: E k = p k D k A( k ): Fm chooses the adetsng leel ( k ) and the pce (p k ) to be tageted to segment k n ode to maxmze ts expected po t n ths segment. Snce a m cannot dentfy whethe o not a consume s eached by the al s adetsng campagn, when choosng the pcng stategy, each m takes nto account the tade-o between extactng suplus fom capte consumes and competng fo the goup of selecte consumes. Followng a smla easonng as n Vaan (980) and Naasmhan (988) t s staghtfowad to poe that thee s no Nash pce equlbum n pue stateges. Hence the pce equlbum wll be n mxed stateges. Popostons and 2 chaacteze a symmetc equlbum n mxed stateges n pces, wth the adetsng components to each segment of the maket beng chosen detemnstcally. Lemma establshes the suppot of ms equlbum pces n the stong makets,.e., [p o mn ; po max ]. Unde symmety the pce suppot n the weak maket s smply [p o mn ; p o max ] Lemma. De ne o and j to be, espectely, the equlbum adetsng ntenstes of m and m j tageted to segment : When o ; (3) j 9

10 the suppot of m s equlbum pce tageted to ts stong maket s [( ) ( o ) + ; ] : Howee, f condton (3)does not hold, m s equlbum pce suppot s ( j ); : Poof. See the Appendx. Lemma shows that the popetes of the equlbum depend on the paametes, and the adetsng costs (though condton (3)). Ths condton s endogenously detemned n ou model snce ms may stategcally manpulate the ato of consumes wth nfomaton about each poduct though the adetsng choces. In what follows, we wll pode a complete chaactezaton of the mxed stategy Nash equlbum. Fst, Poposton chaactezes the equlbum behao of ms when condton (3) n Lemma holds. Poposton. Thee s a symmetc Nash equlbum n whch: () Regadng the stong maket, m chooses a pce andomly fom the dstbuton F o (p) de ned n the Appendx wth suppot [( ) ( o ) + ; ] : Fo each tageted to the stong maket o s mplctly gen by o ; the adetsng 2 o ( ) = A o ( o ) wth A o (0) < : (4) 2 () Regadng the weak maket, m chooses a pce andomly fom the dstbuton F (p) de ned n the Appendx wth suppot [( ) ( o ); wth a densty equal to: m = o The adetsng each tageted to the weak maket whee A (0) < 2 o j 2 ( ) and ]. F (p) has a mass pont at : (5) s mplctly gen by ( ) o j = A ( ) ; (6) o : () Fm s equlbum po t n the stong and the weak makets ae: E o = o A o ( o ) + 2 (o ) 2 ( ) A ( o ) E = A ( ) A ( ) : Poof. See the Appendx. Poposton 2 now chaactezes the equlbum behao of ms when condton (3) n Lemma does not hold. 0

11 Poposton 2. Thee s a symmetc Nash equlbum n whch: () Regadng the stong maket, m chooses a pce andomly fom the dstbuton F o (p) de ned n the onlne Appendx wth suppot [( densty equal to m o = maket o o s mplctly gen by : Fo ); ]. F o (p) has a mass pont at wth a < o ; the adetsng each tageted to the stong ( j ) = A o 2 ( o ) wth A o (0) < : (7) 2 () Regadng the weak maket, m chooses a pce andomly fom the dstbuton F (p) de ned n the Appendx wth suppot [( ) ; ]. The adetsng each tageted to the weak maket s mplctly gen by ( ) = A ( ) and A 2 (0) < ( ) : (8) 2 () Fm s equlbum po t n the stong and the weak makets ae: E o = o A o ( o ) E = A o ( o ) A( o 2 ) A( ): Poof. See the Onlne Appendx. Compang Popostons and 2, we can see that dependng on the paametes ; and the leel of adetsng costs, ms optmal adetsng and pcng stateges wll d e. Fo the quadatc adetsng technology, the complete chaactezaton of the equlbum eques the dstncton between the cases () 2 (n whch the esults n Poposton yeld o ), and () < < 2 (n whch the equlbum behao s descbed n Poposton 2, nstead). In the est of the pape, we wll say that the elate attacteness of the weak maket s hgh when when s hgh ( hgh compaed to ); leadng to the esults n Poposton. In contast s low ( low compaed to ) we wll say that the elate attacteness of the weak maket s low, leadng to the esults n Poposton 2. A geneal esult of the model s that fo costless adetsng,.e. when! 0, egadless of the adetsng cost functon unde consdeaton, ms wll pode full nfomaton only to consumes n one of the maket segments. Spec cally, t s optmal fo each m to nfom all consumes n ts stong maket poded that the attacteness of the weak maket s low. The opposte esult s obtaned when the attacteness of the weak maket s hgh. In the latte case ( s hgh and Poposton holds) each m uses a H-Lo pcng stategy n ts weak

12 maket. When! 0, each m pefes to fully nfom consumes n ts weak maket segment,.e., =, whle n ts stong maket, t pefes to leae some consumes unnfomed, yeldng o < = : Each m, by appeang weak n ts stong maket ( o < ) ntes the al to play less aggessely n that maket, mtgatng pce competton n that segment. When, say m ; educes the adetsng ntensty tageted to ts stong maket t nduces the al ( m j) to play less aggessely n that maket ( m j s weak maket) as t nceases the lkelhood that m j quotes the monopoly pce n the ads tageted to segment (ecall that m s deceasng n o ). Moeoe, t also nceases p j mn = ( ) ( o ). In contast, when s low (Poposton 2 holds), each m uses nstead a H-Lo pcng stategy n ts own stong maket, quotng the hghest pce ; wth a stctly poste pobablty m o ; whch s nceasng n o and deceasng n : When! 0; t s staghtfowad to see that < o =. Now each m ntends to mtgate pce competton n ts weak maket. When say m educes the adetsng ntensty tageted to ts weak maket t nduces the al ( m j) to play less aggessely n that maket ( m j s stong maket) snce by dong so t nceases the lkelhood of m j announcng pce n ads tageted to segment j (due to m o ). Moeoe, a educton on also ases p o mn = ( )). 3. Optmal Adetsng Stateges When consumes ae unnfomed about the poduct f they ae not exposed to adetsng, an mpotant queston that ms face n desgnng the adetsng stateges s how should the adetsng budgets be allocated between stong and weak custome segments. In ths secton, we nestgate n whch ccumstances t s optmal to a m to adetse moe ntensely n ts stong maket o athe to adetse moe ntensely n ts weak maket. In what follows we use the quadatc adetsng cost functon. Consde st the case whee 2: Fom Poposton and Lemma, t s staghtfowad to obtan that the equlbum adetsng ntensty tageted to the stong maket s gen by equaton (4) yeldng: o = ( ) : (9) Fom equaton (6), the equlbum adetsng ntensty tageted to the weak maket s equal to: 8 < = : q f q f < : (0) 2

13 When < 2; fo a quadatc adetsng technology, Poposton 2 holds. The equlbum adetsng ntensty tageted to the stong maket s then gen by equaton (7) yeldng: = ; () and the equlbum adetsng ntensty tageted to the weak maket s gen by equaton (8) yeldng: 8 >< o = >: q f f < 8 q 5+4 : (2) The next poposton summazes ou man ndngs egadng the ms optmal adetsng stateges, fo the quadatc adetsng cost functon. Poposton 3. () When < 2, egadless of the magntude of adetsng costs, each m always adetses moe ntensely n ts stong segment than n ts weak segment,.e. o > > 0: () When 2, each m adetses moe ntensely n ts weak segment than n ts stong one ( > o > 0) when adetsng costs ae low.e., when < = When the eese happens, thus o. ( 2)( ) 4. Poof. See the Appendx. Poposton 3 shows that pefect maket segmentaton n whch ms would send ads only to the hgh pefeence segments ( o = and = 0) nee ases n the pce dscmnaton equlbum. In fact, ms always choose to adetse to both segments of the maket. Pat () of Poposton 3 pedcts that t s always optmal fo each m to adetse moe healy to ts stong maket elate to ts weak maket when the attacteness of the weak maket s low ( low), egadless of the adetsng cost leel. The atonale behnd ths esult s that by appeang weak n ts weak maket (low compaed to o j) m ntes the al ( m j) to play less aggessely n that maket (.e., j s stong maket). Moe nteestngly, pat () of Poposton 3 hghlghts that when s hgh, the standad esult n the lteatue.e., o > only ases n equlbum f adetsng costs ae hgh enough. If s su cently low, then n equlbum, each m pefes to adetse moe ntensely n ts weak segment of the maket than n ts stong segment. To the best of ou knowledge ths 3

14 s a new esult n the context of makets n whch consumes only get nfomaton about the poduct when exposed to adetsng. 2 When s ths stategy of sendng less ads to a m s stong maket (than to ts weak maket) po table? 3 Fo ths esult to occu the weak maket segment needs to be su cently attacte ( hgh compaed to ) and adetsng must be su cently cheap. In fact, when j > o ; each m nceases the chances of gettng capte consumes n ts weak maket and t stategcally ntes the al to play less aggessely n ts own stong maket. Although the latte e ect s clealy bene cal to both ms, the lowe adetsng ntensty n a m s stong maket mples that each m s leang some of ts stong customes unnfomed, whch epesents a loss of eenue. In lght of ths tade-o, the stategy o < s only po table when the followng condtons hold. Fst, een f the numbe of consumes each m sees n ts stong maket s lowe (gen the lowe adetsng ntensty), the pce ms can chage n the maket must be hgh enough ( hgh enough). Secondly, tagetng the weak maket must not be too costly ( needs to be low enough so that poachng consumes n the weak maket s not too costly). Fnally, adetsng costs need to be su cently low (low ) so that ms adetse ntensely enough n the weake maket to geneate a su cent numbe of consumes hee to make up fo the loss of eenue fom the stonge maket, n whch the ms stategcally educe the adetsng ntensty n ode to dampen pce competton. In sum, poded hgh, the stategy o < woks only when adetsng costs ae low enough. s su cently Befoe poceedng t s useful to compae ou esults wth those obtaned n Iye et al. (2005) fo the case n whch wthout adetsng consumes stay out of the maket. In the model each m has an exogenous goup of capte consumes and both ms compete à la Betand fo the compason shoppes (selecte). In ths famewok, they show that when adetsng s the only souce of consumes nfomaton then ms wll always adetse moe n the stong segment than n the weak segment (compason shoppes). The eason s that unde tageted adetsng and pce dscmnaton each m enjoys a monopoly powe oe ts capte con- 2 As sad n footnote 6, moe adetsng to compason shoppes (weak segment) can also ase n Iye et al. (2005) when a sgn cant popoton of consumes n the stong segment (who ae capte) ae aleady nfomed about the m s exstence. The hghe s the popoton of exogenously nfomed (stong) consumes the lowe s the ncente of ms to employ costly adetsng to the stong segment. Howee, n the set-up, as long as wthout adetsng consumes stay out of the maket (lke n ou settng), the esult of moe adetsng n a m s weak segment no longe ases n equlbum. 3 We thank a efeeee fo ugng us to thnk n ths way. 4

15 sumes and by educng the ntensty of adetsng to the shoppes, ms stategcally dampen pce competton n the shoppes segment. Ou model consdes a d eent demand stuctue (Shlony type) and the goup of capte and selecte consumes s endogenously detemned by the ms adetsng decsons. Thus ou analyss complements Iye et al. (2005), by podng a complete pctue of the maket featues that can explan the two possble adetsng outcomes, n makets easonably well epesented by ou model assumptons. We suggest that t can be optmal fo ms to adetse moe ntensely n the stong segment than n the weak segment n ndustes whee: () whatee the magntude of adetsng costs, the attacteness of the weak segment s low, and () the attacteness of the weak segment s hgh and adetsng costs ae su cently hgh. In contast, t can be optmal fo ms to adetse less ntensely to the stong than to the weak segment n makets whee the attacteness of the weak segment s hgh enough and adetsng s su cently cheap (o costless). 4 Theefoe, when 2; the model pedcts that an ndusty shock n the fom of lowe adetsng costs, may completely alte ms optmal adetsng ntenstes to each segment of the maket. Fnally, t s woth notng that ou esults shed some lght on a theoetcal stategc atonale behnd the use of geo-conquestng adetsng stateges, whch ae becomng nceasngly popula n sectos lke estauants, etal, nancal seces/nsuance, tael, gas & conenence stoes. In patcula, the equlbum outcome n whch o < suggests that n some ndustes we mght een see manages spendng moe money on geo-conquestng adetsng campagns than on tadtonal geo-fencng adetsng. 3.2 Pces Anothe mpotant queston that ms face today (when pce dscmnaton s possble) s whethe they should taget lowe pces to the hgh pefeence customes o athe to the low pefeence customes. Most of the exstng academc lteatue suggests that when the maket exhbts best-esponse asymmety one m s weak maket s the othe s stong maket the optmal choce fo each m s to o e a lowe pce to ts low pefeence consumes than to ts hgh pefeence consumes (e.g. Chen, 997; Vllas-Boas, 999; Fudenbeg and Tole, 2000; 4 Ou peous dscusson on the costless adetsng case eeals that ou ndngs ae obust to altenate fomulatons of the adetsng cost functon. We hae checked ths fo a lnea adetsng cost functon A( k ) = k. Usng equatons (4) and (6), fo > 2 and < ; we get 0 < 2 o < and = ; yeldng > o : 5

16 Estees, 200). 5 In ou set-up, the ms dscmnatoy pces ae a ected by the paametes ; and. As the most nteestng outcome of the pape ases when Poposton holds, we be y dscuss how adetsng costs a ect each m s pce decsons to each segment of the maket when 2. Let E(p o ) and E(p ) (computed n the onlne appendx) denote the expected pces announced n ads tageted to the stong and to the weak segments, espectely. We nd that t can be optmal fo each m to ewad ts stong customes athe than ts weak customes (see the Onlne Appendx). Spec cally, when s su cently low (.e., when < mplyng > o (see Poposton 3)), gen the symmety of the model, each m has a hghe popoton of capte consumes n ts weak maket than n ts stong maket. Moeoe, accodng to Poposton each m uses a H-Lo pcng stategy n ts weak maket. In patcula, the lowe s ; the hghe s the lkelhood that an ad tageted to a m s weak maket announces the pce (whch ases E(p )). At the same tme, each m has moe ncentes to compete fo the goup of selecte consumes n ts stong maket, by o eng them a compellng enough pce (whch educes E(p )). Thus, as shown n the onlne appendx, thee s a doman of paametes fo whch E(p o ) s lowe than E(p ). In ou model, the stategy of chagng less to consumes n a m s stong maket woks only when the adetsng costs ae low enough. As adetsng becomes moe expense, the outcome o > s obtaned. In ths case, a smla (but opposte) agument explans why t s optmal fo each m to ewad consumes n ts weak maket, yeldng the standad esult n the lteatue. 4 Compang Tageted Adetsng and Pce Dscmnaton wth Tageted Adetsng and Unfom Pcng In ths secton we examne how the ms adetsng decsons to each segment of the maket and expected equlbum po ts ae a ected by the ablty to pce dscmnate. Wth ths goal n mnd, we dee the equlbum outcomes n the benchmak case whee ms hae the ablty to taget adetsng but can only compete wth unfom pcng stateges. In ths case, thee ae two components to m s stategy: ts adetsng leel to each segment of the maket ( ou and u ) and ts unfom pce (p u ). Poposton 4 chaactezes the equlbum outcomes 5 An excepton s Shn and Sudh (200) who show that ms can chage a low pce to the stong customes when consume pefeences stochastcty acoss tme and consume heteogenety ae smultaneously hgh enough. 6

17 fo the quadatc adetsng cost functon. Poposton 4 () Fo < When adetsng can be tageted and pce dscmnaton s not pemtted: 2 + p 2 the pa of pces (; ) s an equlbum n pue stateges and the coespondng adetsng leels ae u ae u = 2 6 : = 0 and ou = 4 ; wth < 4 : Equlbum po ts () Fo 2 + p 2 and su cently hgh (.e. > e, whose alue s de ned n the onlne Appendx), the pa of pces ( ; ) s an equlbum n pue stateges and the coespondng adetsng leels ae ou = 4 ; wth > 4 and u Equlbum po ts ae u = ( )2 [( 4 ) ] : () Fo = ( )(4+ ) p 2 and < e the pce equlbum s n mxed stateges and the coespondng adetsng leels ae ou = u = +4 : The expected equlbum po ts ae E u = 2( )2 (+4 ) 2 : Poof. See the Onlne Appendx. Poposton 4 shows that ou > u n cases ()-() and ou = u n case (). These esults con m the standad pedctons n the lteatue nestgatng the ms optmal allocaton of adetsng budgets. These ndngs also show that n ou famewok the esult of moe adetsng to the weak maket can only ase n equlbum f ms can engage n pce dscmnaton. We now be y dscuss the esults obtaned unde unfom pcng. If, fo any eason, pce dscmnaton s not pemtted, when a m adetses a lowe pce, as a way to see consumes n both segments of the maket, t foegoes some po ts fom ts stong segment. Not supsngly, when the attacteness of the weak maket s low ( s low), each m decdes to adetse ts poduct only to ts stong maket, gnong the weak maket. In ths case, both ms behae as monopolsts n the own stong makets, chagng a pce equal to. As the eseaton pce nceases compaed to, the same happens to the po ts that ms can possbly ean by educng the pce and captung addtonal consumes. In fact, as long as the condton ( ) u ou j ou u 0 holds at equlbum, each m has an ncente j to taget ads wth the same pce to both segments of the maket. When s hgh enough, the pce equlbum ( ; ) descbed n case () n Poposton 4 ases, as long as > : e Both ms adetse moe ntensely to the stong than to the weak maket segments. Moe 7

18 pecsely, each m sees all the nfomed consumes n ts stong maket and the capte consumes n the weak maket. Snce the weak maket segment s attacte ( s hgh), fo ths case to ase, the adetsng costs must be su cently hgh ( > e ) so that ms efan fom competng fo the selecte consumes. When s hgh but adetsng s su cently cheap (small ), selecte consumes n the weak segment hae a non-neglgble mpact on ms po t. Then, each m s pce equlbum s n mxed stateges as an attempt to peent the al fom systematcally pedctng ts pce. The expected equlbum po t s the guaanteed po t a m can ealze by chagng the eseaton pce p u max = and sellng only to the goup of capte consumes n each maket. Snce ; ms teat the two maket segments n the same way. Not supsngly, ms send the same adetsng ntensty to the stong and the weak segments. Moe pecsely, ms adetse up to the pont whee the cost of the last ad sent to each segment equals the expected eenue of a sale at the hghest pce to an unnfomed consume,.e., Theefoe, t s staghtfowad to see that ou = u. k ( )( j ) = A ( k ); k = o; : (3) 2 4. E ects of Pce Dscmnaton on Adetsng Stateges and Po ts Impotant questons fo maketng scholas and pacttones ae the followng. Does the ablty to pce dscmnate change the ntensty of adetsng tageted to each segment of the maket? What s the mpact of pce dscmnaton on ms equlbum po ts? We shed lght on these questons compang the esults of the model wth pce dscmnaton to the benchmak model of tageted adetsng wth unfom pcng. We look at d eent maket enonments, namely those whee the attacteness of the weak maket s low/hgh combned wth low/hgh adetsng costs. 6 Fo the subsequent dscusson, let od and d denote the equlbum ntensty of adetsng tageted espectely to the m s own stong maket and to the al s maket when pce dscmnaton s allowed. Consde st the case whee the attacteness of the weak maket s su cently low such that ms behae as n Poposton 2 unde pce dscmnaton and as n pat () of Poposton 4 unde unfom pcng. In ths doman of paametes, ms choose to exclusely see the 6 Although the poofs of the man conclusons ae staghtfowad, the nteested eade can obtan them fom the authos upon equest. 8

19 stong maket only when they adopt unfom pcng. Unde pce dscmnaton, ms no longe gnoe the weak maket. Moeoe, fo < 2; t s staghtfowad to poe that mong fom unfom pcng to pce dscmnaton educes the ntensty of adetsng tageted to the stong maket and nceases the ntensty of adetsng tageted to the weak maket,.e. od < ou and d > u = 0: Regadng the e ect of pce dscmnaton on po ts, we nd that po ts ncease when ms become able to talo d eent pces to the hgh and low pefeence segments. Bascally, the ncease n po ts s due to a demand expanson e ect that moe than compensates the negate e ect of pce competton n both segments of the maket. Theefoe, n makets whee s low, pce dscmnaton s a po table stategy egadless the leel of adetsng costs. Consde next those makets whee the attacteness of the weak segment s hgh. Hee conclusons egadng the adetsng and po t e ects of pce dscmnaton ae less clea cut because we need to take nto account whethe adetsng costs ae hgh o low. Suppose st that s hgh and adetsng costs ae su cently low ( < ) e so that ms behae as n Poposton, unde pce dscmnaton, and as n pat () of Poposton 4, unde unfom pcng. If < t follows that d > od (see Poposton 3). Moeoe, fo <, we also hae d > u and ou > od. The ntuton behnd ths esult s staghtfowad. Wth unfom pcng ms would teat the two maket segments n the same way,.e. ou = u : Howee, ths s not tue when ms engage n pce dscmnaton: poded adetsng costs ae su cently low, each m pefes to educe the adetsng ntensty tageted to ts stong maket, n ode to stategcally educe pce competton n that maket. Ths yelds od < ou : In the weak maket, compang equatons (6) and (3) we can see that pce dscmnaton does not dectly a ect each m s adetsng ntensty to the segment of low aluaton consumes. The e ect of pce dscmnaton on s only ndect, though ts mpact on each m s adetsng choce to the stong maket. Accodngly, when adetsng costs ae su cently low ( < ), compaed to unfom pcng, each m stategcally sends moe ads to the weak maket (and less ads to the stong maket) unde pce dscmnaton, wth d > od : Instead, when > ; mong fom unfom pcng to pce dscmnaton leads ms to send moe ads to the stong segment and less ads to the weak segment, wth ou < od and d < u. Fnally, when the attacteness of the weak maket s hgh and adetsng costs ae hgh enough ( > ), e so that ms behae as n pat () of Poposton 4 (n the case of unfom 9

20 pcng) and Poposton (n the case of pce dscmnaton), each m adetses moe n ts weak maket and less n ts stong maket unde pce dscmnaton than unde unfom pcng,.e. e < < b = 2 d > u and ou > od, poded that adetsng costs ae not too hgh (.e., ( ) 2 ). When >, b the opposte esult occus. The atonale behnd these esults s analogous to the one explaned aboe fo pat () of Poposton 4. We now dscuss the po t e ects of pce dscmnaton when the attacteness of the weak maket s hgh. When adetsng costs ae su cently low ( < ) oeall po t wth pce dscmnaton s always aboe ts countepat wth unfom pcng. 7 Accodngly, n ou setup, pce dscmnaton by means of tageted adetsng does not necessaly lead to the classc psone s dlemma esult obtaned n theoetcal models of compette pce dscmnaton. 8 In ou set-up, only when adetsng costs ae su cently hgh ( > ), a psones dlemma may occu, wth ms gettng lowe total po ts wth pce dscmnaton than wth unfom pcng due to the ntens caton of competton fo consumes n the weak maket segment. 9 The peous analyss hghlghts that pce dscmnaton can a ect the ms adetsng stateges and po ts. Ths d es fom Iye et al. (2005), who show that, n the case of a d eentated maket n a Vaan (980) type set-up, adetsng decsons and po ts do not change when ms moe fom tageted adetsng and unfom pcng to tageted adetsng wth pce dscmnaton. Summng up, the pape also contbutes to the ongong debate on the po t mplcatons of new foms of pce dscmnaton, only made possble n the context of dgtal makets. We nd that ms can be bette o wth pce dscmnaton n makets whee: () the attacteness of the weak maket s low, egadless the adetsng costs and () the attacteness of the 7 Note that E d = E o + E ; wth E o = 2 ; 8(+2 ) E = and 8 +2 E u 2( )2 = : (+4 ) 2 8 Estees (200) shows that f consumes ae fully nfomed about the ms exstence and ms can talo d eent pces to the weak and stong segments, Betand competton n each segment of the maket leads to equlbum pces to p o = and p = 0: 9 If we look at the mpact of pce dscmnaton on po ts pe segment, t s staghtfowad to poe that pce dscmnaton ases po ts n the stong maket. Ths s bascally due to the ncease n pces when ms engage n pce dscmnaton. We nd that the expected po t n the weak maket segment s hghe unde pce dscmnaton than unde unfom pcng f < : Inteestngly, when adetsng costs ae low, expected po ts n the weak maket ae hghe unde pce dscmnaton than unde unfom pcng due to a demand expanson e ect (ecall that d > u fo < ). Fo < ; ms stategc adetsng choces also soften pce competton, faong po ts unde pce dscmnaton s-à-s the stuaton wth unfom pcng. smla but opposte agument holds when > : A 20

21 weak maket s hgh and adetsng costs ae su cently low. In contast, ms ae wose o wth pce dscmnaton when the attacteness of the weak maket s hgh and adetsng s expense. 5 Conclusons Ths pape podes useful mplcatons fo manages and maketng pacttones deelopng tageted adetsng stateges. It addesses the followng questons: In whch ccumstances should a m spend moe n adetsng to the low pefeence customes segment (geo-conquestng) than to the stong segment? Unde pce dscmnaton, whch segment of customes should be ewaded? Is pce dscmnaton wth tageted adetsng po table? Regadng the st queston, the pape shows that dependng on the attacteness of the weak maket and the magntude of adetsng costs (hgh/low) t may be optmal fo each m to adetse moe ntensely n ts stong maket (standad esult n the lteatue) o to adetse moe ntensely n ts weak maket. The st esult peals when the attacteness of weak maket s low (egadless of the adetsng costs) and when the attacteness of the weak maket s hgh but adetsng costs ae hgh. The eason behnd ths esult s each ms attempt to mtgate pce competton n ts weak maket. We add to the lteatue a new esult: n a set-up n whch consumes eman unnfomed wthout adetsng, t can be optmal fo each m to adetse moe ntensely n ts weak than n ts stong segment. Ths stategy s po table when the attacteness of the weak maket s hgh enough and adetsng s su cently cheap. In ths case, each m stategcally educes the ntensty of adetsng tageted to ts stong maket as a way to dampen pce competton n that segment. The pape also sheds lght on the key ole that pce dscmnaton can hae both on the ms adetsng choces to each segment of the maket and on the ms equlbum po ts (compaed to a wold of tageted adetsng and unfom pcng). Indeed, moe adetsng to the weak maket can only ase n equlbum f ms hae the ablty to taget smultaneously both pce and adetsng content. The model also podes useful nsghts egadng the po tablty of pce dscmnaton though tageted adetsng, dentfyng the maket featues fo whch pce dscmnaton boosts ms equlbum po ts. Spec cally, ms can be bette o unde pce dscmnaton than unde unfom pcng n makets whee: () the attacteness of the weak maket s 2

22 low (egadless the adetsng costs) and () the attacteness of the weak maket s hgh and adetsng costs ae su cently low. When adetsng costs ae su cently hgh, pce dscmnaton s bad fo po ts. Notwthstandng the model addessed n ths pape s fa fom coeng all complex aspects of eal makets, t podes a theoetcal stategc atonale fo the nceasngly popula geo-conquestng and adetsng/pce dscmnaton stateges only possble n the context of dgtal makets. When ms hae the possblty of tagetng ads and pces to d eent maket segments, the model suggests that as adetsng costs wthn an ndusty fall, manages mght nd good easons to ase the adetsng budgets allocated to geo-conquestng stateges. As the theoetcal model podes empcally testable hypotheses, we hope t can be used fo futhe empcal eseach. Appendx Poof of Lemma. De ne o and to be the equlbum adetsng stateges of m as functons of ; and adetsng costs and let us analyze the pce suppot of m n ts stong maket segment. Hee, m can always guaantee a po t equal to the one obtaned when t sees ts capte consumes at pce : Fomally, 2 po mn o 2 o ( j ) ) p o mn ( j ) (4) Moeoe, t s a domnated stategy fo m to pce below p j mn + : Snce p j mn ( ) ( o ); t must be the case that p o mn ( ) ( o ) + : (5) The nfeo suppot of the pce dstbuton of m s gen by the lowest pce smultaneously satsfyng condtons (4) and (5). As the maxmum pce m s wllng to chage s equal to ; we obtan that the pce suppot of m n ts stong maket s gen by [( ) ( o ) + ; ] fo o j n the stong maket s gen by ( : Instead, when j ); < o j ; the pce suppot of m 22

23 Poof of Poposton. As we focus on symmetc MSNE n pces, the c.d.f. ae such that FA o(p) = F B o (p) = F o (p) ; and FB (p) = F A (p) = F (p) : Fo the sake of smplcty, wth no loss of genealty, we estct ou attenton to ms decsons n segment A; obtanng FA o(p) = F o (p) and FB (p) = F (p) : Gen ms pcng and adetsng stateges tageted to segment A, ms expected po ts n ths segment ae espectely Recall that fo E A = 2 o Ap o A f B + B [ F B(p o A )]g A ( o A) ; and E B = 2 Bp B f o A + o A [ F o A (p B + )]g A ( B) : o A ; the suppot of the equlbum pces fo m A s [( ) ( o B A ) + ; ] whle fo m B s [( ) ( o A ); ] ; snce p B mn = ( ) ( o A ): As usual n a MSNE each m must be nd eent between chagng any pce n the suppot of equlbum pces. Fo m B we must obsee that fo any p B mn p B : 2 p B B f( o A) + o A [ F o A (p B + )]g = 2 ( ) B( o A) whch mples that, n equlbum, 8 >< FA o (p) = >: h o A 0 f p p B mn + A ) f p B mn + p ( )( o p f p 9 >= : >; Analogously, fo m A we must obsee that fo any p B mn + po A : E o A = 2 po A o A f( B) + B [ F B(p o A )]g = 2 (p B mn + ) o A (6) Thus, n equlbum the coespondng dstbuton s 8 0 f p p >< B mn FB(p) ( = o A )+ o A B p+ f p B mn p >: f p 9 >= : (7) >; F ( Note that F ( o j ) = o : Snce ths Poposton s ald fo o A ;we obtan B ) s smalle than ; mplyng that F has a mass pont at ( ) equal to m = : The expected po t obtaned by m A n maket a when t chages any pce n the suppot of equlbum pces s equal to E A = 2 o A [ ( ) o A ] A (o A ) : The po t-maxmzng adetsng ntensty of m A n ts stong maket s then obtaned fom 23