Infomtion Eonomi nd Poliy 24 (2012) 173 186 Content lit vilble t SiVee SieneDiet Infomtion Eonomi nd Poliy ounl homepge: www.elevie.om/lote/iep Uing unenoed ommunition hnnel to divet pm tffi Benmin Chio, Jeffey MKie-Mon Key Lbotoy of Mthemtil Eonomi (SUFE), Minity of Edution, nd Shnghi Univeity of Finne nd Eonomi, Shnghi 200433, Chin Shool of Infomtion, Univ. of Mihign, Ann Abo, MI 48109, United Stte tile info btt Atile hitoy: Reeived 14 Otobe 2011 Reeived in evied fom 5 July 2012 Aepted 23 July 2012 Avilble online 8 Augut 2012 JEL lifition: L86 L96 Keywod: Spm Communition Mket deign We nlyze imple, feible impovement to the uent emil ytem uing n unenoed (open) ommunition hnnel. Suh hnnel ould be n emil folde o ount, to whih popely tgged ommeil oliittion e outed without filteing long the wy. We hteize the iumtne unde whih ende would voluntily move muh of thei pm into the open hnnel, leving the tditionl emil hnnel dominted by peon-to-peon mil. We then how tht unde etin ondition ll emil eipient e bette off when n open hnnel i intodued. Only eipient wnting pm will ue the open hnnel enoying the le diguied mege nd hepe le pie, nd fo ll eipient the ditiftion oited with both undeible mil eeived nd deible mil filteed out deee. Ó 2012 Elevie B.V. All ight eeved. 1. Intodution We identify ptiul (but pevlent) ubpeie of pm, nlyze it eology, nd popoe mehnim tht my inee oil welfe ubtntilly by modifying the flow of thi type of pm. We lo ly goundwok fo ytemti modeling of pm, nd the onequent development of olution tht e effetive beue they dde eonomi fetue of the poblem. We nlyze imple, feible impovement to the uent emil ytem uing n unenoed (open) ommunition hnnel. Suh hnnel ould be n emil folde o ount, to whih popely tgged ommeil oliittion e outed without ny bloking o filteing long the wy. In lte 2009, the lget emil evie povide in Chin, NetEe (with 285 million ount), implemented n nti-pm mehnim vey imil to the one Coeponding utho. E-mil dde: benmin.hio@gmil.om (B. Chio). we popoe. 1 Any ende n put the tg [d] on the emil ubet hede, nd NetEe will utomtilly delive the emil to folde lled the Advetiement Folde. We ll eeive pm; we ll eent it. Jutie Potte Stewt, wee he live, would know it when he w it. Nonethele, it i hd to find onenu definition of pm. 2 We define pm bulk, unoliited, ommeil emil; tht i, effetively identil (but uully ndomly diguied) mege ent unoliited to lge numbe of eipient with the gol of induing willing, mutully-benefiil puhe by the eipient. With thi definition we will ll it pm fo onveniene, but it meely one ubpeie we ule out 1 We do not lim tht NetEe obtined ide fom u, but ou wok w pio: we peented n initil veion t the TPRC Confeene (Alexndi, Vigini) in 2006. 2 Some wnt to inlude ll unoliited ommeil emil; othe only unoliited bulk emil; othe ditinguih between deeptive, infomtive o mliiou emil. We hould not be upied, then, tht it i lo hd to find ytemti nlye of the pm poblem, when thee e o mny notion of wht pm i. 0167-6245/$ - ee font mtte Ó 2012 Elevie B.V. All ight eeved. http://dx.doi.og/10.1016/.infoeopol.2012.07.001
174 B. Chio, J. MKie-Mon / Infomtion Eonomi nd Poliy 24 (2012) 173 186 othe ubpeie. 3 Defined we hve done, pm i n intne of diffeently-nmed, well-known phenomenon: dvetiing. 4,5 To develop ytemti nlyi of (non-deeptive, non-mliiou) ommeil pm, we need gounding piniple. We find tht upiing inight follow fom dopting ut two fmili, imple eonomi piniple: Reveled pefeene. Thee i non-tivil demnd fo the eeipt of pm emil. Rtionl hoie. Spm puveyo will end pm mege to whomeve, wheeve, wheneve, long the expeted benefit exeed the expeted ot. We expet tht only the fit piniple will ie mny eyebow t fit, but we find tht the eond piniple onitently h been hlf-ignoed in mot pio litetue on the pm poblem. Fit, demnd. Spm i not otle to genete o delive, depite ul lim to the onty. 6 While the eveled demnd ould enomp ome puiou demnd indued by mliiou o deeptive d (e.g., fo fke Vig), ome potion of the eveled demnd i likely to be el. Few buye will believe tht $50 Rolex i uthenti. 7 In ny 3 We ule out: mliiou bulk unoliited emil (e.g., emil ying viu pylod); deeptive emil (e.g., phihing mege tht ttempt to tik eipient into eveling vluble peonl infomtion uh bnk pwod); nd emil (though initilly unoliited) ent to miling lit, fom whih one ould unubibe. Wht we ule out i not inignifint; we ut tke ou definition tting point nd leve the tudy of othe emil poblem fo futue eeh. We do doument tht ommeil pm i the mot pevlent fom. And we hve nlyzed how ome of ou eult hnge when the popotion of mliiou nd deeptive emil hnge. 4 Sevel tudie hve imilly dopted view tht ome pm mege e eentilly pomotionl mege tht my bing onumption benefit to onume. See, fo exmple, Andeon nd De Plm (2009), Hnn et l. (2008), nd vn ndt (2004). In ddition, Andeon nd De Plm (2012) point out tht infomtion ovelod fll mot on podut tegoie with low infomtion tnmiion ot nd low pofit. 5 Uing the le-peotive monike emil dvetiing might give u good tt on thoughtful, ytemti onidetion; etinly, it might help u eognize tht t let thi type of pm i not pe e evil o molly defiient (though, with ny dvetiing, ome popultion ubgoup might onlude tht the podut dvetied might fil tht goup molity tet). Nonethele, we will ue ommeil pm o ut pm fo hot, beue we elih the poweful ffetive epone the tem eeive, nd the oppotunity to puntue the peotive bubble it engende. 6 It i tue tht eplition nd tnpot ot e extemely low, omped to non-digitl dvetiing hnnel. But thee e numbe of othe ot: mketing nd ontting ot with dvetie, ontent etion ot, ontent diguiing ot (to get pt tehnologil filte), ditibution tehnology ot (mot pm i now ent out by viu-eted pmbot unning on mny mhine not owned by the pm povide; thee botnet need to be ontinuouly egeneted, whih equie developing new viue to ditibute, mong othe thing). Thee my lo be the ot of expeted legl penltie. Given the non-zeo ot of poviding pmming evie, nd with ou ope limited to ut ommeil pm, fom whih the benefit to the ende i the induement of willing puhe by eipient, we mut onlude the following: by eveled pefeene, thee i non-tivil demnd fo the eeipt of pm emil. Some onenting dult mut be puhing enough Rolex knokoff nd ountefeit podut to py the pmme ot. 7 Thee my be deepe iue fo ome mileding d: fom neutl oil welfe pepetive it my not be ppopite to tet ome miled demnd puiou. Fo exmple, inet imittion Vig my povide deible (plebo) effet imply beue people think it wok. e, we do not ule out puiou demnd. Rthe, we imply nlyze the potentil of ou popoed mehnim to edue non-puiou demnd fo bulk emil dvetiing. We do not lim tht thi mehnim i likely to lo eliminte deeptive d fom the inbox. To motivte nd lify ou ope, we peent ome infoml evidene. Suh evidene i onitent with ou lim tht thee i non-tivil demnd fo muh pm: Cno nd LMhi (1998) how tht the lget ftion of pm ontent i ommeil dvetiing fo podut hd to find though othe dvetiing hnnel. Sopho (2005) find tht thi ptten ontinue; fo exmple, in 2005 medition pm ontitute ound 40% of ll pm, nd dult ontent fo nothe 10 20%. Evett (2006) etimte tht podut pm ontitute ound 25% of ll pm, nd dult ontent fo nothe 19%. 8 We expet thee will lwy be ignifint demnd fo puh dvetiing in ddition to pull (eh-bed) dvetiing. 9,10 Reognizing tht ome eipient wnt to ed pm, while mny othe evidently do not, we immeditely ee tht one oppotunity fo oil welfe impovement i to find wy to mth ommeil pm to thoe who wnt it, nd not to thoe who do not. The ltte emil ede would benefit, nd pm ende would lo benefit by not inuing the ot of ending to people who will not puhe. A oolly, we expet the willing eipient of ommeil pm to benefit well: if pmme n find wy to end to thoe who e inteeted in eeiving the dvetiement, then they n edue thei ot nd inee the infomtion ontent nd qulity in thei d, to the benefit of thoe who wnt the ommeil infomtion. 11 The eond piniple we offe foundtion fo ytemti nlyi of the pm eology i tht pmme e fo the mot pt tionl buinepeople, nd they will end d when the expeted benefit to them exeed the expeted ot. Wht inight do we obtin fom thi unupiing obevtion? We nwe, fit, indietly: mot othe utho ddeing pm hve foued on popol 8 Evett (2006) ompile hi ttiti fom oue tht inlude Google, Bightmil, Jupite Reeh, emkete, Gtne, MilShell, Hi Intetive, nd Fei Reeh. 9 Thi i evidened by the multiple medi fo dvetiing tht o-exit in equilibium (Yellow Pge, lol newppe, billbod, bodt TV nd dio d, bulk unoliited ommeil ufe mil d, et.). Mny podut uing ommeil pm dvetiing do not wnt duble, publi peene. If they e moving thei web ite to new domin fequently, they need ommunition hnnel though whih to dieminte eh new, tempoy lotion. Indeed, we obeve e in whih the link fo ome domin elling medition expied in Google index well befoe Google got hne to enew the link. Fo exmple, MegeLb (2005) how tht bout 30% of pm domin expie within 24 h. 10 Hnn et l. (2008), in modeling voidne behvio by mketing eipient, lo model pm dvetiing fo whih thee i non-zeo demnd. 11 Conide: Yellow Pge e fily ueful bulk dvetiing medium beue the d e genelly viewed only by thoe who wnt to ee them, nd the dvetie hve the inentive to mke the d le nd infomtive, giving the viewe the infomtion they deie. Spmme in ontt inu ubtntil ot to diguie the infomtion in thei d o tht filte nnot eily emove the d fom the emil tem. But then the ede who do wnt the infomtion o they n mke puhe e onfonted with uninfomtive, low-vlue d.
B. Chio, J. MKie-Mon / Infomtion Eonomi nd Poliy 24 (2012) 173 186 175 Fig. 1. Stkeholde in n e-mil eoytem. to ie the ot of pmming wy of eduing the mount of pm podued. Thi ppoh i pinipled, but inomplete. An equivlent edution in the benefit of pmming (e.g., by induing thoe who wnt pm to ed it in diffeent hnnel) hould hve the me (qulittive) inentive effet. If pm wee flood wte, the exiting olution e in the piit of building tonge levee to ie the ive bnk, inted of diveting the flood wte uing floodwy. Both might popely belong in n effetive flood mngement poliy. We build on thee two piniple to ontut model fo ommeil pm tht inlude dvetie, pm evie povide, emil evie povide, nd mil eipient who hve heteogeneou tte fo eeiving pm. 12 See Fig. 1. We then intodue imple but novel mehnim motivted by the two piniple bove: n unenoed (open) ommunition hnnel though whih pm will be epted without filteing o othe ttempt to blok. Suh hnnel ould be imple tnddized mil lient folde tht would ept ll ppopitely lbeled mege. 13 Ou onetue i tht if well-deigned, then unde ome iumtne the intodution of n unenoed hnnel ould eult in ubtntil elf-egegtion by pmme, with emil dvetiement motly tgeted t the open hnnel, nd muh le t the tditionl (enoed) hnnel. Thee hould be little dipute tht if ue ould impliitly opt-in fo ommeil pm by eting n unenoed folde, the pmme would end mil to tht hnnel. But why would they top ending (o t let end le) to the enoed hnnel? Ou hypothei i tht if enough of the ltent demnd fo puhing pm-dvetied podut i ehed though the unenoed hnnel, then the emining ommeil benefit obtinble fom lo pmming the enoed hnnel my fll uffiiently low tht they no longe utify the inementl ot. 14 In ou foml model below we how one et of ondition uffiient to guntee thi eult. Thee i nothe eon fo pmme to keep ending to the tditionl enoed hnnel: peuion. We e uming tht eipient know if they wnt to peiodilly puhe bed on pm dvetiement, nd thu n mke n ex nte tionl hoie bout whih hnnel to ed. Thi itution i known in the litetue infomtive dvetiing 15 : onume know they wnt infomtion (pie, lotion, et.) bout ptiul podut, nd eek out infomtive dveti- 12 In ou uent model we fou on the pefeene nd behvio of eipient, pmme, nd dvetie. We ue edued-fom, nondptive epeenttion fo emil evie povide. 13 On ptil level, the ende hooe whethe to end to the enoed o the open hnnel (o both). When ending to the open hnnel, the ende doe not diguie ontent, nd dd tg tht indite the mege hould be deliveed to the open hnnel. If ending to the enoed hnnel, the ende doe not tg the mege, nd in ft my expend ome effot to diguie the ontent. 14 One eon the benefit in the enoed hnnel might dop i tht if ue looking fo unoliited d tun fit to the moe infomtive (nd pehp bette ognized) open hnnel, the level of demnd fo podut dvetied with le infomtive mege in the open hnnel my fll uffiiently tht the expene of ending to the enoed hnnel nd pending to get ound the filte i no longe wothwhile. 15 See epeilly the etion unde the ub-heding I dvetiing ued to infom o peude? on p. 28 of Tylo (1934). Fo eview on the eonomi of dvetiing, ee Bgwell (2007).
176 B. Chio, J. MKie-Mon / Infomtion Eonomi nd Poliy 24 (2012) 173 186 ing to obtin the infomtion they need. But thee i nothe tegoy: peuive dvetiing, intended to onvine onume to buy podut they peviouly did not elize they wnted. Sine thee d e imed t onume who might genelly opt out of the open hnnel, it would do little good to end them to the open hnnel (whih thee peviouly uninteeted utome hun), o the peuive dvetie will genelly go to whee the unpeuded e (the enoed hnnel). Peuion, howeve, ome t the ot of being filteed moe eily beue of the le diguied ontent. If the open hnnel doe not mke peuion in the enoed hnnel eie thn when thee i only the enoed hnnel, the omiion of peuive dvetiing i not neeily ftl (ee diuion ight befoe Popoition 1). Rell lo tht if pmme do hooe to tget the open hnnel, then we expet tht they will lo top diipting eoue on unpodutive effot to diguie the infomtive ontent of thei mege. Then thoe who wih to eeive emil dvetiement will benefit fom the highe qulity (infomtivene). Thi inee in infomtivene, in tun, likely would indue lge numbe of onume to wnt to eeive ommeil pm. We ontut model o tht we my fomlly identify ondition unde whih the onetue bove hold tue (nd ondition unde whih they do not). Ou min eult e to hteize the degee to whih pm will be hifted to the open hnnel, nd to demontte tht unde etin umption ll ptie benefit fom the intodution of n open hnnel, o tht it ontitute Peto impovement. 2. Model Othe ppohe to pm he one ommon fetue: they e bed on iing the ot of pmming, not on eduing the benefit (ee Setion 3). In ddition, tehnologil nd legl method (nd ome mket method, but le o) impliitly ume tht etin mil (o mil ende) e unifomly undeible; tht i, they ignoe heteogeneity in eipient pefeene. In thi etion we peent model of the two-ided mket fo ommeil pm, in whih podut elle py pmme to delive dvetiement to emil eipient, ome of whom in tun willingly hooe to puhe the dvetied podut. 16 We then nlyze the effet of intoduing n open (i.e., unenoed) hnnel. The open hnnel ppoh i deigned to lowe the benefit to pmme of ending mil to ll eipient, nd wok only nd peiely beue eipient pefeene e heteogeneou: viz., ome eipient wnt to eeive emil dvetiement. 2.1. Mil type Mil type oinide with ende type. Suh type e defined by two ttibute: m o tgeted mil, nd oliited o unoliited. The fit ttibute i minly ot ttibute of ending. The ontent etion ot pe opy of m mil i muh 16 The emil mket i typil poblem of two-ided mket (e.g., Rohet nd Tiole, 2003; Pke nd Vn Altyne, 2005), whih i loely elted to the hiken-nd-egg poblem. Roughly peking, the numbe of ende ffet the numbe of eipient, nd vie ve. lowe thn tht of tgeted mil. 17,18 Alo, beue of infomtion ymmety of eh eipient pefeene fo pm, by definition, m-mil ende bet ttegy i to ndomize eipient ddee. The eond ttibute i minly ot ttibute of bloking. A mil i onideed oliited fo ou pupoe, even if it i initilly unoliited, if one ould eily unubibe (blok) oneelf fom uh miling lit pemnently. In ll, we identify fou type of mil, nd povide exmple: Unoliited m: Vig nd eoti ontent dvetiement. Unoliited tgeted:peonlized dvetiement bed on puhe hitoy obtined elewhee. Soliited m: Advetiement fom onventionl bookelle, non-pofit fundie, nd othe legl nd le oilly obetionble puveyo. Soliited tgeted: Peonl oepondene. Unoliited m mil ontitute the bulk of the unwnted emil fo mot individul. We theefoe implify ou nlyi uing thi onvenient umption: Aumption 1 (Mil Segegtion). M-mil ende end only unoliited mil, nd tgeted-mil ende end only oliited mil. Henefoth, when the ontext i le, we efe to unoliited m mil ende ende, nd the mil they end imply mil. 2.2. The eipient poblem Aume tht fo unoliited m mil, ome individul wnt to eeive ftion 1. The vlue 2½0; 1Š inee if thee e moe undeible popetie with unoliited m mil uh phihing nd mliiou ontent. We ume tht thee e two type of eipient: high nd low. Only high-type deie unoliited m mil (tht i, hve ome demnd fo the good dvetied in uh mil). We define vible to indite the demnd fo unoliited mil: w : fw ¼ 1; w ¼ 0g. Thee i lge numbe of high-type ðþ eipient indexed by on the intevl [0,1] oding to pobbility ditibution w. The oeponding index fo low-type eipient i ditibuted oding to w. We dop the index if the vible i the um o type. Reipient type e exogenou. We ume eipient of given type hve the me budget fo 17 We do not equie tht it i poible to identify whethe mege i m mil o tgeted mil. It i ey to fool genel pupoe filte, nd the eipient often will not know until fte inuing the ot of viewing the mege. 18 Thee h been ubtntil debte bout whethe pmming i inevitble beue the inementl ot of pm mege i eentilly zeo. It i le to u tht the ot i not zeo: ot of diguiing, ot of obtining vlid emil ddee, ot of legl poeeding, nd bndwidth ot ll likely inee with the numbe of pm mege ent. If the pmme i uing pmbot fm of ompomied mhine to povide fee poeing nd bndwidth, thee will be ot of witing the viue tht y the pmbot pylod: the moe pm mege to end, the moe mhine need to be ompomied. See Hnn et l. (2006) fo eent etimte of the non-zeo inementl ot of pmming.
B. Chio, J. MKie-Mon / Infomtion Eonomi nd Poliy 24 (2012) 173 186 177 pending on dvetied good, nd nomlize thi mount to w. They buy good fom d in the hnnel tht offe the lowe vege pie, whee p i the vege pie offeed by d in hnnel. We lte model how eipient epond to n dvetiement bed on how infomtive o tnpent it i. Whethe mil (deied o undeied) i eeived depend on the filteing tehnology employed by the emil evie povide. We model thi below, but fo now imply efe to mil tht get though unfilteed nd mil tht doe not filteed. In the enoed hnnel, filteing tehnology i deigned to blok unoliited m mil, but it doe o impefetly. Eh ende know tht the filte h tength of f 2 [1,1) fo unoliited m-mil. The filte tength i imply the invee of the ftion of mil tht get though the filte. By definition thee i no filteing in the open hnnel, f o =1. Sende n mke n effot to diguie it ontent to edue the filte uehte. i We let ende hooe tnpeny level, t 2 1 ; 1, fo mil ent to hnnel, f whee t i multiplitive fto duting the filte tength. If t ¼ 1, the mil i tnpent with no diguie t ll nd the effetive filte tength i the tehnologil tength f.ift ¼ 1=f, the effetive filte tength i one, whih i to y, ll ontent pe though unfilteed. Diguiing i otly; thee i no effot mde to diguie ontent in the open hnnel. 19 Denote N the volume of mil ent to eipient in hnnel. Eentilly, it i the mil ent veged o ll eipient in. R i the numbe of high-type uing hnnel ; R i the totl numbe of eipient who hooe to ue hnnel. Then the unfilteed potion tht tully ehe eipient i denoted by n N, whee t i the t f weighted vege of tnpeny level in hnnel. We define ¼ 1 if eipient ue hnnel, zeo othewie. To build ttble model, we mke nothe umption to ule out the unlikely enio tht no one i uing the exiting emil hnnel: Aumption 2 (Chnnel Eentility). The enoed hnnel i eentil o tht evey eipient ue it. Tht i, ¼ 1. Let u now tte the eipient poblem fomlly. Given othe vible, eipient mke biny hoie of whethe to opt into the open hnnel, o 2f0; 1g, by mximizing: U o U v g o ;v I o ; v II o : ð1þ When the fit gument inee, U inee. When eithe the eond o thid gument inee, U deee. The fit gument i the volume of dvetied good onumed, whih i given by totl pending divided by pie (pid to the dvetie indexed by ) in the hnnel with the lowe pie (nd whih i ubibed to by the eipient): 20 ( ) v g ¼ mx w ; ð2þ p 19 By definition of the lowe bound of t ; t o ¼ 1 beue fo = 1 implie tht the uppe nd lowe bound oinide. 20 We implified the poblem fom n equivlent but moe expliit fomultion: Reipient hooe o 2f0; 1g nd P v g; to mximize U o ; P v g; P U v g; ;v I ;vii :t: P p v g; ¼ w. whih i zeo fo low-type eipient ine w =0. The eond gument give the Type I eo (the volume of unwnted mil tht i eeived): v I ¼ ð1 w þ w Þ N t f : 2fo;g When eipient i high type ðw ¼ 1Þ; v I i P 2fo;g N. Thi i the ftion of unoliited mil the t f high type doe not wnt to eeive (ummed o the hnnel to whih he ubibe). Fo low type, v I i P 2fo;g N. Thi i ll unoliited mil eeived. t f The thid gument give the Type II eo (the volume of wnted mil tht i filteed out befoe delivey): v II ¼ ð1 Þw N 1 1 ; ð4þ t f 2fo;g whih i zeo fo low-type eipient ine w = 0. Thee i no filteing in the open hnnel, o v II i P 2fo;gð1 Þ N 1 1 t f ð3þ fo high type. Thi i the ftion of deible unoliited mil (1 ) tht i filteed out of the enoed hnnel. We hve not peified the mginl effet of eh gument in the utility funtion. The ovell hnge in utilitie due to the implementtion of the open hnnel i thu n empiil iue, whih nnot be etined theoetilly. It tun out tht we only need to impoe one tehnil umption unde whih we will know the dietion of ovell utility hnge fte the implementtion of the open hnnel: Aumption 3. When ll mil i ent only to the open hnnel, the utility inee with the inee in good puhed titly offet the utility deee with the inee in Type I eo. 2.3. The ende poblem Thee i lge numbe of ende indexed by on the intevl [0,1] oding to pobbility ditibution w. The totl ot funtion fo ende i C N o ; N ; t o No þ N þ dt N o nd N e the emil volume in the open nd enoed hnnel. t i the tnpeny of the mil ent to the enoed hnnel. We ume: Contnt etun to le in eh volume ot: @C ¼ @N > @C ¼ o @N o > 0.21 Note tht nd o e ontnt. Negtive tnpeny (poitive diguie) ot: @C < 0. @t 21 Rthe thn hving zeo mginl ending ot (@C =@N Þ ommonly eted, pmme inu ot to enew tehnologie, whih depeite quikly, to genete pm. Fo exmple, zombie (i.e., home ompute hiked by ke) e onitently detoyed by nti-viu oftwe, o pmme mut ontinuouly develop nd ditibute new viue to ptue new (tempoy) zombie. ombie e eponible fo elying moe thn 60% of the wold pm (Sopho, 2005). One ould hve ued tep funtion to model the ot funtion but mooth funtion would ppoximte tep funtion when the numbe of zombie inee.
178 B. Chio, J. MKie-Mon / Infomtion Eonomi nd Poliy 24 (2012) 173 186 On the evenue ide, ende e pie tke. Advetie py them fo oliittion. Let p be the dvetiing hge pe diguied emil ehing the ue in hnnel. 22,23 Given othe vible, ende hooe N o ; N ; t to mximize: p N o ; N ; t ¼ p o No þ p N t f o No N dt ; ð5þ :t: t 2 1 f ; 1 ; N o ; N P 0: ð6þ Next we tte the olution to the bove mximiztion poblem: Reult 1. The bet epone of ende e: N o > 0 () po P o ; N > 0 () t 8 ¼ 1 >< 2 1 ; 1 f >: ¼ 1 f p t f P ; () E C ;N E C;t whee E C;N nd E C;t e eltiitie. ð7þ ð8þ 8 >< < ¼ 1; ð9þ >: > Poof. See Appendix A.1. h Notie tht the mginl evenue of ending N o nd N e p o nd p. When the mginl evenue of hnnel i t f titly le thn the mginl ot, ende doe not end ny to hnnel. Ele, ende mke ome eonomi pofit beue in hnnel the mginl evenue i wekly gete thn the mginl ot in given hnnel. To inee the totl evenue N p in the enoed hnnel by the me t f mount, ende ould eithe dut N o t by the me mount, depending on thi tio of eltiitie E C;N. E C;t 2.4. The dvetie poblem 22 In ptie, thee i volume diount (tht might, fo intne, be due to diminihing likelihood to epond). Fo intne, Send-Sfe i evie pmme offe to dvetie. One piing heme k fo US$125 pe 1 million edit (poibly poxy of N t f ) when n dvetie py fo 0.4 million edit. The pie dop monotonilly to US$10 pe 1 million edit when n dvetie py fo 300 million edit. Thi piing heme i vilble t http://www.end-fe.om/end-fe.html, eed 29 Mh 2009 (though the pge ppe to hve lt been updted in 2006). 23 Whethe the pie i hged pe delivey o pe lik doe not ffet the min eult of the model, it i lgely nomliztion iue. Thee i lge numbe of dvetie indexed by on the intevl [0, 1] oding to pobbility ditibution w. Advetie totl ot deive fom the podution of good old, nd fom the dvetiing fo them. Let h be the pobbility tht n dvetiement in hnnel led to puhe, nd n i the numbe of mege deliveed on behlf of dvetie (whee N i the numbe ent, the diffeene being due to filteing). Podution ot C P h n P h n, exhibit ontnt-etunto-le tehnology. i the ontnt mginl podution ot. h ¼ h t ; R, whee t R i the tnpeny level of emil in hnnel oited with dvetie, nd R i R the tio of high-type eipient in hnnel. h i ineing in both gument; it equl zeo if R ¼ 0. R Advetiing ot, P p n, i line. Rell tht p i the mginl dvetiing hge in hnnel tht i pid to ende. Fo eh p pid, dvetie ollet expeted le evenue equl to the pie pid by d eipient um onume, p, time the pobbility of mking le in hnnel, h. Given othe vible, dvetie hooe n o ; n to mximize:!! p n o ; n ¼ :t: n P 0: p h t ; R R p n Reult 2. The bet epone of dvetie e: n > 0 () h þ p 6 h p ; n o > 0 () ho þ p o 6 ho p o : h n ; ð10þ ð11þ ð12þ ð13þ Poof. See Appendix A.2. h Thi eult implie tht the volume equeted hould be zeo in both hnnel if the mginl ot exeed the mginl benefit in eh hnnel, nd tht the volume equeted in hnnel hould be titly poitive when the mginl mkup ipoitive. The mginl mkup i the mginl le pie p minu the mginl ot of ue epone nd mginl podution ot ( ). p h 2.5. Equilibium 2.5.1. Competitive equilibium By uming tomiti, pie-tking eipient, dvetie nd pm ende (whih n be utified fo the ltte two by n umption of fee enty), we hve the ondition fo ompetitive equilibium. Uing ht ymbol to denote equilibium vlue, ompetitive equilibium by definition tifie the following: the good nd evie mket i leed: ^v g w ðþd þ ^v g w ðþd 2½0; 1Š ¼ ^h 2½0; 1Š 2½0; 1Š ^nw ðþd þ 2½0; 1Š the mil mket i leed: ^n w ðþd þ ^n w ðþd 2½0; 1Š ¼ 2½0; 1Š 2½0; 1Š ^n w ðþd ¼ 2½0; 1Š! ^n w ðþd ; bn ^t f w ðþd; ð14þ ð15þ the pofit of ende nd dvetie e mximized:
B. Chio, J. MKie-Mon / Infomtion Eonomi nd Poliy 24 (2012) 173 186 179 Tble 1 The bet epone of eipient. Advetiing mil volume in Opt-in i bet epone? Open hnnel Cenoed hnnel High type Low type eo eo Ye nd No Ye nd No eo Poitive Ye nd No Ye nd No Poitive eo Ye No Poitive Poitive Ye nd/o No No p p N b o ; N b ;^t ¼ mx N N o ;N p o ; N ; t ; ð16þ ;t ^n o ; ^n ¼ mx p n o n o ; n ; ð17þ ;n the zeo eonomi pofit ondition e tified: p N b o ; N b ;^t ¼ 0; ð18þ p ^n o ; ^n ¼ 0; ð19þ the utility of eh of the high nd low-type eipient i mximized: U ^ o ¼ mx U o o ; ð20þ U ^ o ¼ mxu o o : ð21þ Note tht the utilitie nd the volume of good nd mil mege e endogenouly detemined. Some of the othe key vible tht e endogenouly detemined inlude the hoie vible of the mximiztion poblem, the epone te, nd the pie. 2.5.2. Aggegtion By homogeneity, integting ove ll gent of the me type give ommonly ued eult: the ggegte vlue i equl to the vege vlue (i.e. R k2½0; 1Š ^z hðkþdk ¼ R k ^z k k2½0; 1Š hðkþdk ¼ ^z k, whee h i the pobbility ditibution funtion of ^z ). In thi ene, we utify the ue of epeenttive gent fo onveniene. The vlue they hve hoen e imply the totl onumed by the me type of gent in the eonomy. The following expeion tte tht the volume of good onumed by ll eipient (nd the epeenttive high nd low type eipient) i equl to the epone te time the unfilteed volume eeived, equeted o ent o ll hnnel. Eq. (14) nd (15) give: ^v g; ¼ ^h ^n ¼ ^h ^n ¼ N b ^h ^t f : ð22þ 2.5.3. Nh equilibi It i imultneou gme. We fit how the following bet epone of the eipient. Note in ptiul tht high-type eipient, nd only they, will ue the open hnnel if the dvetiing mil volume ent to the open hnnel i titly poitive nd tht ent to the enoed hnnel equl zeo. Reult 3. The bet epone of the eipient e lited in Tble 1. Poof. See Appendix A.3. h The fit two ow of Tble 1 e not vey inteeting (though neey to lulte the equilibium): if no mil i ent to the open hnnel, it i mtte of indiffeene to both type of ue whethe they ubibe to tht hnnel o not. Fo the lt two ow, thee i open hnnel mil. It i then not upiing tht low-type eipient do not ue the open hnnel beue eh of the gument in thei utility funtion n only move in the undeible dietion if they opt-in. Fo the high-type eipient, it i not immeditely le tht they will opt-in fo ue beue the utility inee due to the ineed volume of good onumed ould be offet by the utility deee due to the inee in Type I nd II eo. 24 With Aumption 3, the bet epone fo high type i etited to be opting in fo high type when thee i zeo enoed hnnel mil nd poitive open hnnel mil. We now how the only ymmeti pue-ttegy Nh equilibium beide the ttu quo. 25 The ttu quo in thi imultneou gme i tivil one, whih fll into the l of hiken-nd-egg poblem typil in two-ided mket: no gent ue the open hnnel beue no othe gent ue it. The emining pue-ttegy Nh equilibium i ou min eult: the open hnnel diminihe the volume of unoliited m mil in the enoed hnnel to zeo, nd only high-type eipient ue the open hnnel. The intuition i imple. Sende tion n be gouped into fou e: poitive o zeo volume in eh hnnel. Thee n be no bet epone when thee i zeo volume in eh hnnel beue the pofit i undefined due to infinite le pie. If mil i only ent to the enoed hnnel nd no eipient opt in fo the open hnnel, thi enio i identil to the ttu quo. When thee i poitive volume in eh hnnel, the ende e wting eoue on mil ent to the enoed hnnel beue le ould hve been mde in the open hnnel well but with le ot. The only e left i fo mil to be ent only to the open hnnel, whih i optiml fo the ende when the high type hve opted in fo the open hnnel nd when the mginl evenue geneted i gete thn the mginl ot fo the ende. Now when ende end only to the open hnnel, we know fom Reult 3 tht the bet epone fo the high type i to opt-in but not fo the low-type. One my wonde if thi epeenttive gent model ptue the e when evey ende end only to the 24 The ede might woy tht lemon mket would emege whee only undeible emil i peent in the open hnnel. One ould extend the model to leen the effet of the lemon poblem. Fo exmple, one ould ume tht eipient uing the open hnnel e moe utiou beue it ould be tue tht ove time people elize tht mege e not enoed by nyone in the open hnnel. O thee ould be mege in the open hnnel tht diude (e.g. pmme elling fke Vig might tell people to not to epond to etin mege tht would link to ite tht tel one edit d infomtion). 25 The ymmety hee efe to me pmete of gent within eh type (eipient, ende, nd dvetie), whih i ubumed in ou epeenttive gent modeling.
180 B. Chio, J. MKie-Mon / Infomtion Eonomi nd Poliy 24 (2012) 173 186 Fig. 2. Mil volume hnge omped to the ttu quo. open hnnel, will ome dvetie ~ benefit fom deviting to end ome to the enoed hnnel? The nwe i no fo gent with homogeneou ot beue ~ 0 epone te nnot inee. 26 Intuitively, fo eh mil mege ~ end to the enoed hnnel, nothe ende n lwy undeut the pie dvetied in ~ 0 mege by ending n identil mege to the open hnnel with lowe pie. The eond pie i lowe beue thee i no need to diguie the mege nd the ending ot i hepe in the open hnnel. Will the eipient bothe to eh fo the undeutting mege in the open hnnel wheneve they ee mege, in the enoed hnnel, dvetiing good tht inteet them? Vey poibly beue the mginl ot of eh i vey low: the eipient n ut nd pte the fit mege into the eh box in the open hnnel to find n ext mth thee with lowe pie. One ould of oue gue tht the fixed ot of uh eh kill e high beue of lening needed. Popoition 1 (Nh). Beide the ttu quo, the only ymmeti pue-ttegy Nh equilibium i: ^ o ¼ 1; ^o ¼ 0; N b o > 0; N b! 0;^t 6 1; ^n o > 0; ^n! 0Þ, whih exit if ^h ^p < ^h þ ^t f nd ^h o^p o ¼ ^h o þ o. The ttu quo i Nh if ^h ^p ¼ ^h þ ^t f nd ^h o^p o < ^h o þ o. Poof. See Appendix A.4. 2.6. Welfe h When the le pie in ll tntion i loweed, the volume of good old inee given fixed expenditue. 26 Fo eipient to buy fom both hnnel (utifying n ; no ~ > 0), po h to be the me p ~, whih i ontdition. The eon i tht by Reult 1 nd 2, nd the zeo pofit ondition, n ; no > 0 implie tht ^p ~ ¼ ~ þ t f ^h nd ^p o ¼ þ o ^h o. By ot homogeneity, ~ ¼.Ifp o ¼ p ~, we mut hve h > h o beue ^t f > o. h > h o i not poible beue Ro R P R o R nd to P t. Eq. (22) tell u it ould men tht the epone te, the mil volume o both h ineed. It ould lo men tht the epone te beome o high tht the mil volume deee. Denote the ttu quo vible when the open hnnel i bent uing 1 upeipt, 27 we how the ltte: Popoition 2 (Mil Volume). Fo the ttu quo nd the othe Nh equilibium in Popoition 1, bn ^t f 6 N b ;1 ^t ;1 f () ^h o þ ^p o P ^h ;1 þ ^p ;1 ; ð23þ bn o ^t o f 6 N b ;1 o ^t ;1 f () ^h o þ ^p o P R ð ^h;1 þ ^p ;1 Þ; ð24þ R whee ^p ;1 ¼ ^t ;1 f > ^p o ¼ o. Poof. See Appendix A.5. h Expeion (23) tte tht the mil volume eeived by ll eipient i lowe thn tht in the ttu quo if nd only if the totl mginl ot pe mil eeived (i.e., the um of mginl ot of podution ð ^ho Þ nd dvetiing ^p o pe mil eeived) i highe thn the ttu quo vlue ^h;1 þ ^p ;1. Fo the mil volume to deee fte the implementtion of the open hnnel, the new epone te h to be o high tht the inee in the mginl ot of podution pe mil eeived ð ^ho ^h;1 Þ i moe thn the deee in the mginl ot of dvetiing pe mil eeived ^p ;1 ^p o. See Fig. 2. Sine R > 1, (24) implie (23). When eh eipient eeive le, the totl eeived i lo le (the onvee R i 27 When the open hnnel i bent, we intepet it f o? 1. When uh filte tength i infinitely tong, it i if thee i no uh hnnel fo ny ptil ue.
B. Chio, J. MKie-Mon / Infomtion Eonomi nd Poliy 24 (2012) 173 186 181 not tue). It i led by R beue the ompion now i R between the totl mginl ot pe mil eeived by the high-type eipient (tivilly the low-type eipient eeive le beue thee i no unoliited m mil in the only hnnel they opted in). In the ttu quo, fo evey R mil eeived by ll eipient, only one i eeived by R the high-type eipient, tht i why the oeponding totl mginl ot i inflted by R R. In the following popoition, we pove tht in the non-ttu quo Nh equilibium deibed in Popoition 1, eh eipient utility h not deeed fte the oll-out of the open hnnel beue the utility oited with good doe not deee, nd the di-utilitie oited with Type II eo do not inee. Type I eo will not inee fo high-type eipient if Popoition 2 hold o = 0. The ltte ondition ( = 0) i type of fee dipol of unoliited m mil in the open hnnel, whih will depend on lutte o hndling ot (the ot of dipol itelf i vnihingly loe to zeo). Thi ondition i likely to hold (ppoximtely) if thee i good eh engine within the open hnnel, nd if elle who no longe need to diguie thei d to get pt filte will povide infomtion helpful fo oting nd filteing d. Inted of = 0, we lo pove the e in whih we equie lowe unoliited m mil volume thn in the ttu quo. The tutue of the poof i imple. The welfe of the unoliited m-mil ende nd dvetie will be unhnged beue they mke zeo pofit with nd without the open hnnel. The welfe of the eipient ould diffe. To ompe the welfe hnge fo given eipient when thee i n open hnnel, we ompe hi o he utility fte nd befoe the oll-out of the open hnnel: bu lim f o!1 b U. Popoition 3 (Welfe). If Popoition 1 hold nd eithe Popoition 2 hold o = 0, the welfe of the dvetie, unoliited m-mil ende nd ll eipient will be wekly ineed when thee i n open hnnel. Poof. See Appendix A.6. 3. Pio ppohe to pm To dte, mot eeh foue on eduing pm genelly, uully though poliy, tehnil o mket mehnim tht ie the ot of ending pm. Befoe we detil ou model of mehnim tht divet pm to thoe who wnt it, nd wy fom thoe who do not, we eview othe ppohe. 3.1. Tehnologil Tehnologil olution hve gined ome ptil ue but the eult e f fom tiftoy even though they hve been implemented fo ome time. The popol inlude ule-bed, Byein, nd ommunity ( ollbotive ) filteing, dipoble identitie uing extended emil ddee (Bleihenbhe et l., 1998), DominKey Identified Mil (Peez, 2005), Sende ID o Sende Poliy Fmewok (Coke, 2006), 28 hllenge-epone (Dwok nd No, 1993; Luie nd Clyton, 2004), whitelit, nd blklit. See Cno nd LMhi (1998) fo n oveview of thee ide (though not of oue of the moe eent peifi popol). Thee i fundmentl poblem with tehnologil ytem: they typilly ely on the ot to pmme of deviing tehnologil wokound. If the ot i high enough, the net benefit of pmming will be inuffiient nd the quntity of ueful (deliveed) pm will fll. Howeve, the ot of tehnologil wokound fll pidly, tehnology beome exponentilly hepe nd lgoithmi olution to hd omputtionl poblem pidly impove. Thu, the wokound ot fll, the tehnologil bie beome le effetive nd pm deliveed inee. Thi fundmentl ot dynmi ete need fo ongoing invetment to ete impoved nti-pm tehnologie. While n m e my not be the fitbet olution, we hve not een feible method to void thi yle, given the inevitble nd pid deline in tehnology ot. Cetinly, though ome of the ot h been hifted to ISP nd mil evie povide, it ppe tht the oil ot of pm h been ineing, not deeing, depite the polifetion of tehnologil fixe. 3.2. Legl Legl ule e nothe ppoh to pm edution. The US CAN-SPAM t equied foml eommendtion fom the Fedel Tde Commiion egding the etblihment of do-not-pm egity imil in the piit of the do-notll nd do-not-fx egitie eted puunt to the Telephone Conume Potetion At of 1991. Although The FTC eommended gint the etion of the lit, othe CAN- SPAM ule took effet 1 Jnuy 2004. Howeve, legl olution lone e, nd likely will emin inomplete. Fit, to void pohibiting deible emil ommunition, legl ule genelly inlude fe hbo poviion gunteeing the pemiibility of emil exhibiting etin hteiti. It i genelly diffiult o impoible to pevent pmme fom ompoing thei mege o tht they exhibit thee hteiti,thuetingfehbofolgendpobbly gowing quntity of pm. Seond, legl uidition ove pm-ditibuting ogniztion i uil poblem: pmme n eily hnge thei lotion to othe ountie. 3.3. Mket Some popol bed on eonomi inentive hve been gining ttention. Thee he n impotnt fetue with ou ppoh to the poblem: they typilly e bed on peumption tht ue hve heteogeneou vlue fo eeiving viou emil mege. In n expeimentl invetigtion of emil tmp pie fo obtining eipient ttention, Kut et l. (2005) found tht hging ue ende to be moe eletive nd to end fewe mege. Thi method, howeve, equie non-pmme to py pie well. vn ndt 28 A of now, pm-ending domin e ionilly the bigget ue of SPF tg (MLogi, 2005).
182 B. Chio, J. MKie-Mon / Infomtion Eonomi nd Poliy 24 (2012) 173 186 (2004) exmine the deign of n optiml tx tht minimize exploittion of ttention though infomtion ovelod. Viou emil tmp ytem wee implemented. 29 Lode et l. (2006) popoe n ttention-bond mehnim in whih ende depoit monety bond to thid-pty gent, to be eleed only if the eeive tell the gent to do o. Both Lode et l. (2006) nd we eognize heteeogeneou vlution of mil mege; they povide n inentive tht inee pmme ot, while we povide n inentive tht edue pmme benefit. Pyment ytem equie ubtntil inftutue fo full implementtion. The inftutue neey fo wideped miopyment i lking, nd fo ueful doption into evie exhibiting netwok effet, uh emil, it i likely neey tht thee be ely wideped, not inementl, doption, whih i diffiult to oilly enginee. Alo, thee i nom of fee emil evie. Legitimte ende my eit pying fo outgoing emil moe tenuouly thn i titly utified if they took into ount the ytem benefit to thei eipient. 4. Diuion We emphize tht ou popol i tting point. Mny iue beyond the ope of thi nlyi need futhe invetigtion. We diu few hee. It my eem tht n open hnnel i ledy implemented by the ommon mil lient pm folde. Howeve, lient pm folde i uully the lt tge of multi-tge filteing. Mot emil evie povide blok ome tffi ltogethe, nd only mil tht mke it though the fit (o fit n 1) filte () e ndidte fo quntine in ue pm folde. Thu, to get to tht hnnel, ende ledy inued diguie ot. We mentioned t the beginning tht n open hnnel ould be implemented t low ot. Any emil evie povide ould immeditely, t miniml ot, offe to let ll mil to etin lient p though with tg in hede (o even pe-pended to the ubet field) tht would llow immedite nd omplete hnneling to epte milbox; when the emil evie povide itelf povide the mil lient ( do online emil povide like Gmil nd Yhoo!) the open hnnel inbox ould be povided fo ue tht wnted. Wht i le le i whethe inementl implementtion would be ueful t dwing ende nd ede of unoliited ommeil emil into the open hnnel, o whethe wideped, oodinted doption would be neey. Thee e mny potentil eon fo n emil evie povide to not implement n open hnnel uently. Being multi-podut fim, not uing the open hnnel doe not imply tht dding the open hnnel 29 Two of the wold lget povide of e-mil ount, Amei Online nd Yhoo!, nnouned in ely 2006 tht they would give pefeentil tetment to mege fom ompnie pying fom 1/4 of ent to penny eh. An emil tmp ytem w ledy implemented in Koe in 2003. Dum Copotion, the lget potl in Koe, hge bout 0.8 ent to the ende who end moe thn 1000 mege pe dy. Fee le downwd if ende e nked lowe thn the bigget ende o moe ue te the emil ueful. Dt ited by Kut et l. (2005) indite tht pm w edued by bout 40% fom it pek in hlf-ye peiod ound the implementtion. will deee the pofit of thei emil diviion. Howeve, it might not be implemented imply beue it edue pofit in othe diviion (uh Google web eh tht filitte pull veu the minly puh tehnology in the open hnnel). Would the open hnnel be flooded with o muh moe mil ine the ot of ending d would be lowe tht thoe who wnt to ee d will inu ot o high to find deied d tht they bndon uing the open hnnel? Thi i omplited quetion, nd one lgely beyond the ope of thi ppe. Thee e good eon we think thi my not hppen, howeve. Sine dvetie no longe need to diguie thei mege to get into the inbox, they need to only end one mege the thn mny to guntee delivey. Futhe, the dvntge of hving mny moe o le identil mege in the inbox my be edued if eipient n eily find the mege they wnt nd ue indexing nd finding evie to ot though them. Anothe poibility i the implementtion of n expition fetue to the open hnnel inbox: ny mege beyond n expie dte e utomtilly deleted, to edue lutte. Of oue, dvetie will till wnt to ompete with eh othe fo ttention, nd it i poible they will ty to do o by polifeting mege in the open hnnel. The eult on blne nnot be pedited without moe detiled model, nd, mot likely, ome empiil evidene. We hve lgely ignoed wht we ll peuive dvetiing, nmely, dvetiing tht tie to peude people who did not know tht they wnted to puhe nything. Thee eipient in genel will not opt-in to the open hnnel, nd o pmme my till ty to eh them though the enoed hnnel. Ou onetue i tht if enough demnd i hifted to the open hnnel, nd epeilly if pie fo good dvetied thee fll due to the lowe mketing ot, tht demnd in the enoed hnnel fo good old by peuive pmme my fll enough to diouge thi type of dvetiing, but we hve not fomlly nlyzed thi. Howeve, if the open hnnel doe edue the numbe of d, the impt on le of the d in the enoed hnnel will pobbly inee, nd the open hnnel will thu mke peuion in the enoed hnnel eie. But we hve ledy gued tht the peude ould fe lowe ot ompetito in the open hnnel, whih the utome buy fom if the eh ot to find thi ompetito i low enough. In othe wod, the peude onvine the utome to buy the good, but the pie onvine the utome whee to buy the good. 5. Conluion Tehnil filte nd legl ule ie the ot of deliveing pm to ede. Cot e bone by pmme (who mut develop eve-hnging tehnique fo voiding filte, et.), but lo by eipient, who pend time doing the diffiult filteing nd eviewing tht nnot be utomted, nd pying highe ot fo good to ove the mketing expene. On the othe hnd, n equivlent edution in the benefit of pmming (e.g. by moving out pm demnde) hould hve the me inentive effet. Moe genelly, method tht hnnel ommuni-
B. Chio, J. MKie-Mon / Infomtion Eonomi nd Poliy 24 (2012) 173 186 183 tion moe dietly to thoe who wnt them would lowe ot on both ide nd be welfe impoving. We fomlized thi intuition nd exploed uffiient ondition fo ll emil eipient to be bette off with the intodution of n open hnnel when ending nd podution ot exhibit ontnt-etun-to-le. We how tht unde thee ondition only eipient wnting unoliited ommeil dvetiement will ue the open hnnel, nd they will benefit fom le diguied mege nd lowe le pie. In ddition, fo ll eipient the ditiftion oited with both undeible mil eeived nd deible mil filteed out deee. We do not lim tht ou ide would povide omplete olution to the uent pm poblem, but of oue, no othe known nd ptil method povide omplete olution eithe. We do offe novel new tool tht my ontibute to edution in the flow of pm, nd t the me time give dvetie eon to inee the infomtive ontent nd qulity of thei d, to the benefit of thoe who do wnt to buy good. Futhe, if we n tempt ubtntil numbe of onume who wnt to puhe pm-dvetied podut into epte emil hnnel, the puhing vlue emining in the tditionl, filteed, o enoed hnnel my dop uffiiently to diouge pmme fom uing tht ineingly unpodutive hnnel. The impotnt inight we offe, whih likely will led to othe, pm-eduing tehnique, i to eognize tht thee i not ut upply uve but lo demnd uve fo pm. We model the inentive, within the eoytem of exiting pm olution, to indue both upplie nd demnde to move out of the uent enoed hnnel nd into the open hnnel. If utome who wnt to puhe will benefit fom moe infomtive d in epte hnnel, then pm dvetie will benefit fom fouing thei dvetiing pending on tht hnnel. Thi hould not be vey ontoveil ide, but it i, we believe, n ide tht h been lgely miing fom the debte. Thee i nothe illuminting eonomi pepetive on ou wok: pm i fundmentlly poblem tht ie when dipol i not fee. We know fom the Fit Fundmentl Welfe Theoem tht unegulted fee mket e genelly Peto effiient, but tht eult equie fee dipol. Spm i not fee to dipoe: it equie time to open nd onide. Some type of pm e mliiou nd my tully ue hm to one dt file o opeting ytem befoe we n dipoe of it. Ou popol eete fee mket the open hnnel fo thoe who do not wnt to dipoe of pm. It diffe fom othe fee-mket olution (e.g. emil tmp nd bond fo emil pm, nd Google AdWod fo web pm): The open hnnel give eipient the ight to eeive pm; it emove the ight of the emil evie povide to deide whethe the eipient hould eeive pm. (Moe genelly, the eipient ight to hooe the level of enohip i one of the mny othe poible popety ight eignment in the emil eoytem tht hve been lgely unexploed in the litetue.) Alo, we povide thoe fo whom the dipol ot e uffiiently high (not fee) the hoie to opt out nd ptiipte only in the enoed hnnel. Menwhile, ende (nd pm demnde) do not intenlize the dipol ot of uninteeted eipient, but the ende nonethele hooe to end le to the enoed hnnel beue the vege popenity to buy fll pm demnde move to the open hnnel. An open dvetiing hnnel i poible t low ot, nd it i oneivble tht it would mke emil ue t let wekly bette off (no woe off) thn the ttu quo. At the vey let, thi mehnim i fully eveible. If welldeigned, n inentive-omptible dvetiing hnnel tht hnee the imultneou foe of demnd nd upply ould ignifintly edue the flow of unoliited bulk ommeil emil. Aknowledgement We ppeite omment fom Nt Bulkley, huon Chen, Angu Chu, Nik Eonomide, Joeph Fell, Mihel He, Pete Honeymn, Pul Renik, Doug Vn Houweling, Ruell Neumn, Hl Vin, Mike Wellmn, the membe of the Inentive-Centeed Deign Lb (epeilly Joh Chey, Geg Gmette, Lin Jin, Kil-Sng Kim, John Lin, Any Oepyhvili, Toinu Reeve, Ben Sten, nd Rik Wh), the Peking Univeity Infomtion Soiety Goup (epeilly Gung Shi), nd the Mihign Chin Fellow (epeilly Ye Du, nd Lei hong), nd ptiipnt t the STIET wokhop in My 2006, the Teleommunition Poliy Reeh Confeene, nd the Fouth Bi-nnul Confeene on the Eonomi of the Softwe nd Intenet Indutie. We gtefully knowledge finnil uppot fom the NET Intitute nd fom NSF Gnt IIS-0414710 nd IGERT-0114368. Thi eeh i lo uppoted by the Leding Ademi Pogm, 211 Poet fo the Shnghi Univeity of Finne nd Eonomi nd the Leding Ademi Diipline Poet (Poet Numbe B801). We thnk the edito nd efeee fo vey helpful omment. Appendix A A.1. Poof of Reult 1 p The ende pofit funtion i N o ; N ; t ¼ p o No þ p N t f C N o ; N ; t : ð25þ The Lgngin i: L ¼ pðþ k 1 ðt 1Þþk 2 ðt 1 f Þþlo N o þ l N ; ð26þ whee k 1 ; k 2 ; l ; l o P 0. The omplementy lkne ondition e: k 1 t 1 ¼ 0; ð27þ k 2 t 1 ¼ 0; ð28þ f l o N o ¼ 0; l N ¼ 0: ð29þ ð30þ
184 B. Chio, J. MKie-Mon / Infomtion Eonomi nd Poliy 24 (2012) 173 186 FOC: p o ¼ @C @N o l o ; p t f ¼ @C @N l ; p N ð31þ ð32þ ðt Þ2 f k 1 þ k 2 ¼ @C : ð33þ @t Ce 1: N o ; N > 0 ) lo ¼ l ¼ 0. Eq. (31) implie p o ¼ @C. Eq. (32) implie p @N o ¼ @C t f @N. Sube 1: t ¼ 1 ) k 2 ¼ 0 Combining (32) nd (33), we hve N @C k @N 1 ¼ @C. @t Thi implie N @C P @N @C. @t Sube 2: t ¼ 1 ) k f 1 ¼ 0 Combining (32) nd (33), we hve N @C þ k @N 2 ¼ @C. @t Thi implie N @C 6 @N @C. @t Sube 3: t 2 1 ; 1 ) k f 1 ¼ k 2 ¼ 0. Eq. (33) implie N @C ¼t @N @C. @t Ce 2: N o > 0; N ¼ 0 ) lo ¼ 0. Eq. (31) implie p o ¼ @C @N o Sube 1: t ¼ 1 ) k 2 ¼ 0. Eq. (32) implie @C @N P p t f. Eq. (33) implie k 1 ¼ @C. Eq. (32) implie @C P p @t @N. f Sube 2: t ¼ 1 ) k f 1 ¼ 0 Eq. (33) impliek 2 ¼ @C, whih ontdit @C < 0. @t @t Sube 3: t 2 1 ; 1 ) k f 1 ¼ k 2 ¼ 0. Eq. (33) implie @C ¼ 0; whih i ontdition @t beue @C < 0. @t Ce 3: N o ¼ 0; N > 0 ) l ¼ 0. Eq. (31) implie @C P p o @N o. Eq. (32) implie p ¼ @C t f @N. The ube eult of t e the me Ce 1. Ce 4: N o ¼ N ¼ 0. Sube 1: t ¼ 1 ) k 2 ¼ 0 Eq. (33) implie @C @t P 0. Eq. (31) implie @C @N o P p o. (32) implie @C P p @N. f Sube 2: t ¼ 1 ) k f 1 ¼ 0 Eq. (33) implie k 2 ¼ @C, whih ontdit @C < 0. @t @t Sube 3: t 2 1 ; 1 ) k f 1 ¼ k 2 ¼ 0 Eq. (33) implie @C ¼ 0; whih ontdit @C < 0. @t @t Ltly, note tht @C @N A.2. Poof of Reult 2 The Lgngin i: L ¼ @C @t N t ðp h p Þn C ¼ @ ln C @ ln N C N N @ ln ¼ @ ln C @ ln N C @ ln t C t t @ ln C @ ln t E C;N E C;t. h! h n þ l o n o þ l n ; whee l, l o P 0. The omplementy lkne ondition e: l o n o ¼ 0; l n ¼ 0: ð34þ ð35þ ð36þ FOC: 8 : p h ¼ p þ h C 0 p h ¼ p þ h C 0 nd p o ho ¼ p o þ ho C 0! h n l ;! h n l! h n l o : Ce 1: n o > 0; n > 0. n > 0 ) l ¼ 0. Eq. (38) implie h C 0 P h n ð37þ ð38þ ð39þ þp ¼ h p. n o > 0 )lo ¼ 0. Eq. (39) implie h o C 0 P h n þp o ¼ ho p o. Ce 2: n o ¼ 0; n > 0. n > 0 ) l ¼ 0. Eq. (38) implie h C 0 P h n þ p ¼ h p. (39) implie h o C 0 P h n þ p o P ho p o. Ce 3: n o ¼ 0; n ¼ 0. (38) implie h C 0 P h n þ p P h p. (39) implie h o C 0 P h n þ p o P ho p o. Ce 4: n o > 0; n ¼ 0.no > 0 ) lo ¼ 0. Eq. (39) implie h o C 0 P h n þ p o ¼ ho p o. Eq. (38) implie h C 0 P h n þ p P h p. h A.3. Poof of Reult 3 Fo low-type eipient, v g nd v II e zeo nywy, but o ¼ 1 implie tht v I only titly inee (emin unhnged) if N o > ð¼þ0. Thu, the bet epone fo lowtype eipient e o ¼ 0ifNo > 0 nd o ¼ 0 nd 1 if N o ¼ 0. Fo high-type eipient, thee i no effet on Type II eo (4) beue fo the open hnnel t = f = 1, o the tem fo = o i zeo. Howeve, o ¼ 1 implie tht vg wekly inee fo high-type eipient beue of the mx opeto in (2). Fo high-type eipient, the quetion then i whethe the utility inee with the inee in v g would t let offet the utility deee with the inee in v I. When No ¼ 0, the bet epone e o ¼ 0 nd 1 beue both the hnge in v g nd v I e zeo. When No > 0 nd N ¼ 0, the bet epone i o ¼ 1 beue the utility inee in v g exeed the utility deee in v I by Aumption 3. We mut hve U o ¼ 1 U o ¼ 0 > 0. When N o > 0 nd N > 0, the bet epone e o ¼ 0 o 1 o both, depending on the mgnitude of hnge in v g nd v I. In thi e, o ¼ 1 n be bet epone only if p > po, ele v g t bet unhnged but v I inee. h A.4. Poof of Popoition 1 Rell tht N b o ¼ ^no ¼ ^no nd b N ¼ ^n ^t f ¼ ^n. Aumption 2 implie ^ ¼ ^ ¼ 1: Thee e fou e.
B. Chio, J. MKie-Mon / Infomtion Eonomi nd Poliy 24 (2012) 173 186 185 Ce : ^n o ¼ ^n ¼ 0. n o ¼ n ¼ 0 implie tht v g ¼ 0by(22). v g ¼ 0 ) p o ; p ¼1 beue v g ¼ mx f w g (fom p (2)). p o ; p ¼1 implie tht the dvetie mximiztion poblem i not well defined, ontditing n o ¼ n ¼ 0 being the olution. Ce b: ^n o ¼ 0; ^n > 0. Note tht p 0; n ¼ p h p h n ¼ w p n w (ine w ¼ h n p p ), nd p n o ; 0 ¼ p o ho p o h o n o ¼ w p o no w (ine p o w ¼ h o n o p o ). ^no ¼ 0 nd ^n > 0 pofit mximize implie tht p 0; ^n p n o ; 0 ¼ p o n o ^p ^n þ w w p o P 0 fo ll n ^p o. (i) When o ¼ ¼ 1, we need po no ^p ^n P 0 w w beue p o 6 0. (The lt inequlity i ^p implied by ^p 6 po, whih i tue beue n > 0. Suppoe othewie tht ^p > po ; o ¼ v ¼ 1 implie g; ¼ 0 nd h = 0, violting the ondition to enue ^n > 0byReult 2.) But po no ^p ^n P 0 nnot be tified unle n o > ^n beue ^p > po (implied by Reult 1 nd the zeo pofit ondition tht mke the wek inequlitie in the bet epone tit). But n o > ^n ontdit with ^no ¼ 0 nd ^n > 0. (ii) When o ¼ 0, we hve ho = 0. Thi implie tht n o ¼ 0 by Reult 2. We now hek if n ¼ 0on > 0 ontitute pt of the equilibium, if ny. If n o ¼ n ¼ 0, it nnot be n equilibium explined in Ce. Ele if n o ¼ 0 nd n > 0, both eipient type ould hooe to opt-in o not bet epone by Reult 3. When o ¼ 1, we e bk to (i), whih we eliminted. o ¼ 0 then i the uneliminted bet epone fo the high type. Fo the low type, o ¼ 1 nd 0 e till the uneliminted bet epone. To enue ^n > 0 nd ^no ¼ 0, we need ^h ^p ¼ ^h þ ^p ¼ ^h þ ^t f nd ^h o^p o < ^h o þ ^p o < ^h o þ o by Reult 1 nd 2, nd the zeo pofit ondition. We ll thi goup of equilibi the ttu quo Nh equilibi beue o ¼ o ¼ 0 i the me in the ttu quo in tem of deiion mde, nd o ¼ 0 nd o ¼ 1 i the me in the ttu quo in tem of the utilitie nd pofit elized. Ce : ^n o > 0; ^n ¼ 0. Reult 3 implie tht if n o > 0 nd n ¼ 0; o ¼ 1 nd o ¼ 0 i the bet epone. Wht i left i to how tht if o ¼ 1 nd o ¼ 0; no > 0 nd n ¼ 0 i the bet epone. Sine t 6 to ¼ 1 nd o ¼ ¼ 1, we hve ho P h. When n o > 0, etting n > 0 wekly inee pofit only if p o ¼ p to utify why eipient buy fom both hnnel ðv g;o ; v g; > 0Þ (fom (2)). But p o ¼ p implie tht v g i the me whethe n > 0. But fo eh ftion of v g tified by the le in the enoed hnnel inted of the open hnnel, the deee in n o h to be ompented by n even gete inee in n. With no inee in le but the need, by h o P h, to inee mil volume uing the moe otly enoed hnnel, the pofit i not mximized. The only bet epone left i n o ¼ 0, whih i ledy eliminted in Ce. To enue ^n ¼ 0 nd ^no > 0, we need ^h ^p < ^h þ^p < ^h þ ^t f nd ^h o^p o ¼ ^h o þ ^p o ¼ ^h o þ o by Reult 1 nd 2, nd the zeo pofit ondition. Ce d: ^n o > 0; ^n > 0. We ledy howed in Ce tht when o ¼ 1; n ; no > 0 i not bet epone. When o ¼ 0, we ledy howed in Ce b (ii) tht n o > 0 i not bet epone. Thu, n ; no > 0i not n equilibium. h A.5. Poof of Popoition 2 (i) Fo high-type eipient: bn o ^t o f 6 N b ;1 o ^t ;1 f ^v g;o ^h 6 R o R () ^no 6 R R ^n;1 () ; ð40þ ^v g;;1 w () ^h ;1 ^h o^p 6 R o R ^h w ;1 ;1^p : ð41þ Sine the dvetie poblem give ^p o ^h o ¼ ^h o þ ^p o nd ;1 ^h ;1^p ¼ ^h ;1 þ ^p ;1, nd the ende poblem give ^p o ¼ o nd ^p;1 ¼ ^t ;1 f, the lt inequlity beome: ^h o þ o P R ^h ;1 þ ^t ;1 f () ^h o : ð42þ R Fo low-type eipient, they eeive le mil beue they do not ue the open hnnel nd the mil ent to the enoed hnnel i zeo. (ii) Fo the totl volume eeived by ll eipient: bn ^t f 6 N b ;1 ^t ;1 f () ; ð43þ ^n o 6 ^n;1 þ ^n ;1 * N b o ¼ N b ¼ 0 () ; ð44þ ^v g;o g;;1 ^v 6 w () ^h o ^h ;1 ^h o^p 6 w () ; ð45þ o ;1 ^h ;1^p ^h o þ o P ^h ;1 þ ^t ;1 f () ^h o P ^h ;1 þ ^t ;1 f o : A.6. Poof of Popoition 3 lim f o!1 U ¼ U lim ^v g ; ^vi ; ^v II f o!1 ^v g ; lim f o!1 ^v I ; lim f o!1 ^v II ð46þ : ð47þ Sine U b lim b f o!1u P 0 if () ^v g P lim ^v f o!1 g (with ^v g > lim ^v f o!1 g ), (b) ^v I 6 lim ^v f o!1 I (with ^vi < lim ^v I f o!1 ), nd () ^v II below. 6 lim f o!1 II ^v, we pove eh of thee inequlitie (i) Inequlity () i ^v g P lim f o!1 ^v g, o: ( ) mx w P p ^ ;1 ^p ;1 w : ð48þ It hold fo w = 0 beue both ide e zeo. Fo w ¼ 1; ^ o ¼ 1byReult 3 nd ¼ ^;1 ¼ 1byAumption 2. (48) beome:
186 B. Chio, J. MKie-Mon / Infomtion Eonomi nd Poliy 24 (2012) 173 186 ( ) mx 1 P 1 ; ð49þ p ^p ;1 whih hold with tit inequlity ine ^p o < ^p;1. Thi i beue ^p ;1 ¼ þ ^p;1 nd ^p ^h o ;1 ¼ þ ^po, nd ^h ^h o ;1 > ^h o ( Ro ¼ 1 by Popoition 1) nd R o ^po < ^p;1 (whee ^p ;1 ¼ ^t ;1 f ;1 ; ^p o ¼ o ; ^t ;1 f P 1 nd ;1 > o ). (ii) Inequlity (b) i ^v I 6 lim f o!1 ^v I, o: ð1 w þ w Þ^ ^t f 2fo;g 6 ð1 w þ w Þ^ ;1 bn bn ;1 ^t ;1 f : Fo w = 0, ine ^ o ¼ 0 by Reult 3, ¼ ^;1 Aumption 2, (50) beome: bn ;1 ^N ^t f 6 ^t ;1 f ; ð50þ ¼ 1 by whih i tue beue N b ¼ 0byPopoition 1. If N b ;1 > 0, the inequlity will hold with tit ign. Fo w ¼ 1; N b ¼ 0 nd ¼ ^;1 ¼ 1 implie tht (50) beome (note tht if =0,(50) will be tified beue both ide equl zeo): bn o ^t o f 6 N b ;1 o ^t ;1 f : ð51þ But we ledy poved in Popoition 2 the neey nd uffiient ondition fo b N o 6 b N ;1 to hold. ^t o f o ^t ;1 f (iii) Inequlity () i ^v II 6 lim f o II!1 ^v, o: ð1 Þw ^ b N 1 1 ^t f 2fo;g 6 ð1 Þw ^ ;1 bn ;1 1 1 ^t ;1 f : ð52þ It hold fo w = 0 beue both ide e zeo when =0. Fo w ¼ 1, ine ^ o ¼ 1 by Reult 3, ¼ ^;1 ¼ 1 by Aumption 2, (48) beome: bn 1 1 6 N ^t b ;1 f 1 1 ; ð53þ ^t ;1 f 2fo;g whih i tue beue N b ¼ 0 by Popoition 1 nd ^t o f o ¼ 1. h Refeene Andeon, Simon P., De Plm, Ande, 2009. Infomtion ongetion. The RAND Jounl of Eonomi 40 (4), 688 709. Andeon, Simon P., De Plm, Ande, 2012. Competition fo ttention in the infomtion (ovelod) ge. RAND Jounl of Eonomi 43 (1), 1 25. Bgwell, K., 2007. The eonomi nlyi of dvetiing. In: Amtong, M., Pote, R. (Ed.), Hndbook of Indutil Ogniztion, 1701 1844. Elevie. Bleihenbhe, D., Gbbe, E., Jkobon, M., Mti, Y., Mye, A., 1998. Cubing unk e-mil vi eue lifition. In: Po. of the 2nd Intentionl Confeene on Finnil Cyptogphy, pp. 198 213. Cno, Loie Fith, LMhi, Bin A., 1998. Spm! Communition of the ACM 41 (8), 74 83. Coke, Dve, 2006. Chllenge in nti-pm effot. The Intenet Potool Jounl 8 (4). Dwok, Cynthi, No, Moni, 1993. Piing vi poeing o ombtting unk mil. In: Advne in Cyptology-CRYPTO 1992. Letue Note in Compute Siene, vol. 740. Spinge-Velg, pp. 139 147. Evett, Don. 2006. Spm Sttiti. <http://pm-filte-eview. topteneview.om/pm-ttiti.html>. Hnn, Il-Hon, Lung Hui, Ki, Li Lin, Yee, Lee, Sng Yong T., Png, I.P.L., 2006. Who get pmmed? Communition of the ACM 49 (10), 83 87. Hnn, Il-Hon, Lung Hui, Ki, Lee, Sng Yong T., Png, I.P.L., 2008. Conume pivy nd mketing voidne: tti model. Mngement Siene 54 (6), 1094 1103. Kut, Robet, Sunde, Shym, Telng, Rhul, Moi, Jme, 2005. Piing eletoni mil to olve the poblem of pm. Humn Compute Intetion 20 (1 2), 195 223. Luie, Ben, Clyton, Rihd, 2004. Poof-of-wok pove not to wok. In: Wokhop on Eonomi nd Infomtion Seuity. <http:// www.dt.umn.edu/wei2004/lyton.pdf>. Lode, Thede, Vn Altyne, Mhll, Wh, Rik, 2006. An eonomi epone to unoliited ommunition. Advne in Eonomi Anlyi nd Poliy 6 (1). Atile 2. MegeLb, 2005 Megelb Intelligene Repot. MLogi, 2005. Mxlogi Repot Spm Aount fo 67 Peent of All Emil in 2005. Pe Relee, 22 Septembe 2005. <http:// www.mxlogi.om/new_event/pe_elee/ 09_22_05_SpmStt.html>. Pke, Geoffey, Vn Altyne, Mhll, 2005. Two-ided netwok effet: theoy of infomtion podut deign. Mngement Siene 51 (10). Peez, Jun Clo, 2005. Yhoo nd Cio to Submit E-mil ID Spe to IETF. NetwokWold, 11 July, 2005. <http://www.netwokwold.om/ new/2005/071105-yhoo-io.html>. Rohet, J.C., Tiole, J., 2003. Pltfom ompetition in two-ided mket. Jounl of the Euopen Eonomi Aoition 1 (4). Sopho, 2005. Sopho Seuity Thet Mngement Repot. Sopho. Tylo, F.W., 1934. The Eonomi of Advetiing. Geoge Allen nd Unwin Ltd. vn ndt, Timothy, 2004. Infomtion ovelod in netwok of tgeted ommunition. RAND Jounl of Eonomi 35 (3), 542 560.