NET Institute*

Transcription

1 NET Institute* Woking Pape #06-20 Octobe 2006 Using Uncensoed Counication Channels to Divet Spa Taffic Benjain Chiao and Jeffey MacKie-Mason Univesity of Michigan * The Netwoks, Electonic Coece, and Telecounications ( NET ) Institute, is a non-pofit institution devoted to eseach on netwok industies, electonic coece, telecounications, the Intenet, vitual netwoks copised of coputes that shae the sae technical standad o opeating syste, and on netwok issues in geneal.

2 Using Uncensoed Counication Channels to Divet Spa Taffic Benjain Chiao and Jeffey MacKie-Mason 8/31/06 (Revised: 10/15/06) {bchiao, Abstact We offe a icoeconoic odel of the two-sided aket fo the doinant fo of spa: bulk, unsolicited, and coecial advetising eail. We adopt an incentive-centeed design appoach to develop a siple, feasible ipoveent to the cuent eail syste using an uncensoed counication channel. Such a channel could be an eail folde o account, to which popely tagged coecial solicitations ae outed. We chaacteize the cicustances unde which spaes would voluntaily ove uch of thei spa into the open channel, leaving the taditional eail channel doinated by peson-to-peson, non-spa ail. Ou ethod follows fo obseving that thee is a eal deand fo unsolicited coecial eail, so that eveyone can be ade bette off if a channel is povided fo spaes to eet spadeandes. As a bonus, the absence of filteing in an open channel estoes to advetises the incentive to ake essages tuthful, athe than to disguise the to avoid filtes. We show that unde cetain conditions all eail ecipients ae bette off when an open channel is intoduced. Only ecipients wanting spa will use the open channel enjoying the less disguised essages, and We appeciate coents fo Nat Bulkley, Zhuoan Chen, Nick Econoides, Michael Hess, Pete Honeyan, Paul Resnick, Doug Van Houweling, Michigan China Fellows, the ebes of the Incentive-Centeed Design Lab (especially Geg Gaette, Lian Jian, Kil-Sang Ki, John Lin, Anya Osepayshvili, Toinu Reeves, Ben Steans, and Rick Wash), and paticipants at the STIET wokshop in May 2006 and at the Telecounications Policy Reseach Confeence. We gatefully acknowledge financial suppot fo the NET Institute and fo NSF gants IIS and IGERT School of Infoation, Univ. of Michigan, Ann Abo, MI Dept. of Econoics, and School of Infoation, Univ. of Michigan, Ann Abo, MI

3 fo all ecipients the satisfaction associated with desiable ail eceived inceases, and dissatisfaction associated with both undesiable ail eceived and desiable ail filteed out deceases. 1 Intoduction We all eceive spa; we all esent it. Justice Potte Stewat, wee he alive, would know it when he saw it. Nonetheless, it is had to find a consensus definition of spa. Soe want to include all unsolicited coecial eail; othes include unsolicited bulk eail; othes distinguish between deceptive, infoative o alicious eail. We should not be supised, then, that it is also had to find systeatic analyses of the spa poble, when thee ae so any notions of what spa is. Ou odest goal is to identify a paticula (but pevalent) subspecies of spa, analyze its ecology, and popose a echanis that ay incease substantially the social welfae by odifying the flows of this type of spa. Ou iodest goal is to lay goundwok fo systeatic odeling of spa, and the consequent developent of solutions that ae effective because they addess systeatic featues of the poble. We liit ou consideation to spa defined as bulk, unsolicited, coecial eail; that is, effectively identical (but usually andoly disguised) essages sent unsolicited to lage nubes of ecipients with the goal of inducing a willing, utually-beneficial puchase by the ecipients. With this definition (we will call it spa fo convenience, but it s eely one subspecies) we ule out alicious bulk unsolicited eail (e.g., eail caying a vius payload); we ule out deceptive eail (e.g., phishing essages that attept to tick ecipients into evealing valuable pesonal infoation such as bank passwods); and we ule out eail (though initially unsolicited) sent to ailing list, which one could unsubscibe fo. Defined as we have done, coecial spa is an instance of a diffeently-naed, well-known phenoenon: advetising. Using the lesspejoative onike eail advetising ight give us a good stat on a thoughtful, systeatic consideation; cetainly, it ight help us ecognize that at least this type of spa is not pe se evil o oally deficient (though, as with any advetising, soe population subgoups ight conclude that the poducts advetised ight fail that goup s oality test). Nonetheless, we will use coecial spa o just spa fo shot, because we elish the poweful affective esponse the te eceives, and the oppotunity to punctue the pejoative bubble it engendes. To develop a systeatic analysis of (non-deceptive, non-alicious) coecial spa, we need gounding pinciples. We find that supising insights follow fo adopting just two failia, siple econoic pinci- 2

4 ples: Revealed pefeence Thee is a non-tivial deand fo the eceipt of spa eail. Rational choice Spa puveyos will send spa essages to whoeve, wheeve, wheneve, as long as the expected benefits exceed the expected costs. We expect that only the fist pinciple will aise any eyebows at fist, but we find that the second pinciple consistently has been halfignoed in ost pio liteatue on the spa poble. Fist, deand. Spa is not costless to geneate o delive, despite casual clais to the contay. It is tue that eplication and tanspot costs ae exteely low, copaed to non-digital advetising channels. But thee ae a nube of othe costs: aketing and contacting costs with advetises, content ceation costs, content disguising costs (to get past technological filtes), distibution technology costs (ost spa is now sent out by vius-ceated spabots unning on any achines not owned by the spa povide; these botnets need to be continuously egeneated, which equies developing new viuses to distibute, aong othe things). Thee ay also be the cost of expected legal penalties. Given the non-zeo costs of poviding a spaing sevice, and the fact that we ae liiting ouselves to coecial spa, fo which the benefit to the sende is the induceent of willing puchases by ecipients, we ust conclude the following: by evealed pefeence, thee is a nontivial deand fo the eceipt of spa eail. Soe consenting adults ust be puchasing enough Rolex knock-offs and countefeit poducts to pay the spae s costs. While the evealed deand could encopass soe spuious deand induced by alicious o deceptive poducts (e.g. fake Viaga), a potion of the evealed deand should be eal. No buyes will believe that a $50 Rolex is authentic. Casual evidence is consistent with ou clai that thee is non-tivial deand fo uch spa: Cano and LaMacchia [1998] show that the lagest faction of spa content is coecial advetising fo poducts had to find though othe advetising channels. We efe to these as censoed coecial solicitations. Such censoship, incanated as filtes and doain-blocking ules, ae ubiquitous at the eail sevice povide level. Of couse, the censoship of which we speak is not necessaily explicit o govenent-suppoted. Explicitly censoed exaples include ads fo non-pesciption povides of egulated dugs, o fo povides of knock-off poducts that intentionally violate copyights o tadeaks of well-known bands. An exaple that, while not govenent censoed, ay have eason to avoid othe advetising channels (o 3

5 ay not be accepted by othe channels) is (legal) ponogaphy. Sophos [2005] finds that this patten continues; fo exaple, in 2005 edication spa constitutes aound 40% of all spa, and adult content fo anothe 10-20%. Evett [2006] estiates that poduct spa constitutes aound 25% of all spa, and adult content fo anothe 19% 1. Recognizing that soe ecipients want to ead spa, while any othes evidently do not, we iediately see that one oppotunity fo social welfae ipoveent is to find a way to atch coecial spa to those who want it, and not to those who do not. The latte eail eades would benefit, and spa sendes would also benefit by not incuing the costs of sending to people who will not want to puchase. As a coollay, we expect the willing ecipients of coecial spa to benefit as well: if spaes can find a way to send to those who ae inteested in eceiving the advetiseents, then they can educe thei costs and incease the infoation content and quality in thei ads, to the benefit of those who want the coecial infoation. Conside: Yellow Pages ae a faily successful bulk advetising ediu because its ads ae geneally viewed only by those who want to see the, and the advetises have the incentive to ake the ads clea and infoative, giving the viewes the infoation they desie. Spaes in contast incu substantial costs to disguise the infoation in thei ads so that filtes cannot easily eove the ads fo the eail stea. But then the eades who do want the infoation so they can ake a puchase ae confonted with uninfoative, low-value ads. The second pinciple we offe as a foundation fo systeatic analysis of the spa ecology is that spaes ae fo the ost pat ational businesspeople, and they will send ads when the expected benefit to the exceeds the expected cost. What insight do we obtain fo this unsupising obsevation? 2 We answe, fist, indiectly: ost othe authos addessing spa have focused on poposals to aise the cost of spaing as a way of educing the aount of spa poduced. This appoach is pincipled, but incoplete. An equivalent eduction in the benefits of spaing (e.g., by inducing those who want spa to ead it in a diffeent channel) should have the sae (qualitative) incentive effect. If spa wee flood wates, the existing solutions ae in the spiit of building stonge levees to aise the ive banks, instead of diveting 1 Evett [2006] copiles the statistics fo souces including Google, Bightail, Jupite Reseach, emakete, Gatne, MailShell, Hais Inteactive, and Feis Reseach. 2 We know, of couse, that not evey decision, in evey cicustance, satisfies a test fo decision-theoetic ationality. We only equie that costly business decisions in geneal follow fo easonable copaisons of benefits to costs. 4

6 the flood wates using a floodway. Both ight popely belong in an effective flood anageent policy. We build on these two pinciples to constuct a odel fo coecial spa that includes advetises, spa sevice povides, eail sevice povides and ail ecipients who have heteogeneous tastes fo eceiving spa. 3 See Figue 1. We then intoduce a siple but novel echanis otivated by the two pinciples above: an uncensoed counication channel though which coecial spa will be accepted without filteing o othe attepts to block. Such a channel could be as siple as a standadized ail client folde that would accept all appopiately labeled essages. See Figue 2. Ou conjectue is that if well-designed, then unde soe cicustances the intoduction of an uncensoed channel could esult in substantial self-segegation by spaes, with eail advetiseents ostly tageted at spa boxes, and uch less at the taditional (censoed) channel. See Figue 3. 4 Note that eail fo lage legitiate businesses such as ebay and IBM is not consideed spa in ou ealie definition because it is only initially (but not pesistently) unsolicited. Though such eail could be quite bothesoe, especially if one needs to eceive a sall potion of wanted eail fo such businesses. Thee should be little dispute that if uses could iplicitly opt-in fo coecial spa by ceating an uncensoed folde, the spaes would send ail to that channel. But why would they stop sending (o at least send less) to the censoed channel? Ou conjectue is that if enough of the latent deand fo puchasing spa-advetised poducts is eached though the uncensoed spa box channel, then the eaining coecial benefits obtainable fo also spaing the taditional censoed channel ay fall sufficiently low that they no longe justify the inceental costs. 3 In ou cuent odel we focus on the pefeences and behavios of ecipients, spaes, and advetises. We use a educed-fo, non-adaptive epesentation fo eail sevice povides. 4 One ight ague that the Wold Wide Web is close to an uncensoed channel. If so, why doesn t the Web satisfy the deand fo advetising? One obvious eason is that soe o any of the poducts using coecial spa advetising do not want a duable, public pesence. If they ae oving thei web sites to new doains fequently, they need a counication channel though which to disseinate each new, tepoay location. Indeed, we obseve cases in which the links fo soe doains selling edications expied in Google s index well befoe Google got a chance to enew the links. MessageLabs (2005) shows that about 30% of spa doains expie within 24 hous. Moe geneally, we expect thee to always be significant deand fo push advetising in addition to pull (seach-based) advetising, as evidenced by the ultiple edia fo advetising that co-exist in equilibiu (Yellow Pages, local newspapes, billboads, boadcast TV and adio ads, bulk unsolicited coecial suface ail ads, etc.). 5

7 incu c pay p 1 Sendes Eail Sevice Povides pass thu pay p 2 fo puchases Good & Sevices Povides Uses Viaga, ebay, IBM Eail Clients Seve Filtes ake type 1 & 2 eos Client Filtes ake type 1 & 2 eos pass thu Figue 1: Stakeholdes in an e-ail ecosyste. Thee is anothe eason fo spaes to keep sending to the taditional censoed channel: pesuasion. We ae assuing that ecipients know if they want to peiodically puchase based on spa advetiseents, and thus can ake an ex ante ational choice about which channel to ead. This situation is known in the liteatue as infoative advetising 5 : consues know they want infoation (pice, location, etc.) about paticula poducts, and seek out infoative advetising to obtain the infoation they need. But thee is anothe categoy: pesuasive advetising, intended to convince consues to buy poducts they peviously did not ealize they wanted. Since these ads ae aied at consues who ight geneally opt out of the open channel, it would do little good to send the to the open channel (which these peviously uninteested custoes shun), so the pesuasive advetise will geneally go to whee the unpesuaded ae (the censoed channel). Recall also, that if spaes do choose to taget the open channel, then we expect that they will also stop dissipating esouces on unpoductive effots to disguise the infoative content of thei essages. Then those who wish to eceive eail advetiseents will benefit fo the highe quality (infoativeness). This incease in infoativeness, in tun, likely would induce a lage nube of consues to want to eceive coecial spa. We constuct a odel so that we ay foally identify conditions un- 5 See especially the section unde the sub-heading Is advetising used to info o pesuade? on p. 28 of Taylo [1934]. 6

8 Figue 2: An hypothetical open channel. 7

9 Sendes Eail Sevice Povides Good & Sevices Povides ebay, IBM Seve Filtes Good & Sevices Povides Viaga Uses Uses Client Filtes Eail Clients Sendes Eail Sevice Povides Figue 3: Sepaating the deand fo and supply of bulk unsolicited coecial advetising. de which the conjectues above hold tue (and conditions unde which they do not). Ou ain esults ae to chaacteize the degee to which spa will be shifted to the open channel, and to deonstate that all paties benefit fo the intoduction of an open channel, so that it constitutes a Paeto ipoveent. 2 Pio appoaches to spa To date, ost eseach focuses on educing spa geneally, usually though policy, technical o aket echaniss that aise the cost of sending spa. Befoe we detail ou odel of a echanis that divets spa to those who want it, and away fo those who don t, we eview othe appoaches. 2.1 Technological Technological solutions have gained soe patial success but the esults ae fa fo satisfactoy even though they have been ipleented fo soe tie. The poposals include ule-based, Bayesian, and counity ( collaboative ) filteing, disposable identities using extended eail addesses [Bleichenbache et al., 1998], DoainKeys Identified Mail [Peez, 2005], Sende ID o Sende Policy Faewok [Cocke, 2006] 6, challenge-esponse [Dwok and Nao, 1993, Lauie and Clayton, 6 As of now, spa-sending doains ae ionically the biggest uses of SPF tags [MXLogic, 2005] 8

10 2004], whitelists, and blacklists. See Cano and LaMacchia [1998] fo an oveview. Thee is a fundaental poble with technological systes: they typically ely on the cost to spaes of devising technological wokaounds. If the cost is high enough, the net benefit of spaing will be insufficient and the quantity of successful (deliveed) spa will fall. Howeve, the costs of technological wokaounds falls apidly, as technology becoes exponentially cheape and as algoithic solutions to had coputational pobles apidly ipove. Thus, as the wokaound cost falls, the technological baie becoes less effective and spa deliveed inceases. This fundaental cost dynaic ceates a need fo ongoing investent to ceate ipoved anti-spa technologies. While an as ace ay not be the fist-best solution, we have not see feasible ethods to avoid this cycle, given the inevitable and apid decline in technology costs. 2.2 Legal Legal ules ae anothe appoach to spa eduction. The U.S. CAN- SPAM act equied a foal ecoendation fo the Fedeal Tade Coission egading the establishent of a do-not-spa egisty siila in the spiit of the do-not-call and do-not-fax egisties ceated pusuant to the Telephone Consue Potection Act of Although The FTC ecoended against the ceation of the list, othe CAN-SPAM ules took effect 1 Januay Howeve, legal solutions alone ae, and likely will eain incoplete. Fist, to avoid pohibiting desiable eail counications, legal ules geneally include safe habo povisions guaanteeing the peissibility of eail exhibiting cetain chaacteistics. It is geneally difficult o ipossible to pevent spaes fo coposing thei essages so that they exhibit these chaacteistics, thus ceating a safe habo fo a lage and pobably gowing quantity of spa. Second, legal juisdiction ove spa-distibuting oganizations is a cucial poble: spaes can easily change thei locations to othe counties. 2.3 Makets Soe poposals based on econoic incentives have been gaining attention. These shae an ipotant featue with ou appoach to the poble: they typically ae based on a pesuption that uses have heteogeneous values fo eceiving vaious eail essages. In an expeiental investigation of eail staps as a pice fo obtaining a ecipient s attention, Kaut et al. [2005] found that chaging causes sendes to be oe selective and to send fewe essages. This ethod, 9

11 howeve, equies non-spaes to pay a pice as well. van Zandt [2004] exaines the design of an optial tax that iniizes exploitation of attention though infoation oveload. Vaious eail stap systes have been o ae about to be ipleented. 7 Lode et al. [2006] popose an attention-bond echanis in which a sende deposits a onetay bond to a thid-paty agent, to be eleased only if the eceive tells the agent to do so. Payent systes equie substantial infastuctue fo full ipleentation. The infastuctue necessay fo widespead icopayent is lacking, and fo successful adoption into a sevice exhibiting netwok effects, such as eail, it is likely necessay that thee be ealy widespead, not inceental, adoption, which is difficult to socially enginee. Also, thee is a no of fee eail sevice. Legitiate sendes ay esist paying fo outgoing eail oe stenuously than is stictly justified if they took into account the syste benefits to thei ecipients. 3 Theoy In ou bief eview of othe appoaches to spa we highlighted one coon featue: they ae geneally based on aising the costs of spaing, not on educing the benefits. In addition, technological and legal ethods (and soe aket ethods, but less so) iplicitly assue that cetain ail (o ail sendes) ae unifoly undesiable; that is, they ignoe heteogeneity in ecipient pefeences. In this section we pesent a odel of the two-sided aket fo coecial spa, in which poduct selles pay spaes to delive advetiseents to eail ecipients, soe of who in tun willingly choose to puchase the advetised poducts 8. We then analyze the effect of intoducing an open (i.e., uncensoed) channel. The open channel appoach is designed to lowe the benefits to spaes of sending ail to all ecipients, and woks only and pecisely because ecipient pefeences ae heteogeneous: viz., soe ecipients want to eceive eail advetiseents. 7 Two of the wold s lagest povides of e-ail accounts, Aeica Online and Yahoo!, announced in ealy 2006 that they would give pefeential teatent to essages fo copanies paying fo 1/4 of a cent to a penny each. An eail stap syste was aleady ipleented in Koea in Dau Copoation, the lagest potal in Koea, chages about 0.8 cents to the sendes who send oe than 1000 essages pe day. Fees scale downwads if sendes ae anked lowe than the biggest sendes o oe uses ate the eail as useful. Data cited by Kaut et al. [2005] indicate that spa was educed by about 40% fo its peak in a half-yea peiod aound the ipleentation. 8 The eail aket is a typical poble of two-sided akets (e.g., Rochet and Tiole [2003]), which is closely elated to the chicken-and-egg poble. In essence, the nube of sendes affects the nube of ecipients, and vice vesa. 10

12 3.1 Mail Types Mail types coincide with sendes types. Such types ae defined by two attibutes: ass o tageted ail, and censoed o uncensoed content. 9 The fist attibute is ainly a cost attibute. The content ceation cost pe copy of ass ail is uch lowe than that of tageted ail. 10 Also, because of infoation asyety of each ecipient s pefeence fo spa, by definition, ass-ail sendes best stategy is to andoize ecipients addesses. The second attibute is whethe the sende sends content of a type that is censoed (if ecognized) by the eail sevice povide. 11,12 In all, we identify fou types of ail: Censoed-content ass Exaples include Viaga and eotic content advetiseents. Censoed-content tageted Exaples include pesonalized adult ateials, pehaps sent by a pay subsciption sevice. Uncensoed-content ass Exaples include advetiseents fo conventional bookselles, non-pofit fundaises, and othe legal and less socially objectionable puveyos. Uncensoed-content tageted Exaples include pesonal coespondence. Ou design goal was to develop a social welfae-inceasing echanis that induces censoed-content ass-ail sendes to educe the supply 9 By censoed content we ean content of a type that conventional eail sevice povides outinely attept to filte out of the ecipient s eail stea. Such content ay o ay not be illegal, and the filteing effots geneally will be ipefect. Thus, as we ake explicit below, soe censoed content ay be unfilteed, and thus be eceived. 10 We do not equie that it is possible to identify whethe a essage is ass ail o tageted ail. It is easy to fool geneal pupose filtes, and the ecipient often will not know until afte incuing the cost of viewing the essage. 11 Recipient censoship (with, fo exaple, pesonal spa filtes) is not vey ipotant to ou cental esults, as long as the value of spa that evades these filtes is, on aveage, negative to a segent of the population. 12 Content-based filteing can ely on any available infoation heades and body text. Fo exaple, Gail, Hotail and Yahoo! usually filte adult content and all ail fo soe blacklisted sendes (usually based on IP addesses). On the othe hand, we assue that sendes can, at a cost, disguise content to soe degee. In pactice, uch spa can be autoatically identified as being sent fo a censoedcontent ass-ail sende, but ou esults ae obust as long as consideable spa cannot. 11

13 of thei essages deliveed to the cuent standad eail channel (the censoed channel). Theefoe, we siplify by aking this assuption: Assuption 1 Mass-ail sendes send only censoed content, and tagetedail sendes send only uncensoed content The Recipients Poble To odel the use poble we suppose that ecipient chooses which channel(s) to ead in ode to axiize utility, which depends on the quantity of vaious categoies of eail: U (desied ail eceived, undesied ail eceived, desied ail not eceived) (1) The utility function is inceasing in the fist aguent, and deceasing in the othes. Befoe explaining the aguents above, we intoduce futhe notations. Channel j is eithe (o)pen o (c)ensoed. Assue that fo all ecipients, thee is a (pehaps sall) faction ɛ of uncensoed ail that is not desied. We assue that individuals eithe desie (all) censoed-content ail in a given channel o not, and use the indicato φ j t to epesent those pefeences. If a ecipient of type t {(h)igh, (l)ow} desies censoedcontent ail in channel j, then φ j t = 1; othewise φ j t = We assue that only high type ecipients put a positive value on censoed content (φ j l = 0, φ j h = 1). Whethe ail (desied o undesied) is eceived depends on the filteing technology eployed by the eail sevice povide. We odel this below, but fo now siply efe to ail that gets though as unfilteed and ail that does not as filteed. Then the fist aguent of the full utility function (1), desied ail eceived, becoes: (1 ɛ) unfilteed uncensoed ail+unfilteed censoed ail φ j t (2) 13 Thee ae inteesting eseach questions associated with the othe two eail types as well, but they fall outside the scope of ou pesent analysis. Adding the to ou odel fo the questions we ask in this pape would coplicate notation and poofs, but would not change the qualitative esults. 14 We have an asyety between the faction of desiable censoed- and uncensoed-content ail in a channel: ecipients ay not want 100% of the uncensoed ail sent to the in a channel, but if they want any censoed-content ail, then want all of it. We do this to siplify the algeba, without losing anything qualitatively ipotant. In both cases, not all ail is desied: fo uncensoed, each individual ay not want soe; fo censoed, soe individuals do not want any. Thus, thee is the possibility of both Type 1 and Type 2 eos fo each. 12

14 The second aguent of utility function (1), undesied ail eceived, becoes: ɛ unfilteed uncensoed ail+unfilteed censoed ail (1 φ j t) (3) The thid aguent of the utility function (1), desied ail not eceived, becoes: (1 ɛ) filteed uncensoed ail+filteed censoed ail φ j t (4) In the censoed channel filteing technology is designed to distinguish between censoed and uncensoed content, but it does so ipefectly. Each sende knows that the filte has a stength of γ c [1, ) fo censoed content, and stength ˆγ c [1, ) fo uncensoed content, with γ c ˆγ c. The filte stength is siply the invese of the faction of ail that gets though the filte. By definition thee is no filteing in the open channel, γ o = Sende s can ake an effot to disguise its content to educe the filte s success ate. We let sende s choose a disguise level, d j s [ 1, 1], γ j fo ail sent to channel j, whee d j s is a ultiplicative facto adjusting the filte stength. If d j s = 1, disguising has no ipact and the effective filte stength is the technological stength γ j. If d j s = 1/γ j, the effective filte stength is one, which is to say, all content passes though unfilteed. Disguising is costly; we assue that thee is no effot ade to disguise content in the open channel (by definition of the lowe bound of d j s, d o s = 1 because γ o = 1 iplies that the uppe and lowe bounds coincide). Ealie on, we assued that censoed-content ail is sent only by ass-ail sendes, who evenly distibute such ail to all ecipients. We theefoe define n j = nj as the volue of censoed-content ail sent R j to ecipient in channel j, whee n j is the censoed-content ass-ail sent by sende to channel j, and R j is the nube of ecipients using channel j. Then the potion that actually eaches ecipient is nj, d j γ j whee d j is the weighted aveage of disguise levels. Siilaly, except of couse that tageted ail does not have to be aveaged out acoss ecipients, we use the hat sybol to denote the coesponding uncensoedcontent vaiables: ˆn j, ˆd j and ˆγ j. Since we assue that thee is no need to disguise uncensoed content, ˆd j = An appoach, which is pehaps less adical in pactice, is to extend the cuent odel such that 1 < γ o < γ c. Ou cental esults should still hold fo γ o to be sufficiently sall. The agnitude of which, howeve, is an epiical question. We theefoe only solve fo the baseline case of γ o = 1, which should have the sae qualitative effects. 13

15 In ou infoal specification (1), ecipient utility depends on the undiffeentiated volue of vaious ail categoies. Howeve, by intoducing content disguising, we cannot avoid anothe diension of quality: the value of a given type of ail to a ecipient will now also depend on how infoative it is, which geneally will be invesely popotional to the aount of disguising the sende does. That is, clutteing a essage with extaneous gabage text to get past a filte also akes it difficult fo the ecipient to find the useful infoation. Theefoe, we allow utility to depend on the infoativeness-adjusted volue of eail eceived. To adjust fo essage infoativeness afte disguising, we intoduce an infoation pefeence function, which is inceasing in the effot ade to disguise censoed-content ail. To allow fo oe geneality that will be clea shotly, we specify that this function can be diffeent fo diffeent ail. Naely, the functions ae I(d j ) and Ī(dj ) fo filteed and unfilteed ail. We define κ j = 1 if ecipient uses channel j, zeo othewise. Now we can foally expess the utility function (1). The fist aguent, which is infoativeness-adjusted desied ail eceived, becoes: u desied eceived = j {o,c} (1 ɛ)κ j ˆn j + ˆγ } {{ j } uncensoed-content ail j {o,c} φ j tκ j I(d j )n j d j γ } {{ j } censoed-content ail (5) in which the fist te is (desiable) unfilteed uncensoed-content ail, and the second te is unfilteed, censoed-content, and disguised ail fo high type ecipients (i.e., those who find it desiable to facilitate puchases ). The second aguent of the utility function (1), which is infoativeness-adjusted undesied ail eceived, becoes: u Type 1 eos = j {o,c} ɛκ j ˆn j ˆγ + (1 φ j t)κ j I(d j )n j j (6) d j γ j j {o,c} in which the fist te is undesiable unfilteed uncensoed ail, and the second te is unfilteed, censoed-content, disguised ail fo low type ecipients (who suffe fo eceiving it). The thid aguent of utility function (1), desied ail not eceived, becoes: u Type 2 eos = j {o,c} (1 ɛ)κ j ˆn j (1 )+ 1ˆγj j {o,c} φ j tκ j Ī(dj )n j (1 1 d j γ j ) (7) 14

16 whee the fist te is desied filteed uncensoed ail, and the second te is filteed censoed-content ail fo high type ecipients. 16 To siplify the odel, we ule out the unlikely scenaio that no one is using the existing eail channel: Assuption 2 The censoed channel is essential so that evey ecipient uses it. That is, κ c = 1. We also ake anothe assuption that will geatly siplifying the notations and algeba: Assuption 3 Thee is no uncensoed-content ail in the open channel. That is, ˆn o = 0. This assuption is justified in two senses. Fist, when thee is less spa in the censoed channel, uncensoed-content sendes will not want to use the open channel if the isk of it being filteed out in the open channel is getting less. Second, uncensoed-content ail will be ingled with possibly uch censoed-content ail, uncensoed-content sendes will need to weigh the chances of the ail being filteed in the censoed channel and being ingled in the open channel, especially if sending to an additional channel (even without filteing as in the open channel) incus exta costs. Assuption 4 The infoation pefeence functions take the following fo: I(d j ) = (d j ) β and Ī(dj ) = (d j ) β. The basic idea of the infoation pefeence function is to specify how an individual akes the tadeoff between infoation and volue. The above assuption iplies that the (dis-)utility associated with unfilteed censoed-content ail, which is I(dj )n j, becoes (d j ) β 1 n j d j γ j. Fo γ j β n = 0, such (dis-)utility becoes j. Recipient caes about the effective unfilteed volue not the infoation content. Fo β = 1, d j γ j such 16 One could elaboate by allowing Type 2 eos associated with tageted ail to be oe annoying. This is because ass ail always appeas in ultiple and soeties alost identical copies in a given ecipient s inbox. This highe substitutability iplies that thee is a low Type 2 eo cost associated with ass ail. That is, one could edefine spa as ail with lowe Type 2 eo cost. In othe wods, ass ail wongly filteed will cause uch less inconvenience than the countepat of tageted ail, even fo those ecipients who want ass-ail. The convese is not tue. Soe ecipients pefe even to neglect tageted ail fo soe people they know. Matheatically, one could define the fist te to incease at a highe ate than the second te in u Type 2 eos. 15

17 (dis-)utility becoes nj, ecipient is indiffeent o neutal to any disguise levels associated with unfilteed censoed-content ail. Fo β γ j (0, 1), (d j ) β 1 1, such (dis-)utility is weakly geate than nj. That is, γ j conditional on the sae volue of ail sent (n j ), high (low) type ecipients would athe (not) have a highe volue of disguised ail unfilteed than a lowe volue (since γ j is not adjusted by the disguise level that equals 1) of undisguised ail unfilteed. Fo β > 1, such (dis-)utility is weakly less than nj. That is, conditional on the sae n j γ, high (low) j type ecipients would athe (not) have a lowe volue of undisguised ail unfilteed than a highe volue of disguised ail unfilteed. Siilaly, the infoation neutal cuttoff fo the dis-utility associated with filteed censoed-content ail is β = β log( 1 1 γ j )/ log d j d j γ j If the copaison to the infoation neutal benchak cases offes a useful tool to undestanding the tadeoff between volue and infoation, having a diffeent function fo filteed and unfilteed ail, just as what we did using I(d j ) and Ī(dj ), allows a consistent desciption of a given individual s pefeence fo infoation acoss ail types. Fo exaple, a theoist could equie that a given individual ust be eithe one of the following: {(β = 1 and β = β ), (β < 1 and β < β ), (β > 1 and β > β )}. On the othe hand, one could also not ely on such tiplet to leave oo fo behavioal inconsistencies. As a siplification, we assue that the infoation pefeence functions ae hoogenous. That is,, β = β,and β = β. Let us now state the ecipient s poble foally. Given the filte stengths, disguise levels, eail volue and actions of othe ecipients, 1 17 Note that only high type ecipients expeience the dis-utility of Ī(dj )n j (1 d j γ ) = (d j ) β n j j (d j ) β 1 n j γ. Fo β = 0, such dis-utility becoes n j j nj d j γ. High j type ecipients suffe fo the effective filteed volue not the infoation content. Fo β = β log( 1 1 γ j )/ log d j, such dis-utility becoes n j 1 1 n j d j γ j γ, high type ecipients ae indiffeent to any disguise levels associated with filteed j censoed-content ail. To find β,equate (d j ) β n j (d j ) β 1 n j γ j with n j nj γ j (d j ) β (1 1 d j γ j ) = 1 1 γ j β log d j = log( 1 1 γ j getting: 1 1 d j γ j ) β = log( 1 1 γ j 1 1 d j γ j ) log d j Fo β (0, β ), such dis-utility is less than n j nj γ. That is, conditional on the j sae n j, high type ecipients would suffe less with a salle volue of disguised ail filteed than a highe volue of undisguised ail filteed. Fo β > β, such dis-utility is oe than n j nj γ. That is, conditional on the sae n j, high type j ecipients would suffe oe with a salle volue of disguised ail filteed than a highe volue of undisguised ail filteed. 16

18 ecipient akes a binay choice of whethe to ead ail in the open channel, κ o {0, 1}, by axiizing: U (u desied eceived, u Type 1 eos, u Type 2 eos) (8) Poposition 1 With Assuptions 1, 2, and 3, ecipients who have a positive value fo censoed contents, and only they, will use also the open channel. Poof. The esult is obtained staightfowadly fo the thee coponents of (dis-)utility, (5) (6). Fist, fo a ecipient who finds censoed content undesiable (φ j l = 0), eading the open channel povides no benefit, but ceates dis-utility by inceasing the aount of objectionable ail (see the second suand in (6)). Fo a ecipient who values censoed content, eading ail in the open channel inceases the second suand in (5) (desied ail eceived). It has no effect on Type 1 eos (6). Likewise it has no effect on Type 2 eos (7) because fo the open channel d j = γ j = 1, so the second suand is zeo when j = o. Thus, if an open channel is intoduced, h-type ecipients will use it to obtain benefit fo desied coecial spa, but l-types, who do not want spa, will not (as long as pesonal sendes do not stat sending (uch) to the open channel). We now tun to sendes to find the behavio of spaes when an open channel is intoduced, afte which we analyze the advetises poble, and the welfae effects of an open channel. 3.3 The Sendes Poble We will descibe in detail the cost and evenue functions of the censoedcontent ass-ail sendes only. Again, this is because the focus of the pape is to ove the supply of and deand fo censoed-content ass ail out of the cuent eail syste. The total cost function fo ass-ail sende, c (n o, n c, d c ), eflects the costs of geneating the eail volues, and of disguising ail sent to the censoed channel. The disguise cost is captued by c / d j < 0, and the volue geneating cost by c / n j > We allow fo econoies of scale in the sense of sub-additivity, 18 Rathe than having a zeo aginal cost as coonly asseted, spaes incu cost to enew technologies, which depeciate quickly, to geneate spa. Fo exaple, zobies (ie. hoe coputes hijacked by cackes) ae consistently destoyed by antivius softwae, so spaes ust continuously develop and distibute new viuses to captue new (tepoay) zobies. Zobies ae esponsible fo elaying oe than 60% of the wold s spa [Sophos, 2005]. 17

19 c (n o, 0, d c )+c (0, n o, d c ) > c (n o, n c, d c ), and cost copleentaity (ie., < 0, i j). To be concete, we specify c (n o, n c, d c ) = 2 c n j n i F C +g (d c )+δn o n c (no ) (nc ) 2, in which g (d c ) = , d c so that the cost of no disguising (d c = 1) is g (1) = 0. Cost copleentaity and subadditivity ae both ensued by letting δ < We also assue a egulaity condition of δ 2 < 1. On the evenue side, sendes ae pice takes. Selles of censoed goods pay the fo solicitations. Let p j be the advetising chage pe disguised eail ( nj ) eaching the uses in channel d j γ j j21. On a pactical level, the sende chooses whethe to send to the censoed o the open channel (o both). If sending to the open channel, the sende does not disguise content, and adds a tag that indicates the essage should be deliveed to the open channel. If sending to the censoed channel, the sende does not tag the essage, and in fact ay expend soe effot to disguise the content. We assue that ass ail sent is distibuted unifoly to the ecipients in a given channel. Given the pices and filte stengths, sende chooses (n o, n c, d c ) to axiize: s.t. π (n o, n c, d c ) = p o n o + pc n c d c γ c c (n o, n c, d c ) (9) d c [ 1, 1]. (10) γc Next we state the solutions to the above axiization poble: 19 We could have used a deceasing aginal cost function such as g(d c ) = 1 (d 1. c )2 20 Cost copleentaity follows fo δ < 0 because c n = δn o c + n c, and c n = o δn c + n o. Subadditivty does as well because c (n o, n c, d c ) [c (n o, 0, d c ) + c (0, n c, d c )] =F C + g (d c ) + δn o n c (no ) (nc ) 2 [F C (no ) 2 + F C + g (d c ) (nc ) 2 ] = δn o n c F C < In pactice, thee is a volue discount (that ight o ight not due to diinishing likelihood to espond). Fo instance, Send-Safe is a sevice spaes offe to advetises. One picing schee asks fo US$125 pe 1 illion cedits (a poxy of n j ) when an advetise pays fo 0.4 illion cedits. The pice dops onotonically d j j γ to US$10 pe 1 illion cedits when an advetise pays fo 300 illion cedits. This picing schee is available at 18

20 Poposition 2 The best esponses of sende ae 22 : Case (a), p o pc γc (1 δ 2 ) : δγ c δp c d c = 1; n o = 1 1 δ 2 (po δpc γ Case (b), p o pc δ γc (1 δ 2 ) δp c : c ); n c = 1 1 δ ( pc 2 γ c δpo ) (11) d c = 1 γ ; c n o = 1 1 δ 2 (po δp c ); n c = 1 1 δ 2 (pc δp o ) (12) We next discuss the iplications of Poposition 2. Mass ail sent to a paticula channel is inceasing in the advetising pice of that channel, and of the othe channel only when thee is copleentaity (δ 0). Any possible incease is at a lowe ate when the copleentaity is weak (i.e., δ is sall). In fact, when copleentaity is weake, ass ail sent will be lowe in both channels. Also, as long as eithe p o o p c is (o both ae) stictly positive, thee will be ass-ail sent to both channels unless δ = 0. In othe wods, spa will not be totally eliinated when δ 0. When thee is copleentaity, it is optial to send soe positive volue to the channel even though the pice thee is zeo. This is because this helps educe the volue geneation cost in the othe channel. Notice that the aginal evenues of sending n o and n c ae p o and d c γ c p c. Altenatively, one could egad the aginal evenues of each n o and n c as p o and pc. To incease the total evenue in the censoed channel d c γ c by the sae aount, a sende could eithe adjust n c o d c, depending on which is cheape. Since the ecipocal of the disguise cost is linea and the volue cost is convex, if they ae on the sae plane, they intesect at one point. Left of this point, the volue cost is less convex, so the aginal volue cost is less than the aginal disguise cost. Adjusting volue but not disguising is cheape. Right of this point, the opposite happens. Disguising is cheape so one will neve incease n c beyond the intesection point. The intuition fo the effects of γ c is the following. In case (a), d c is unchanged fo the default level. The only degees of feedo to adjusting evenue ae n o and n c. When γ c inceases, pc deceases. Befoe γ c the change of γ c, pofit axiization ust iplies that the aginal 22 Fo the tivial case of p o = p c = 0, we have shown in Appendix 6.1 that: d c = 1; n o = 0; n c = 0. 19

21 evenue pc ust equal soe aginal cost. Thus, when pc deceases, it γ c γ c ust equal soe lowe aginal cost. But since the total cost is convex, n c ust be loweed conditional on the sae o salle n o. This can be confied fo the best esponse of n c in case (a), whee both n c and n o ae deceasing in γ c. n o is deceasing in γ c fo a diffeent eason. Now we knew that an incease in γ c deceases n c. But the aginal cost of sending n o is c = δn c n o + n o, educing n c inceases c since n o δ < 0. Again, by equating the aginal evenue p o with soe aginal cost, n o ust be loweed. Moe geneally, γ c is negatively elated to n o and n c. In case (b), d c vaies invesely with γ c. In fact, d c is at the 1 lowest bound of. In this case, only d c γ c adjusts because educing d c is always cheape than inceasing n c when γ c changes. Again, since n o and d c ae only elated though n c in c, when n c n o is unchanged, so is n o. It is ipotant to ephasize again that the volues sent ae not necessaily the sae as the volues eceived. The latte is what the ecipients should be concened about in addition to the disguise levels. We defe the utility changes due to disguise levels until the welfae analysis in the next section. With soe intuition explained above, we ae eady to suaized the popeties of volues sent and eceived in the following poposition: Poposition 3 Conside the two cases in Poposition 2. (1) In the censoed channel, the total volue of eail eceived is: i) inceasing in both p o and p c ; ii) deceasing in δ; iii) deceasing in γ c in case a, and independent in case b. The total volue of eail sent is: i) inceasing in p o and p c, deceasing in p c ; ii) unchanged in δ; iii) deceasing, and unchanged in γ c in cases a and b, espectively. (2) In the open channel, the total volue of eail eceived vis-a-vis sent n o d o γo ae the sae by constuction (i.e., = n o ). Such volues ae: i) inceasing in p o and p c ; iii) deceasing in δ; iv) deceasing, and unchanged in γ c in cases a and b, espectively. Poof. In the censoed channel, the total volue of eail eceived ae: Case (a), p o pc γc (1 δ 2 ) : δγ c δp c Case (b), p o pc δ γc (1 δ 2 ) δp c : n c d c γ = 1 c 1 δ [ p c 2 (γ c ) δpo 2 γ ] (13) c n c d c γ = c n c = 1 1 δ 2 (pc δp o ) (14) 20

22 All diections of change hee can be seen by inspection o staightfowad diffeentiations. 3.4 The Advetises Poble Advetise a pays an advetising chage of p j fo each eail essage that passes though the filte in channel j. Fo each poduct o sevice sold, the advetise collects a sales evenue of s. The pobability of puchase is θ j θ( R φ j t =1, d j R j a d i a) fo each p j paid, whee R φ j t =1 is the nube of high type ecipients in channel j, and d j a [ 1, 1] is the disguise level γ j associated with n j a, which is the volue of eail advetise a asks the R φ j t =1 R j spaes to successfully pass though the filte in channel j. 23 easues the aveage φ j t in channel j.d j a d i a easues the infoativeness of the essages elative to the countepat in the othe channel. θ 1 > 0 because of a highe popensity to puchase is tautologically associated with a highe aveage φ j t. θ 2 > 0 because of an assuption that a geate infoativeness of the essages elative to the countepat in the othe channel is assued to facilitate puchase bette. The cost function consists of two pats: poduction and advetising. The total poduction cost, k( j θj n j a), is a convex function as usual, whee j θj n j a is the total quantity of goods o sevices sold. The total advetising cost, j pj n j a, is linea howeve. The spae s aket is copetitive. Spaes as pice takes teats the aginal evenue of spaing, p j, as given. Fo such aket to clea, p j ust also equal to the aginal advetising cost fo the advetises. Hence, the total advetising cost is linea. In othe wods, it only chooses {n j a} j=c,o to axiize expected pofits because {n j a} j=c,o is sufficiently sall aong the any advetises that its advetising deand does not dive up o down the aginal advetising cost p j. That is, p j is independent of {n j a} j=c,o. Of couse, the aggegate level { a nj a} j=c,o will affect p j but we will ignoe this effect. Matheatically, advetise a chooses {n j a} j=c,o to axiize: 23 Note that θ is not a function of the volue of eail advetise a asks the spaes to successfully pass though the filte in each channel. It is easonable in the sense that ecipients ae oe likely to ake a puchase if they ae being epeatedly einded of, and that such volue is sufficient sall so that each ecipient is not likely to eceive ultiple eail by the sae advetise. We theefoe ule out the case in which the diinishing etuns kick in a significant way when thee ae ultiple advetises selling the sae sevices o poducts. 21

23 π a = j [sθ( R φ j t =1, d j R j a d i a) p j ]n j a k( j θ j n j a) (15) The advetises axiization poble gives the aginal evenue equals aginal cost condition: j i : p j = θ j [s k ( j θ j n j a)] (16) Now we will show the elationships between advetising chages in each channel, befoe and afte the ipleentation of the open channel. (Note that we use to denote vaiables when the open channel is absent. When the open channel is absent, we define it by saying that δ = 0, and p o = 0 [o equivalently γ o, ˆγ o ]. Denote θ ( R φ c t =1, d c, R c a ) as the esponse function when the open channel is absent.) Poposition 4 (i) The advetising chage in the open channel is weakly highe than that in the censoed channel (and than that in the censoed channel when the open channel is absent if a sufficient condition is et). (ii) The advetising chage in the censoed channel weakly deceases when the open channel is ipleented. (iii) The advetising chages ae inceasing in the aveage popensity to puchase. Poof. (i) By (16), p o p c = (θ o θ c )[s k ( j θj n j a)]. Again by (16), [s k ( j θj n j a)] is positive fo positive pices. We just need to show that (θ o θ c ) 0. By Poposition 1, R φ o t =1 = Rφo t =1 R φ c R o t =1. Also, by R φ o t =1 R c constuction, d o a = 1 d c a. So d o a d c a 0, and d c a d o a 0. These iply that θ o θ( R φ o t =1, d o R o a d c a) θ( Rφc t =1, d c R c a d o a) θ c. Hence, we have p o p c. To have p o p c,, by (16), we equie a sufficient condition of θ o θ c, o equivalently: θ(1, 1 d c a) θ ( R φ c t =1, d c, R c a ). (17) (ii) Fist, by Poposition 1, R φ c t =1 eains the sae when the open channel is ipleented because the high type ecipients only use the open R c channel additionally while continue using the censoed channel. Second, d c a d o a = d c a 1 0, so d c, a 0 d c a d o a. These iply that θ ( R φ c t =1, d c, R c a ) θ( R φ c t =1, d c R c a d o a). We have p c, p c by (16) because [s k ( j θj n j a)] and [s k (θ c, n c a)] ae positive fo positive pices. (iii) Taking a deivative of (16) w..t. R φ j t =1 R j : 22

24 p j ( R φ j t =1 R j ) = θ j 1[s k ( j = θ j 1[s k ( j θ j n j a)] + θ j k ( j θj n j a) ( R φ j t =1 R j ) θ j n j a)] + θ j k n j aθ j 1 0 To solve fo the sufficient condition in Poposition 4, one needs to specify a functional fo of the esponse function. Assuption 5 The esponse function takes the fo of an exponential distibution. Moe specifically, θ( R φ j t =1 R j, d j a d i a) 1 e ( R φ j t =1 R j +e dj a di a). The sufficient condition takes a siple fo unde this exponential distibution, which is 1 d c a d c, a Welfae Poposition 5 Unde a sufficient condition, the ipleentation of the open channel deceases the volue of censoed-content ass ail unfilteed in o sent to the censoed channel and its associated dis-utility fo ecipients who do not want it. Poof. We have showed that n c, n c n, c, n c d c, γ c and I(d c, )n c, d c γc d c, γ c I(d c )n c in Appendix 6.2 unde soe sufficient conditions. d c γ c Whethe such sufficient condition will be satisfied depends on the values of the paaetes and futhe specifying soe functional fos, which will necessaily estict the geneality of ou esults. We will leave it as it is but instead offe soe geneal intuition about when the sufficient condition is oe likely to satisfy. It is tue that the intoduction of the open channel deceases the pobability of a sale in the censoed channel because θ( R φ c t =1, d c R c a d o a) θ( Rφc t =1, d c, R c a ). Subsequently, p c, p c as we have seen in Poposition (4). It does not necessaily iply that afte equating aginal cost with aginal evenue (p c, and p c ), the 24 θ(1, 1 d c a) θ ( R φ c t =1 R c (1 + e 1 dc a ) R φ j t =1 R j, d c, a + e d c, a c ) 1 e (1+e1 d 1 d c a d c, a a ) 1 e ( R φ j t =1 R j +e dc, a ) 23

25 volue of eail sent will decease. This is because with the intoduction of the open channel, sendes benefit fo copleentaity so that the aginal cost of sending is cheape. In all, to the extent that the copleentaity effect does not cowd out the effect fo the decease in aginal evenue, the volue of censoed-content ass ail sent will decease. The associated dis-utility in tun will have to depend on the tadeoff between the pefeence of infoation ove volue as detailed by the I( ) in the ecipient s poble. Now we ake one siplifying assuption befoe we analyze the welfae effects. Assuption 6 The uncensoed-content ail sendes do not change the eail volue they sent to the censoed channel afte the open channel is intoduced. That is, ˆn c = ˆn c,. Assuption 3 aleady iplied that the uncensoed-content ail sendes find it pofit-axiizing to use only the censoed channel. Assuption 6 futhe assets that when the open channel is absent, the censoed channel is no less o oe poductive fo such sendes. Of couse, in eality, it is possible to have a scenaio that we nonetheless uled out below. When the open channel is absent, thee could be uch censoed-content ail in the censoed channel (as we have shown in Poposition 5) that could intefee with othe counications such as uncensoed-content ail. Thus, with the intoduction of the open channel, the censoed channel is becoing oe poductive fo uncensoed-content ail sendes, and it is possible that ˆn c ˆn c,. To be oe pecise, we ule this out because we want to have a benchak to copae the welfae with and without the open channel. If one allows ˆn c ˆn c, to happen, then thee ight be only welfae loss when the open channel siply because ˆn c becoes vey high and the dis-utility associated with the potion of this that is wongly filteed (at a ate of ˆγ c ) copletely offset the utility associated with oe (less) spa eceived fo ecipients who (do not) want it. We theefoe think Assuption 6 as a benchak is easonable. Poposition 6 Unde Popositions 1, 2, 4, 5, Assuptions 1, 2, 3, 4, and a sufficient condition, the welfae of the advetises, censoed-content ass-ail sendes and all ecipients will be unchanged o inceased when thee is an open channel. Poof. The welfae of the censoed-content ass-ail sendes and advetises will be unchanged because they ake zeo pofit with and without the open channel. The welfae of the ecipients could diffe. To copae the welfae change fo a given ecipient when thee is an open 24

26 channel, we copae his o he utility afte and befoe the oll-out of the open channel in Appendix : U li U (18) γ o,ˆγ o Ou intepetation is that when the filte stengths associated with the open channel ae infinitely stong, it is as if thee is no such channel fo any pactical use. Essentially, we have poved that each use s utility has not deceased afte the oll-out of the open channel because the utility associated with desied ail eceived does not decease, and the dis-utilities associated with Type 1 and 2 eos do not incease. 4 Ipleentation Issues We ephasize that ou poposal is a stating point. Thee ae ipleentation issues, which ae outside the scope of this eseach, that ust be addessed: Will the total tade volue of censoed goods incease? Is it easonable to assue that the open channel siply shifts the supply of such goods fo othe outlets? What is the agnitude of the aginal exposue of ponogaphy fo inos in the open channel? Have they aleady been exposed significantly by websites on the Intenet? Should we add inial censoship to the open channel by blocking sexually explicit iages o equiing cedit cad nubes to access the open channel? Will the ain aguent still hold as long as the open channel is significantly less censoed than othe channels? Moe geneally, what ae the social iplications if it is easie to obtain countefeit poducts o piated softwae because of the open channel? The open channel is a typical poble of two-sided akets with the sides of buyes and selles. Is it desiable fo the lage eail sevice povides to unilateally opt-in fo all the ecipients (so at least one side of the aket is on boad)? 26 Cuently, Gail lists 25 Technically, the liit is well defined only if the disguise levels convege to zeo faste than the filte stengths to divege to infinity (note: the bounds of a disguise level is zeo and 1 in the liit) because soe of the denoinatos could othewise becoe zeo s. But the disguise levels will indeed not tend to zeo. Since the disguise cost is assued to be convex, given a fixed advetising pice, the sendes cannot ake enough oney to justify the inceasing disguise costs when the disguise levels tend to zeo. 26 Gail, Yahoo!, and Hotail ae thee lagest online eail sevice povides, each with a aket shae close to 1/3. 25

27 side-by-side soe advetiseents even fo soe spa essages. Will the possibly inceased eail volue (at least eail with censoed contents) be sufficient incentives fo the pivate povision of the open channel? How any povides adoptions do we need fo the open channel to be effective? Ae the custoes willing to switch to the few adoptes? Will the open channel be flooded with eail? Even if yes, the eail is not disguised. Will a seach function sufficiently offset the inconvenience of such flooding? Also, will spaes, who ight no longe disguise thei identities, weed out each othe (and thei associated volue) by establishing eputation? Lastly, will the Type-2 eos associated with spa sufficiently sall (so flooding does not cause uch inconvenience) as we have subsued in the definition of spa? What ae the othe easons to stop spaes fo sending pesuasive advetising to the censoed channel? Will the undisguised ail in the open channel be sufficient theats to any pesuasive ail in the censoed channel? Will selles utilizing the open channel be able to undecut the pice of any goods o sevices sold in the censoed channel since thee is no need fo the to incu disguise costs? 5 Conclusions We popose a pincipled appoach to developing and analyzing spa policies. Ou appoach is gounded in an econoic, ational choice chaacteization of the choices ade by ecipients, spaes, and advetises. Ou novel insight is to induce the supplies fo and deandes of coecial spa to ove out of the cuent eail syste (a censoed channel), by poviding an open channel in which those who want the advetiseents can find the. As a coollay benefit, esouces ae not wasted on unpoductive content disguising, and eades eceive highe quality (oe infoative) ads. Technical filtes and legal ules aise the cost of deliveing spa to eades. Costs ae bone by advetises (who ust develop eve-changing techniques fo avoiding filtes, etc.), but also by ecipients, who spend tie doing the difficult filteing and eviewing that cannot be autoated. On the othe hand, an equivalent eduction in the benefits of spaing (e.g. by oving out spa deandes) should have the sae incentive effect. Moe geneally, ethods that channel counications oe diectly to those who want the would lowe costs on both sides and be welfae ipoving. 26

28 In ou atheatical odel, we have shown that unde cetain conditions, all eail ecipients ae bette off with the intoduction of such open channel: only ecipients wanting spa will use the open channel enjoying the less disguised essages, and fo all ecipients the satisfaction associated with desiable ail eceived inceases, and dissatisfaction associated with both undesiable ail eceived and desiable ail filteed out deceases. We especially have taken into account of how ecipients tade off between infoation and volue by intoducing the concept of deviations fo infoation neutality. We do not clai that ou idea would povide a coplete solution to the cuent spa poble, but we do offe a novel new tool that, togethe with the othe well-known tools (technical, legal and econoic), ay contibute to a eduction in the flow of low-infoation, unsolicited coecial bulk eail. The ultiate solution, siple econoics pedicts, is fo the value of puchasing stiulated by spa to fall sufficiently low that it is less than the aleady low cost of sending spa. If we can tept a substantial nube of consues who want to puchase spaadvetised poducts into a sepaate eail channel (tept the with the expectation of highe quality, oe infoative ads to help the find the poducts they want), the puchasing value eaining in the taditional, filteed channel ay dop sufficiently to stat discouaging spaes fo using that inceasingly unpoductive channel. In othe wods, we take a staightfowad econoic appoach to the question, by ecognizing that thee is not just a supply cuve but also a deand cuve fo spa. We odel the incentives, within the ecosyste of existing spa solutions, to induce both supplies and deandes to ove out of the cuent censoed channel and into the open channel. If custoes who want to puchase will benefit fo oe infoative ads in a sepaate channel, then spa advetises will benefit fo focusing thei advetising spending on that channel. This should not be a vey contovesial idea, but it is, we believe, an idea that has been lagely issing fo the debate. Thee is anothe illuinating econoic pespective on ou wok: spa is fundaentally a poble that aises when disposal is not fee. We know fo the Fist Fundaental Welfae Theoe that unegulated fee akets ae geneally Paeto efficient, but that esult equies fee disposal. Spa is not fee to dispose: it equies tie to open and conside. Soe types of spa ae alicious and ay actually cause ha to one s data files o opeating syste befoe we can dispose of it. Ou poposal eceates a fee aket the open channel fo those who do not want to dispose of spa. It contasts with othe fee-aket solutions (e.g. eail staps and bonds fo eail spa, and Google s 27

29 AdWods fo web spa) in the following way. The open channel gives the ight to ecipients to eceiving spa; it eoves the ight of the eail sevice povides to decide whethe the ecipients should eceive spa. (Moe geneally, the ecipients ight to choose the level of censoship is one of the any othe possible popety ight eassignents in the eail ecosyste that have been lagely unexploed in the liteatue.) Also, we povide those fo who the disposal costs ae sufficiently high (not fee) the choice to opt out and paticipate only in the censoed channel. Meanwhile, sendes (and also spa deandes) do not intenalize the disposal costs of uninteested ecipients, but the sendes nonetheless choose to send less to the censoed channel because the aveage popensity to buy falls as spa eades ove to the open channel. Of couse, not all spa is designed to delive infoative advetising essages to willing custoes. A significant potion of spa is intended to deceive eades (e.g., phishing and othe scas), and othe spa essages ae intended to pesuade eades who ay not have peviously thought they wanted to puchase a spa-advetised poduct (and thus, who would not ead the essages in the uncensoed advetising channel). We do not suggest that ou poposal will have a diect effect on the quantity of isleading spa eail (it ight affect pesuasive advetising because a lage faction of those susceptible to this ay aleady be inclined to ead the uncensoed and oe infoative advetising channel). An open advetising channel is possible at low cost, and it is conceivable that it would ake eail uses at least weakly bette off (no wose off) than the status quo. At the vey least, the solution is fully evesible. If well-designed, an incentive-copatible advetising channel that hanesses the siultaneous foces of deand and supply could significantly educe the flow of unsolicited bulk coecial eail. 6 Appendix 6.1 Poof of Poposition 2 The sende s pofit function is the Lagangian is: π (n o, n c, d c ) = p o n o + pc n c d c γ c c (n o, n c, d c ), (19) L = π( ) λ c 1(d c 1) + λ c 2(d c 1 γ c ) + µo n o + µ c n c (20) whee λ c 1, λ c 2, µ c, µ o 0. 28

30 The copleentay slackness conditions ae: FOCs: λ c 1(d c 1) = 0 (21) λ c 2(d c 1 γ c ) = 0 (22) µ o n o = 0 (23) µ c n c = 0 (24) p o = c µ o = δn c n o + n o µ o = n o = p o δn c + µ o (25) p c d c γ = c µ c = δn o c n c + n c µ c = n c = pc d c γ c δno + µ c (26) p c n c (d c ) 2 γ c λc 1 + λ c 2 = c d c Cobining (25) and (26): = g (d c ) = (d c ) 2 1 = pc n c γ c + (λ c 1 λ c 2)(d c ) 2 (27) = d c = ( 1 pcnc γ c ) 1/2, λ c λ c 1 λ c 1 λ c 2 (28) 2 n o = p o δ( pc d c γ c δno + µ c ) + µ o = 1 1 δ 2 [po δ( pc d c γ c + µc ) + µ o ] (29) n c = pc d c γ c δ(po δn c + µ o ) + µ c = 1 1 δ 2 [ p c d c γ c δ(po + µ o ) + µ c ] (30) Befoe doing oe substitutions in the above nonlinea equations to solve fo d c, n o, n c oe explicitly, we fist see if we could eliinate soe cases below. 29

31 Case 1: n o, n c > 0 = µ o = µ c = 0. Fo (29), n o = 1 p c 1 δ 2 [po δ( )] (31) d c γ c Fo (30), Subcase 1: d c = 1 = λ c 2 = 0 Fo (31), Fo (32), Fo (27), n c = 1 1 δ 2 [ p c d c γ c δpo ] (32) n o = 1 1 δ 2 [po δ( pc )] (33) γ c n c = 1 1 δ 2 [ pc γ c δpo ] (34) Fo (35), λ c 1 > 0 λ c 1 = γc p c n c γ c (35) Fo (35), λ c 1 = 0 γ c > p c n c (36) γ c > pc 1 δ ( pc 2 γ c δpo ) (37) γ c = p c n c γ c = pc 1 δ ( pc 2 γ c δpo ) Theefoe, subcase 1 is adissible when γ c pc ( pc 1 δ 2 γ c equivalently p o pc γc (1 δ 2 ). 27 δγ c δp c Subcase 2: d c = 1 γ c = λ c 1 = 0 Fo (31), Fo (32), Fo (27), δp o ), o n o = 1 1 δ 2 [po δp c ] (38) n c = 1 1 δ 2 [pc δp o ] (39) 27 The inequality eveses diection because we ultiplied both sides by δ < 0. 30

32 Fo (41), λ c 2 > 0 1 = pc n c λc 2 γ c (γ c ) 2 (40) λ c 2 = γ c p c n c (γ c ) 2 (41) Fo (41), λ c 2 = 0 γ c p c n c (γ c ) 2 > 0 (42) p c n c > γ c (43) p c (p c δp o ) > γ c 1 δ 2 (44) p c n c = γ c (45) p c (p c δp o ) = γ c 1 δ 2 (46) Theefoe, subcase 2 is adissible when γ c pc 1 δ 2 (p c δp o ) o equivalently p o pc δ γc (1 δ 2 ) 28 δp c. Subcase 3: d c ( 1, 1) = λ c γ c 1 = λ c 2 = 0. Equation (27) and the peises fo this subcase iply that: Substitute (47) into (32) to get 28 : d c = γ c = n c p c (47) (p c ) 2 (1 δ 2 )(γ c ) 2 + δp o p c γ c (48) δp o + (1 δ 2 ) γc p c = pc d c γ c n c = 1 1 δ 2 ( p c d c γ c δpo ) γ c p c = 1 1 δ 2 ( p c d c γ c δpo ) d c (p c ) 2 = (1 δ 2 )(γ c ) 2 + δp o p c γ c 31

33 By d c ( 1 γ c, 1), we ust have O equivalently, 1 γ c < (p c ) 2 (1 δ 2 )(γ c ) 2 + δp o p c γ c < 1 (49) p c δ γc (1 δ 2 ) δp c < p o < pc δγ c γc (1 δ 2 ) δp c (50) Note that the inteval in which subcases 1 and 2 ovelap is: p c δ γc (1 δ 2 ) δp c p o pc δγ c γc (1 δ 2 ) δp c (51) Note fist that subcase 3 cannot coexist with eithe subcases 1 o 2 because the endpoints of the open inteval of d c in subcase 3 coincides that of the othe subcases. So the only possibility is that eithe of the following is tue (but not both). (a) subcase 3 is tue; (b) subcases 1 and (o) 2 ae tue. Suppose (a) is tue, then (b) is not tue. But this iplies (50) and NOT (51) ust be both tue. This contadicts with (50) being subsued in (51). Theefoe, subcase 3 is eliinated. Case 2: n o > 0, n c = 0 Fo (26), n c = pc d c γ c δno + µ c 0 = pc d c γ c δno + µ c Since the ight hand side is non-negative, the only peissible values ae p c = µ c = n o = 0,which contadicts with n o > 0. Case 3: n o = 0, n c > 0 Fo (25), n o = p o δn c + µ o (52) 0 = p o δn c + µ o (53) Since the ight hand side is non-negative, the only peissible values ae p o = µ o = n c = 0,which contadicts with n c > 0. Case 4: n o = n c = 0. Fo (25), 32

34 n o = p o δn c + µ o (54) 0 = p o + µ o (55) Since the ight hand side is non-negative, the only peissible values ae p o = µ o = 0. Fo (26), n c = pc d c γ c δno + µ c (56) 0 = pc d c γ c + µc (57) Since the ight hand side is non-negative, the only peissible values ae p c = µ c = 0. n c = 0 iplies that (28) gives: d c 1 = ( ) 1/2 (58) λ c 1 λ c 2 Subcase 1: If λ c 1 = 0 and λ c 2 = 0, (27) iplies a contadiction because: p c n c γ c = 1 (59) n c = γc p c 0 (60) Subcase 2: If λ c 1 = 0 and λ c 2 > 0, it gives a contadiction of d c being negative by (58). Subcase 3: If λ c 1 > 0 = d c = 1 (see (21)). Theefoe, case 4 is adissible when Q.E.D. 6.2 Poof of Poposition 5 d c = 1; p o = p c = 0 (61) We will show that n c, n c and n c, n c d c, γ c. And by hoogeneity d c of sendes and even distibution of ass ail, γc it is equivalent to poving I(d c, )n c, I(d c d c, γ c )n c to show that I(d c, )n c, I(d c )n c d c γc d c, γ c because d c γ c 1 R c nc, n c, and 1 R c nc n c. Recall that when the open channel is pesent: Case (a), p o pc γc (1 δ 2 ) : δγ c δp c 33

35 n c = 1 1 δ ( pc 2 γ c δpo ) (62) n c d c γ = n c c γ = 1 c 1 δ [ p c 2 (γ c ) δpo 2 γ ] c (63) I(d c )n c = I(1)n c = 1 d c γ c γ c 1 δ [ p c 2 (γ c ) δpo 2 γ ] c (64) Case (b), p o pc δ γc (1 δ 2 ) δp c : n c d c γ = c n c = 1 1 δ 2 (pc δp o ) (65) I(d c )n c = I( 1 d c γ c γ c )n c = 1 1 δ [ p c 2 (γ c ) δpo β (γ c ) ] β (66) Again we use to denote vaiables when the open channel is absent. When the open channel is absent, it can be shown that we could siply substitute δ = 0, and p o = 0 (o equivalently γ o ) into the above equations and the adissible anges (but fist ultiply both sides with δ fo the anges befoe the substitutions so the anges will not be undefined): Case (a), p c, γ c : n c, n c, d c, I(d c, )n c, d c, Case (b), p c, (γ c ) 1/2 : I(d c, = pc, γ c (67) γ = nc, c γ c = I(1)nc, γ c γ c n c, d c, )n c, = pc, (γ c ) 2 (68) = pc, (γ c ) 2 (69) γ = c n c, = p c, (70) d c, = I( 1 γ c γ c )n c, = pc, (γ c ) β (71) Without futhe specifying oe functional fos of θ j and k in the advetise s poble, it is not possible to decide which case the paaetes will fall into unde the scenaios of whethe the open channel is pesent o absent, it ay not be appopiate to copae the sae case 34

36 acoss scenaios. Fo exaple, it ay not be appopiate to copae the case (a) with the open channel with the case (a) without the open channel. But we know that the case (b) vaiables at issues ae always weakly lage with and without the open channel when β [0, 1]. It is then sufficient to show that the vaiables at issue in case (a) without the open channel is always weakly lage than the countepat vaiables in case (b) with the open channel fo β [0, 1]. Essentially, we will show a sufficient condition so that: I(d c, n c, d c, )n c, n c,,case a n c,case b (72) γ c case a d c, γ c case a n c d c γ c case b I(d c )n c d c γ c case b (73) (74) In fact, the second inequality iplies the thid because I(d c, ) case a = 1 I(d c ) case b = 1. (γ c ) β Equivalently, the second inequality can be ewitten as: p c, (γ c ) δ 2 (pc δp o ) (75) And the fist inequality can be ewitten as: p c, γ c 1 1 δ 2 (pc δp o ) (76) Note that the second inequality also iplies the fist inequality because (75) = (76). Applying the fist-ode condition of the advetises poble, we have p o = θ o (s k ); p c, = θ o, (s k 1 ). So (p c δp o ) = 1 (θ c 1 δ 2 1 δ 2 δθ o )(s k ) and (75) becoes: θ o, (s k ) (γ c ) δ 2 (θc δθ o )(s k ), (77) whee R φ o t =1 R o = 1 by Poposition 1. This is the fist pat of the sufficient condition fo this poposition. Fo β > 1, we have to additionally show the second pat of the sufficient condition: I(d c, )n c, d c, γ c case a I(d c, d c, )n c, γ c case b 35 I(d c )n c d c γ c case a I(d c )n c, d c γ c case b (78)

37 o equivalently: p c, (γ c ) 2 pc, (γ c ) β 1 1 δ 2 [ p c (γ c ) 2 δpo γ c ] 1 1 δ 2 [ p c (γ c ) β δpo (γ c ) β ] (79) Siilaly, one could futhe substitute in the fist-ode condition of the advetises poble. Q.E.D. 6.3 Poof of Poposition 6 Assue the intechangeability of the liit signs fo U : li U (u γ o,ˆγ o desied eceived, u Type 1 eos, u Type 2 eos) (80) = U ( li li γ o,ˆγ o u desied eceived, γ o,ˆγ o u Type 1 eos, γ o,ˆγ o u Type 2 eos) li (81) whee (use as a supescipt to denote the best esponses of the sendes when γ o, ˆγ o ): li γ o,ˆγ o u desied eceived = (1 ɛ) κc ˆn c, ˆγ c + φc tκ c I(d c, )n c, (82) d c, γ c li γ o,ˆγ o u Type 1 eos = ɛ κc ˆn c, ˆγ c + (1 φc t)κ c I(d c, )n c, (83) d c, γ c li γ o,ˆγ o u Type 2 eos (84) = (1 ɛ)κ c ˆn c, (1 1ˆγ ) + c φc tκ c Ī(dc, )n c, (1 1 d c, γ ) (85) c Since U li γ o,ˆγ o U 0 if (a) u desied eceived li γ o,ˆγ o u desied eceived, (b) u Type 1 eos li γ o,ˆγ o u Type 1 eos, and (c) u Type 2 eos li γ o,ˆγ o u Type 2 eos, we pove each of these inequalities below. (i) Inequality (a) is u desied eceived li γ o,ˆγ o u desied eceived, o equivalently: j {o,c} (1 ɛ)κ j (1 ɛ) κc ˆn c, ˆγ c ˆn j ˆγ + j j {o,c} φ j tκ j I(d j )n j d j γ j + φc tκ c I(d c, )n c, (86) d c, γ c 36

38 Assuption 3 iplies that (1 ɛ)κ o ˆn o (1 ɛ)κ c ˆn c ˆγ c = (1 ɛ) κc ˆnc, ˆγ c φ c ti(d o )κ o n o d o γ o ˆγ o. (86) becoes: = 0. Assuption 6 iplies that φc tκ c I(d c, )n c, (87) d c, γ c The above is tue fo φ o t = 0 because both sides ae zeo. Fo φ o t = 1, κ o = κ c = 1 by Poposition 1. Note that d o = 1, γ o s = 1, and I(1) = 1. (87) becoes: n o n c, (88) To pove that n o n c,. Let s fist look at the censoed-content assail sende s poble. Fo n o, the aginal evenue is p o and the aginal cost is c = δn c + n o. Fo n c,, the aginal evenue is p c, d c, n o = δno, and the aginal cost is n c, γ c (set δ = 0 in c + n c, n c, ). Pofit axiization iplies that each censoed-content ass-ail sende equates aginal evenue with aginal cost: and p o = δn c + n o (89) p c, d c, γ = c nc, (90) By Poposition 4, p o p c,. Togethe with d c, γ c 1, we have p o pc, d c, γ c (91) Substitute the value of the above inequalities fo the two pofit axiization conditions above, we have: δn c + n o n c, (92) n o n c, because δ < 0 (93) n o no R o n o n c, n c, by hoogeneity of sendes (94) nc, R since c, Rc, R o by Poposition 1 (95) because by definition nj = n j R j (96) (ii) Inequality (b) is u Type 1 eos li γ o,ˆγ o u Type 1 eos, o equivalently: 37

39 j {o,c} ɛ κc ˆn c, ˆγ c Assuption 3 iplies that ɛ κo ˆno ˆγ o ɛ κc ˆn c,. (97) becoes: ˆγ c j {o,c} ɛκ j ˆn j ˆγ + (1 φ j t)κ j I(d j )n j j d j γ j j {o,c} (1 φ j t)κ j I(d j )n j d j γ j + (1 φc t)κ c I(d c, )n c, (97) d c, γ c = 0. Assuption 6 iplies that ɛ κc ˆnc ˆγ c = (1 φc t)κ c I(d c, )n c, (98) d c, γ c The above is tue fo φ o t = 1 because both sides ae zeo. Fo φ o t = 0, because κ c = 1 and κ o = 0 by Poposition 1, it is sufficient to pove fo all low type ecipients that: I(d c )n c I(dc, )n c,, (99) d c d c, which has aleady been poved unde a sufficient condition in Appendix 6.2. (iii) Inequality (c) is u Type 2 eos li γ o,ˆγ o u Type 2 eos, o equivalently: j {o,c} (1 ɛ)κ j ˆn j (1 1ˆγj ) + j {o,c} φ j tκ j Ī(dj )n j (1 1 d j γ j ) (1 ɛ)κ c ˆn c, (1 1ˆγ ) + c φc tκ c Ī(dc, )n c, (1 1 d c, γ ) (100) c Assuption 3 iplies that(1 ɛ)κ o ˆn o (1 1ˆγ ) = 0. Assuption 6 iplies o that (1 ɛ)κ c ˆn c (1 1ˆγ ) = (1 ɛ)κ c ˆn c, c (1 1ˆγ ). (100) becoes: c j {o,c} φ j tκ j Ī(dj )n j (1 1 d j γ j ) φc tκ c Ī(dc, )n c, (1 1 d c, γ c ) (101) The above is tue fo φ o t = 0 because both sides ae zeo. Fo φ o t = 1, because κ c = 1 and κ o = 1 by Poposition 2, (101) becoes: j=o,c Ī(d j s)n j (1 1 d j γ j ) Ī(dc, )n c, (1 1 d c, γ c ) (102) 38

40 But thee is no Type 2 eos with censoed-content ail in the open channel because γ o = 1 (iplying d o = Ī(do ) = 1), so it is equivalent to poving that: Ī(d c )n c (1 1 d c γ c ) Ī(dc, )n c, (1 1 d c, γ c ) (103) By Appendix 6.2, we aleady knew that unde a sufficient condition, n c n c,, and since Ī( ) is an inceasing function, we just need to show d c d c, to pove (103). Since fo Appendix 6.2, we aleady knew that d c and d c, ae eithe 1 in case (a) o 1 in case (b) depending γ c on the paaetes that deteined which cases will happen with and without the open channel. Without the actual values of the paaetes o oe specific functional fos, it is possible to tell whethe we should copae case (a) with the open channel with case (a) o case (b) without the open channel, etc. We theefoe will state a sufficient condition fo d c d c, to hold. This sufficient condition is that the case (a) in the with-open-channel scenaio iplies the case (a) in the without-openchannel scenaio, and that the case (b) in the without-open-channel scenaio iplies the case (b) in the with-open-channel scenaio. Q.E.D. 39

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