How To Compare Frm To An Isac

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1 Informaton Systems Research Vol. 16, No. 2, June 2005, pp ssn essn nforms do /sre INFORMS The Economc Incentves for Sharng Securty Informaton Esther Gal-Or Katz Graduate School of Busness, 368 A Mervs Hall, Unversty of Pttsburgh, Pttsburgh, Pennsylvana 15260, esther@katz.ptt.edu Anndya Ghose Leonard Stern School of Busness, New York Unversty, New York, New York 10012, aghose@stern.nyu.edu Gven that nformaton technology (IT) securty has emerged as an mportant ssue n the last few years, the subject of securty nformaton sharng among frms, as a tool to mnmze securty breaches, has ganed the nterest of practtoners and academcs. To promote the dsclosure and sharng of cyber securty nformaton among frms, the U.S. federal government has encouraged the establshment of many ndustry-based Informaton Sharng and Analyss Centers (ISACs) under Presdental Decson Drectve (PDD) 63. Sharng securty vulnerabltes and technologcal solutons related to methods for preventng, detectng, and correctng securty breaches s the fundamental goal of the ISACs. However, there are a number of nterestng economc ssues that wll affect the achevement of ths goal. Usng game theory, we develop an analytcal framework to nvestgate the compettve mplcatons of sharng securty nformaton and nvestments n securty technologes. We fnd that securty technology nvestments and securty nformaton sharng act as strategc complements n equlbrum. Our results suggest that nformaton sharng s more valuable when product substtutablty s hgher, mplyng that such sharng allances yeld greater benefts n more compettve ndustres. We also hghlght that the benefts from such nformaton-sharng allances ncrease wth the sze of the frm. We compare the levels of nformaton sharng and technology nvestments obtaned when frms behave ndependently (Bertrand-Nash) to those selected by an ISAC, whch maxmzes socal welfare or jont ndustry profts. Our results help us predct the consequences of establshng organzatons such as ISACs, Computer Emergency Response Team (CERT), or InfraGard by the federal government. Key words: securty technology nvestment; nformaton sharng; securty breaches; externalty beneft; socal welfare; spllover effect Hstory: C. Kemerer and V. Sambamurthy, Senor Edtors; M. Van Alstyne, Assocate Edtor. Ths paper was receved on August 29, 2003, and was wth the authors 5 1 months for 4 revsons Introducton The ncreasng ubquty of the Internet provdes cyber attackers more opportuntes to msapproprate or corrupt an organzaton s data resources. Accordng to Jupter Meda Metrx, computer securty breaches could potentally cost e-busnesses almost $25 bllon by 2006 up from $5.5 bllon n There are many well-known examples of cyber hackng. Egghead.com faced a massve backlash from ts customers after beng hacked n 2000, whch contrbuted to ts eventual bankruptcy flng. A securty breach at Travelocty n 2001 exposed the personal nformaton 1 Prvacy Worres Plague E-Bz, markets/retalng/artcle.html. of thousands of customers who had partcpated n a promoton. Establshed frms lke Ctbank, Mcrosoft, and NASA, among others have been targeted too. Hence both the federal government and the prvate sector have recognzed a strong need to mprove ther cyber securty and to treat the securty of crtcal nfrastructure assets lke a strategc ntatve, rather than a complance burden. For awhle now, t has been recognzed that a key factor requred to mprove computer securty s the gatherng, analyss, and sharng of nformaton related to successful, as well as unsuccessful, attempts at computer securty breaches. Ths has led the U.S. federal government to encourage the establshment of ndustry-based Informaton Sharng and Analyss 186

2 Gal-Or and Ghose: The Economc Incentves for Sharng Securty Informaton Informaton Systems Research 16(2), pp , 2005 INFORMS 187 Centers (ISACs) under PDD Further, n February 2003, the Presdent also ssued The Natonal Strategy to Secure Cyberspace. ISACs are meant to facltate the sharng of securty nformaton to enhance and protect crtcal cyber nfrastructure. In January 2001, 19 of the naton s leadng hgh-tech companes announced the formaton of a new Informaton Technology Informaton Sharng and Analyss Center (IT-ISAC) to cooperate on cyber securty ssues n the prvate sector. Usng the shared nformaton, the IT-ISAC dssemnates an ntegrated vew of relevant nformaton system vulnerabltes, threats, and ncdents to ts members. It also shares the best securty practces and solutons among ts members, and thus provdes an mpetus for contnuous mprovement n the effectveness of securty products. 3 Obvously, such mutual collaboraton s ntended to ncrease the technologcal effectveness of IT securty products, thereby ncreasng ther demand. Revealng nformaton about securty breaches to an nformaton-sharng allance (ISA) results n both costs and benefts for the revealng frm. Losses can occur when a competng frm or a thrd party hacks the database of the ISA tself and leverages the shared nformaton to make compettve gans. Further, t could malgn the reputaton of the breachrevealng frm, by anonymously reportng t to the publc. In January 2003, Next Generaton Software Servces (NGSS) clamed that Computer Emergency Response Team (CERT), the government-sponsored Internet securty reportng center, passed vulnerablty nformaton to thrd partes about whch NGSS had notfed CERT. NGSS felt that ths was a drect volaton of trust, because the nformaton was leaked to potental compettors of NGSS. Eventually, NGSS severed tes wth CERT. 4 Another recent ncdent nvolved leakage of nformaton on a fatal flaw n a Sun Mcrosystems Internet software package to 2 In addton, on October 16, 2001, Presdent Bush ssued Executve Order 13231, Crtcal Infrastructure Protecton n the Informaton Age, whch contnued many PDD 63 actvtes. 3 A smlar organzaton ncludes the Chemcal Industry Cyber- Securty Informaton Sharng Network. Other ISACs have been formed n fnancal servces, telecommuncatons, energy, chemcals, etc. 4 NGSS Severs Tes wth CERT, dsplaynewsarchve.pl?day=030129&week=yes. a publc malng lst. The hacker ntercepted the documents from CERT and posted an advsory contanng the bug s specfcs to the full dsclosure securty malng lst. 5 The potental costs of sharng securty nformaton can have a snowball effect, accrung from the resultant loss of market share and stock market value from negatve publcty (Cavusoglu et al. 2004, Campbell et al. 2003). In a 2002 report by Jupter Meda Metrx, IT executves revealed that they were more concerned wth the rpple effects of onlne securty breaches on consumer confdence and trust n e-busness than the actual fnancal losses of physcal nfrastructure. Negatve exposure and loss of reputaton as a result of reports of nformaton nfrastructure volatons could be a threat to consumer confdence n a frm s products. Dmnshed customer confdence and a tarnshed reputaton can lead to reduced revenues at an ncreasng rate. However, there are several postve aspects to sharng securty nformaton. Formally, the beneft from mutual sharng of actual or attempted securty breach nformaton can be parttoned nto a prvate frmspecfc beneft and an external ndustry-level beneft. Ths prvate beneft ncludes both the preventon of further securty breaches n the future (e.g., dentfyng and reparng vulnerabltes n ther nformaton securty systems) as well as ncreased sales resultng from more effectve securty products and better securty reputaton among consumers. 6 Schechter and Smth (2003) show that nformaton sharng by frms can act as a deterrent for hackers, thereby ndrectly ncreasng the effectveness of securty technologes. One reason for enterng nformaton securty allances s cost reducton by mnmzng securty breaches. In fact, n many cases, ths mght be the man motve for formng the allance. However, there exst strong arguments for ndrect, demand-sde benefts as well. In busness-to-busness markets, frms 5 Leaked Bug Alerts Cause a Str, nfostructure, 03/19/03. 6 By reportng a securty breach to a central montorng agency lke CERT, a frm can send a strong message to ts customers that t s commtted to developng rgorous nformaton securty procedures and that t takes all necessary steps to mtgate damages from future breaches (Schenk and Schenk 2002).

3 Gal-Or and Ghose: The Economc Incentves for Sharng Securty Informaton 188 Informaton Systems Research 16(2), pp , 2005 INFORMS that jon an ISAC often have bg corporatons as customers. For nstance, n the IT-ISAC, the customers of securty vendors lke Symantec and Computer Assocates nclude bg corporatons lke Procter & Gamble, Lockheed Martn, and Ctbank, among others. As customers perceve mprovement n the effectveness of cyber securty products accrung from the nformaton-sharng behavor of securty vendors (whch members of the IT-ISAC) ther overall confdence ncreases, leadng to ncreased demand for IT securty products. Hence securty technology nvestments and securty nformaton sharng can nvolve demand-sde spllovers, whch result n postve externaltes for the ndustry as a whole. One of the man purposes of ths paper s to focus on such demandenhancng benefts of securty nformaton-sharng allances, whle stll keepng n mnd the mportance of cost sde benefts Research Questons and Results For any organzaton focused on the reportng and dssemnaton of nformaton related to securty breaches, there are a number of nterestng economc ssues that wll affect ts behavor. We seek to address the followng questons n ths paper. () What are the economc ncentves for competng frms n a gven ndustry to share securty nformaton through an nformaton-sharng organzaton lke an ISA? () How do market characterstcs such as the degree of ntrandustry compettveness, frm sze, and mode of conduct mpact such sharng behavor among competng frms? () Do spllover effects on demand sde or cost sde dscourage frms from sharng securty nformaton and result n suboptmal levels of securty technology nvestment? (v) What s the mpact of such sharng allances on socal welfare when frms ndvdually engage n proft maxmzaton, when the ISA dons the role of a socal planner, and when t acts as a jont proft maxmzer? We fnd that securty nformaton sharng and securty technology nvestments can act as strategc complements n that an ncrease n nformaton sharng or technology nvestments by one frm wll nduce the other frm to ncrease ts own level of nformaton sharng or technology nvestments. In fact, ths nclnaton to share nformaton and nvest n securty technologes ncreases as the degree of compettveness n an ndustry ncreases. The extent of nformaton sharng and nvestment levels of frms ntroduce two effects n our model: () a drect effect of expandng demand n the product market and () a strategc effect of allevatng prce competton among supplers of competng products. We demonstrate that these two effects ncrease wth the sze of the frm. We extend our model to show that the nature of securty technology cost plays a pvotal role n determnng whether cost-based spllovers boost nformaton sharng or subdue t. In partcular, the ncentves for sharng and nvestment are weakened f sales volume-related cost spllovers are present, n comparson to spllovers on fxed costs. We further show that nformaton-sharng levels and technology nvestments are hgher when frms jon an ISA sequentally than when frms compete smultaneously. Ths happens because of the tact colluson that s nduced by the frst entrant s precommtment to share a gven level of securty nformaton and nvest a gven amount n securty technology. Ths leads to hgher profts for both frms. Fnally, we pont out that f a federally funded ISA were to don a socal planner s role, t would need to provde hgher ncentves for frms to share welfare-maxmzng levels of securty nformaton, rather than the ndvdual or jont proft-maxmzng levels. In Appendx B, we also allude to an ncentve mechansm desgned by the government for fosterng socally optmal levels of dsclosure Pror Lterature Questons on nformaton sharng, economc ncentves, and socal welfare, smlar to those noted above, have been prevously studed n the context of other organzatons. Of partcular relevance s the extensve lterature on trade assocatons (TAs). Prevous relevant work ncludes that on nformaton sharng (e.g., Gal-Or 1985a, Shapro 1986, Vves 1990). 7 The second stream of lterature relevant to our work s that on mode of conduct and strategc effects (Bulow et al. 1985, Gal-Or 1985b). More recently, Parker and 7 The nformaton shared n these models s ether nformaton concernng an ndustry s demand parameter (common to all partcpants) or nformaton concernng a cost parameter that s specfc (a prvate value) to the ndvdual frm. In our model, the nformaton shared s about nformaton securty.

4 Gal-Or and Ghose: The Economc Incentves for Sharng Securty Informaton Informaton Systems Research 16(2), pp , 2005 INFORMS 189 Van Alstyne (2001) show how free strategc complements can rase a frm s own profts. Of course, because an organzaton must expend resources to develop technology, methods, and procedures to deal wth nformaton securty breaches, sharng of ths nformaton wll be qualtatvely dfferent than sharng the type of nformaton modeled n the TA lterature. 8 Fnally, our model consders spllovers from securty technology nvestments. Spllovers have been addressed n the extensve economcs-based lterature on research jont ventures (d Aspremont and Jacquemn 1988, Kamen et al. 1992). Recent papers dealng wth the economcs of nformaton securty and protecton of crtcal nfrastructure nclude Anderson (2001) who dscusses varous dstorted ncentves n the nformaton securty doman mpled by the exstence of moral hazard and adverse selecton problems. Gordon and Loeb (2002) present a framework to determne the optmal amount of nvestment to protect a gven set of nformaton and Gordon et al. (2003) dscuss the mportance of securty nformaton sharng. The focus of Gordon et al. (2003) s on how nformaton sharng affects the overall level of nformaton securty. They hghlght the trade-off that frms face between mproved nformaton securty and the potental for free rdng, whch can lead to undernvestment n securty expendtures. Whle Gordon et al. (2003) focus on the cost sde effects of securty breaches and nformaton sharng, our paper focuses on the demand sde effects. In partcular, we hghlght the strategc mplcaton of competton n the product market on nformaton sharng- and securty technology nvestment levels. 9 As we proceed through ths paper, we clearly dentfy how our results are related to Gordon et al. (2003) wherever relevant. 8 In partcular, we do not consder any uncertanty n the nformaton that s avalable to frms. Rather, we fnd a dfferent way to capture the extent of nformaton sharng wthout ncorporatng the nosness of the nformaton. Specfcally, the extent of nformaton sharng s measured n terms of the varable s 0 1, wth s = 0 desgnatng no nformaton sharng and s = 1 desgnatng maxmum sharng. The value of s determnes the extent of postve spllover effects among frms. 9 In Gordon et al. (2003), nformaton sharng costs and benefts are captured by examnng the effect of securty nvestment on expected securty breach losses. In contrast, we explctly model such costs and benefts on the demand and cost facng each frm. The rest of ths paper s organzed as follows. Secton 2 descrbes the model n detal and presents the man results under smultaneous competton (Bertrand-Nash) mode. We contrast these wth a socal planner s level of nformaton sharng and technology nvestments. In 3, we analyze the equlbrum under a sequental mode of entry. Secton 4 consders the scenaro when technology costs are nfluenced by the volume of sales. We conclude wth some mplcatons n 5. All proofs are relegated to Appendx A. 2. Model We consder a market consstng of two frms producng a dfferentated product n a two-stage noncooperatve game. In the frst stage, frms and j smultaneously choose optmal levels of securty technology nvestment, whch we denote as t t j and securty nformaton-sharng levels, whch we denote as s s j. In the second stage, they choose prces p j smultaneously. We consder a subgameperfect equlbrum of ths game usng backward nducton. In ths paper, we nterchangeably use the words Bertrand-Nash and smultaneous, to denote ths mode of frm conduct. 10 We normalze the amount of securty nformaton beng shared so that t always les between 0 and 1,.e., s 0 1. Ifs = 0, no nformaton s shared; f s = 1, all nformaton s shared. The varable t s an aggregate measure of the extent of nvestment n securty technology. Because such nvestment entals allocatng resources to possbly multple technologes measured n terms of dfferent physcal unts, we measure t n terms of one selected technology as a numerare. We assume that the cost of nvestng n mproved securty technology depends on the frm s own nvestment level as well as the level of securty chosen by the compettor and the extent to whch the compettor s wllng to share nformaton about ts vulnerabltes. Essentally, the ntuton s that the dsclosure of vulnerabltes n a partcular type of securty technology by one frm leads the other frm to nvest less n 10 Although frms compete à la Bertrand, they never reach margnal cost prcng because they sell dfferentated products. We use the termnology Bertrand-Nash to ndcate that frms compete by choosng prces as ther strateges.

5 Gal-Or and Ghose: The Economc Incentves for Sharng Securty Informaton 190 Informaton Systems Research 16(2), pp , 2005 INFORMS that technology or procure a smaller amount of that product. For nstance, f frm were to report a hgher number of securty breaches because of a partcular knd of frewall, frm j would nvest less n that specfc technology. A drect consequence of such nformaton sharng would be preemptve cost savngs n technology nvestment. 11 Incorporatng the exstence of postve cost spllovers, we specfy the costs of nvestng n securty technology n terms of the functon f t y j, where y j = c t j s j, f / t > 0, and f / y j < 0. Hence each frm s costs rse wth ts own aggregate nvestment, but declne wth the compettor s aggregate nvestment and ts wllngness to share nformaton. The coeffcent c s a cost spllover parameter that we normalze to be n the unt nterval. (Gordon et al use a smlar formulaton.) We also assume that f 0 y / t = 0, 2 f / t y j < 0, and 2 f / t 2 > 0. That s, the margnal cost of ncreased securty nvestment s zero when no such nvestment s made. The margnal cost s decreasng when the compettor ncreases ts nvestment n securty technologes or shares more nformaton about ts securty vulnerabltes, and ths margnal cost s ncreasng wth the frm s own nvestment level. 12 For smplcty, we assume that frms do not ncur any producton costs other than those stemmng from nvestments n mproved securty technology. We assume that the demand facng each product s lnear n self and cross-prce effects (see McGure and Staeln 1983). q = a b 1 p + b 2 p j + B j = 1 2 j (1) where 0 b 2 <b 1. From ths pont onward, we wll contnue to desgnate the frm under consderaton as 11 Note that the varable t can be nterpreted as the overall level of nformaton securty attaned by the frm. Securty nformaton dsclosure allows the frm to acheve ths level at a lower aggregate cost. In the present model, we gnore ssues related to the tmng at whch ths securty s attaned for a frm that has already nvested n ths technology. 12 Ths assumpton s requred to guarantee the exstence of an nteror soluton. frm and ts compettor as frm j. As well, n descrbng the behavor of both frms n terms of a system of equatons, as expressed n (1), we wll drop the qualfcaton, j = 1 2 j for brevty. The varable a n (1) s the ntal ntercept of demand facng. Ths ntercept may shft upward because of the frms nvestments n mprovng securty as well as sharng nformaton about ther vulnerabltes. The varable B n (1) measures the potental shft of the demand ntercept facng frm. We descrbe t n detal subsequently n Equaton (3). The slope b 1 can be nterpreted as the extent to whch consumers are prce senstve or dsloyal to a frm s product, and the slope b 2 provdes a measure of the degree of product substtutablty. Thus, b 2 = 0 mples that frms act as local monopolsts, whereas b 1 = b 2 corresponds to the case when products are perfectly homogenous. In Appendx A, we demonstrate that the lnear demand model s mpled by a quadratc, and separable of ncome, utlty functon. When consumers decde upon the consumpton of two products, 13 subject to ther budget constrants, the above lnear demand s mpled. The lnear demand model has been used extensvely n marketng and economcs, and there s some research suggestng that comparatve statcs derved from smpler models may often hold for more general formulatons (Mlgrom 1994). We now proceed to explan how the varable B, whch measures the potental shft of the demand ntercept of, depends upon the nvestments n securty and the extent of nformaton sharng by the frms. We start by evaluatng the possble consequences of frms decsons to share nformaton about ther securty breaches. We desgnate the leakage costs that mght be nflcted on frm as a result of such sharng by g s s j. Hence the level of these costs to frm depends on whether or not frm j has also revealed nformaton about ts securty breaches to the ISA. Ths specfcaton s smlar to the loss functon L assumed n Gordon et al. (2003), whch measures the cost of a securty breach ncurred by frm, ncludng, n partcular, the value of profts lost from sales. In our formulaton though, those losses are a functon of the 13 Consumers can decde to dversfy ther consumpton bundle and buy both products n ther maxmzaton.

6 Gal-Or and Ghose: The Economc Incentves for Sharng Securty Informaton Informaton Systems Research 16(2), pp , 2005 INFORMS 191 extent of sharng by the frms nstead of beng a fxed amount. We assume that g s s j s ncreasng n s but decreasng n s j. As the extent of sharng by ncreases, t s more lkely that there could be a leakage of the securty breach nformaton that ths frm has experenced. Ths, n turn, would ncrease consumers apprehenson of transactng wth ths frm, and thereby reduce ts demand ntercept. However, as the compettor s sharng level ncreases as well, some consumers may fnd t optmal to swtch from frm j to frm, gven that j s securty breaches are more lkely to be revealed. We assume that the rate at whch these leakage costs ncrease n s and decrease n s j s ncreasng. Specfcally, 2 g / s 2 > 0 and 2 g / sj 2 < 0. Ths assumpton s consstent wth the possble deleterous rpple effects of a securty breach nformaton leak on frms own market share, as cted n the Introducton. We also assume that 2 g / s s j 0, mplyng that ntensfed sharng by the compettor reduces the margnal leakage cost ncurred by the frm. 14 To guarantee that own effects of sharng on leakage costs exceed cross effects of sharng, we assume that when s 1 = s 2, g / s > g / s j, and 2 g / s 2 > 2 g j / s 2. The ratonale for ths assumpton relates to the two types of consumers who may face each frm: loyal consumers and swtchers. Ths dstncton has been wdely used n the marketng lterature. (See, for nstance, Narasmhan 1988.) Whle loyal customers buy ether product or nothng at all, swtchers can be nduced to purchase the competng brand j. When s ncreases around a symmetrc equlbrum, frm loses both the loyal consumers and the swtchers because of the reduced utlty they face from the possblty of ncreased leakage costs. However, when s j ncreases around ths equlbrum, frm gans only the swtchers. Hence, any changes n ts own level of sharng affects leakage costs more than changes n the level of sharng by the compettor. 15 The followng example satsfes all of the above-mentoned 14 In Appendx A, we also llustrate how these assumptons can be derved from a specfc utlty functon. 15 In Appendx A, we provde an alternatve explanaton for the result that own effects on leakage costs are larger than cross-effects. Ths explanaton s based on the quadratc utlty functon formulaton that generates the lnear demand functons. propertes of the functon g s s j : g s s j = 1 s 2 2s 2 j 3s s j where 1 > (2) The wllngness of the compettor to share nformaton about ts securty breaches may have another postve mplcaton on the demand facng the frm. When the consumers know that the frm s cooperatng wth a compettor as part of the ISA, to dentfy the most effectve ways to prevent breaches, they are more confdent that the frm s efforts wll ndeed be successful. 16 We measure ths addtonal beneft derved by frm n terms of the decson varables chosen by ts compettor, frm j, as d t j s j. Such a specfcaton captures the fact that the extent of beneft to frm from nformaton sharng by frm j depends on what frm j has to share, whch, n turn, depends on the amount that frm j spends on nformaton securty technology. 17 Ths postve externalty that accrues to the frm depends on the value of the spllover parameter d. As wth the cost spllover parameter, here as well, we assume that d les n the unt nterval. Note that the term t j s j n the above formulaton concdes wth the varable y j n Gordon et al. (2003). Whle n Gordon et al. (2003), ths term affects the probablty of a securty breach, n the present model t affects the sze of the demand. In both cases though, sharng nformaton results n a postve externalty conferred on compettors. Informaton on threats, vulnerabltes, and ncdents experenced by others can help frms dentfy trends, better understand the rsks faced, and determne what preventve measures should be mplemented (Dacey 2003b). ISACs also seek to promote the sharng of technology related to detectng and stoppng nformaton securty breaches, as well as ways to repar damage caused by such breaches. Havng access to nformaton about securty vulnerabltes and the proposed solutons of the compettor can lead to more effectve nvestments n securty technologes by the frm Because consumers are ratonal, such enhancements n ther percepton translates nto ncreased demand. 17 The qualtatve nature of our analyss wll contnue to hold as long as the securty nformaton of the two frms are not perfect substtutes. We thank the assocate edtor for pontng ths out. 18 Thus, actons undertaken by frms that boost the consumer comfort level, n terms of allevatng ther perceved securty rsk, can

7 Gal-Or and Ghose: The Economc Incentves for Sharng Securty Informaton 192 Informaton Systems Research 16(2), pp , 2005 INFORMS Fnally, the demand ntercept facng each frm may shft because of the nvestments undertaken by both frms, even n the absence of any nformaton sharng between them. When a gven frm ncreases ts nvestment n securty technology to prevent securty breaches or enhance the effectveness of securty products, and consumers become nformed of ths ncrease, ther level of anxety about transactng wth the frm declnes, thus enhancng ther expected utlty and wllngness to pay for the product. In contrast, f the compettor ncreases ts level of nvestment and consumers become aware of t, the frm may experence a negatve demand shock and lose some customers (for example, the swtchers) because the compettor may now be consdered the more relable and secure source of supply. We summarze ths net effect of the frms nvestments on the demand ntercept of frm n terms of the dfference t t j, where 0 <1. Once agan, snce s a fracton, own effects of nvestment exceed cross-effects. Combnng the benefts and costs of nvestments n securty technology as well as nformaton sharng yelds the followng net beneft functon that can shft the demand ntercept of frm 19 : B = t t j + d t j s j g s s j (3) Note that the compettor s level of nvestment has both postve and negatve mplcatons on frm s demand. On the postve sde, consumers are reassured that s membershp n the ISA s more benefcal to t, gven that j reveals nformaton concernng a larger level of nvestment. On the negatve sde, the compettor now appears a more attractve opton to consumers. Snce the former effect depends on the extent of sharng by j, the postve spllover expresson depends on the product t j s j Analyss At the second stage, frm chooses ts prce p to maxmze ts objectve. The proft functon of frm can be n the long run lead to an ncrease n ther own product sales as well as an expanson n the whole market. 19 The qualtatve nature of our results hold wth dfferent formulatons of the beneft functon. In partcular, any ncreasng and concave functon of t t j + d t j s j can replace the lnear specfcaton above wthout changng our results. As well, n Appendx A we provde an alternatve nterpretaton to the demand effect beneft component B. wrtten as = p q f t y j From the frst-order condtons (FOCs) for proft maxmzaton, we derve the second-stage equlbrum prces, whch are summarzed n Appendx A. These become the startng pont for dervng comparatve statcs to examne how changes n the exogenous and endogenous varables affect frm strateges and profts under dfferent market condtons. In dervng some of the comparatve statcs, we wll need the followng assumptons: Assumpton 1. ( d mn s 1 s 2 + b ) 2 = 2b 1 Assumpton 2. [ g (2b g j 1 + b s 2 s ) ] + b 2 d t > 0 s =s j =0 [ ) ] g (2b g j 1 + b s 2 + b s 2 d t < 0 s =s j =1 Assumpton 1 asserts that the negatve mplcatons of ncreased securty nvestment by the compettor on the frm s demand s not too large. Ths assumpton s more lkely to be vald when the demand spllover parameter d or the degree of substtutablty between products, b 2, s relatvely hgh. Assumpton 2 conssts of two parts. The frst relates to the possblty that both frms share no nformaton wth each other and the second relates to the case that they share full nformaton. In the former case, Assumpton 2 asserts that the negatve consequences of ncreasng the extent of sharng, as measured by the margnal leakage costs, are outweghed by the postve mpact of such sharng, as measured by the margnal demand spllover effect. The second part of Assumpton 2 asserts that the opposte s the case when both frms share full nformaton wth each other. Proposton 1. () A frm s prce ncreases wth an ncrease n ts own nvestment n securty technology. As well, under Assumpton 1, prce also ncreases wth the compettor s level of nvestment. Hence, dp /dt > 0 and dp /dt j > 0 () Under Assumpton 2, each frm s prce follows an nverted U-shaped curve wth an ncrease n securty

8 Gal-Or and Ghose: The Economc Incentves for Sharng Securty Informaton Informaton Systems Research 16(2), pp , 2005 INFORMS 193 nformaton sharng,.e., / s > 0 for s 0 s c and / s < 0 for s s c 1, where 0 <sc < 1. Increased nvestment n securty technology by the frm shfts ts demand outward and rases ts prce reacton functon. As a result, the frm chooses to rase ts prces. When the compettor ncreases ts securty nvestment level, the compettor s prce reacton functon shfts up. Wth upward slopng reacton functons, ths shft leads the frm to rase ts own prce as well, as long as the parameter s not too large. Recall that ths parameter measures the negatve consequences of the compettor s nvestment level on the frm s demand ntercept. When the frm ntensfes ts extent of sharng, there are two countervalng effects on ts own demand and that of ts compettor. Intensfed sharng of securty nformaton ncreases the frm s own leakage costs, thus reducng the demand facng t. On the other hand, because of spllover effects and reduced leakage costs of the compettor, the demand facng the compettor shfts outward. Because of the former, drect effect, the frm has an ncentve to reduce ts prce. However, because of the latter, strategc effect, the compettor has an ncentve to rase ts prce, whch wth upward slopng reacton functons, provdes an ncentve for the frm to rase ts own prce as well. The second part of Proposton 1 states that for small values of s <s c, the latter strategc effect domnates and for large value of s >s c, the former drect effect domnates. Assumpton 2 guarantees that perfect nformaton sharng can never arse n equlbrum, thus leadng to an nteror soluton, so that s c s a fracton. Bascally, because the margnal leakage cost wth perfect nformaton sharng s relatvely large compared to postve spllovers on demand, full nformaton sharng cannot be an equlbrum; and conversely, snce the margnal leakage costs wth no nformaton sharng s relatvely small n comparson to the postve demand spllovers, some nformaton sharng does arse at the equlbrum. Substtutng the second-stage prces back nto each frm s objectve functon, we can obtan the frst-stage payoff functon n reduced form as = b 1 p 2 f t y j (4) where p solve the FOCs. Dfferentatng wth respect to the frst-stage decson varables yelds the followng two FOCs. 20 d ds H = d dt = 2b 1 p s = 0 (5) = 2b 1 p t f t = 0 (6) Lemma 1. () Under Assumpton 2, full nformaton sharng s nconsstent wth a symmetrc equlbrum. Specfcally, the optmal levels of nformaton sharng and securty technology nvestment are gven as the soluton to ( ) ( )] g g j [2b 1 + b 2 = b 2 d t f t s = 2b 1 p s ( 2b1 + b 2 d s 4b 2 1 () The reacton functons of both frms wth respect to the extent of securty nformaton sharng are upward slopng,.e., s / s j > 0 and t / s j > 0. As well, under Assumpton 1, the reacton functons of both frms wth respect to the extent of securty nvestment are also upward slopng,.e., s / t j > 0, t / t j > 0. A drect nterpretaton of the results reported n Lemma 1 s provded n Proposton 2. Proposton 2. () A hgher level of securty nformaton sharng by one frm leads to a hgher level of nformaton sharng and securty nvestment by ts compettor. As well, f, () A hgher level of securty technology nvestment by one frm leads to a hgher level of nformaton sharng and securty nvestment by ts compettor. () Securty technology nvestment and securty nformaton sharng act as strategc complements n ths case. Our analyss reveals that the reacton functons are upward slopng; that s, an ncrease n securty technology nvestment by frm nduces a hgher level of nformaton sharng by frm j and vce versa. The two nputs act as strategc complements. Ths s evdent from the fact that 2 / s t j > 0,.e., the ncrease n profts wth ncreased nformaton sharng for frm s hgher for hgher levels of technology nvestment by frm j and vce versa. Further, 2 / s s j > 0,.e., the 20 Because we do not get closed-form solutons for the frst-stage decson varables, we adopt the mplct functon approach to present our results and gan nsght. )

9 Gal-Or and Ghose: The Economc Incentves for Sharng Securty Informaton 194 Informaton Systems Research 16(2), pp , 2005 INFORMS ncrease n profts wth ncreased nformaton sharng for frm s hgher for hgher levels of nformaton sharng by frm j and vce versa. Hence, as we observed n Lemma 1, frm responds to less aggressve play by frm j by beng less aggressve tself. The same ntuton apples to the change n a frm s profts wth a change n securty technology nvestment by the other frm, where we fnd that 2 / t t j > 0, when s suffcently small. Note that the upper bound on that s stated n Proposton 2 s stronger than necessary. To guarantee that the slopes s / t j and t / t j are postve, the parameter cannot be too large, but a weaker condton than the one stated n Proposton 2 s suffcent (a hgher upper bound on ). Contrary to our results, when Gordon et al. (2003) use the restrcted cost functon, f t y j = f t y j, they fnd that when frms share nformaton, each frm has reduced ncentves to nvest n nformaton securty. The man reason for the dfferent result s the exstence of the demand-enhancng effects of nformaton securty sharng and technology nvestments n our model. 21 It s mportant to note that the exstence of postve demand spllovers (.e., d > 0) s essental to obtan a certan degree of sharng between the frms n our model. If d < 0, so that there are negatve demand spllovers, the only possble symmetrc equlbrum s for frms not to share any nformaton at all; namely, s = s j = 0. To see t, note that s s1 =s 2 =s [ ) g (2b g j 1 + b s 2 +b s 2 d t ] s1 =s 2 =s Hence, f d < 0, the above s negatve for all values of s 0 1, gven our assumpton that ther own effects always domnate cross-effects. From Equaton (5), therefore, no nformaton sharng s the only possble outcome. However, even n ths case, securty nvestment reacton functons may stll slope upward (.e., t / t j > 0) provded that the parameter s suffcently small (.e., b 2 /2b Usng an unrestrcted case, Gordon et al. (2003) also show that nformaton sharng can lead to an ncrease n sharng and n the acheved level of nformaton securty. Proposton 3. () A lower level of frm loyalty leads to lower levels of securty nformaton sharng and securty technology nvestment,.e., s / b 1 < 0 t / b 1 < 0. () When, the extent of nformaton sharng and amount of securty technology nvestment by both frms ncrease when the degree of product substtutablty ncreases,.e., s / b 2 > 0 t / b 2 > 0. We hghlght that a steeper demand schedule, b 1, lowers a frm s propensty to nvest n securty technology and share securty nformaton. A steeper slope mples that each frm sells fewer unts of the product for a gven level of the equlbrum prces. 22 Smaller quanttes mply, n turn, that the margnal return to any knd of technology nvestment s more lmted. As a result, the frms have reduced ncentves to nvest n enhanced securty technology. Further, the strategc complementarty between technology nvestment and nformaton sharng mples also that the extent of sharng declnes when demand schedules are steeper. Qute nterestngly, to the extent that product substtutablty s ndcatve of the degree of competton n an ndustry, we fnd that a hgher level of ntrandustry compettveness may lead to hgher levels of securty nformaton sharng and ncreased nvestment n securty technologes by both frms, when s suffcently small. Frms generally respond to ncreased competton wth aggressve prce cuts. To allevate such aggressve prce competton, frms have greater ncentves to nvest n mechansms that allevate prce competton. 23 Because ncreases n s and t may help n mtgatng prce competton, both frms may decde to rase the extent of nformaton sharng and nvestments when the degree of substtutablty between the frms products ncreases. We would lke to pont out that the ntuton for our comparatve statcs results wth respect to parameters b 1 and b 2 follows from the exstence of two effects: a drect effect and a strategc effect. Ths s evdent when optmzng the objectve functon n Stage 1 wth respect to the decson varables s and t. Dfferentatng w.r.t. s and t separately, yelds the followng 22 Because an ncrease n b 1 mples that consumers are more prce senstve, t leads to a lower level of demand at a gven prce. 23 For nstance, n the arlne ndustry, whch has been characterzed by stff prce competton, frms have developed Frequent Flyer Programs as a mechansm to reduce cut-throat prcng.

10 Gal-Or and Ghose: The Economc Incentves for Sharng Securty Informaton Informaton Systems Research 16(2), pp , 2005 INFORMS 195 equatons: d ds d dt = s = t + p j p j s + s (7) + p j p j t + t (8) Because the prces selected n the second stage solve the condton / = 0, n equlbrum the thrd term n both Equatons (7) and (8) s equal to 0 (by the envelope theorem). The frst terms n Equatons (7) and (8) measure the drect effect of ncreased nformaton sharng, and the second terms n the equatons measure the strategc effect. The degree of substtutablty, b 2, affects prmarly the magntude of the strategc effect and the degree of dsloyalty, b 1, affects prmarly the magntude of the drect effect. Note that the sgn of the strategc effect s postve snce from Proposton 1, the compettor rases prces when the frm shares more securty nformaton or ncreases securty technology nvestment ( p j / s > 0 and p j / t > 0. When b 2 ncreases, the mportance of allevatng prce competton becomes especally pronounced, and as a result frms are wllng to share more nformaton and nvest more n securty technology. In contrast, when b 1 ncreases the magntude of the drect effect declnes because each producer sells smaller volumes as a result of the ncrease n dsloyalty of consumers. Wth smaller volumes, frms have lower ncentves to make any knd of nvestment, ncludng n mprovng nformaton securty. Because securty technology and nformaton sharng are complementary, they also cut back on ther extent of sharng. In general, n all the comparatve statcs, the two effects mentoned above are present. Changes that reduce sze (quantty) reduce the drect effect and, therefore, the ncentves to nvest n technology and share securty nformaton. On the other hand, changes that ntensfy prce competton ncrease the strategc effect and, therefore, the ncentves to nvest and share. Proposton 4. () Securty nformaton sharng and securty technology nvestment levels ncrease wth frm sze. () A lower level of demand spllover and cost spllover dscourages securty nformaton sharng and technology nvestments,.e., s / d > 0, s / c > 0, t / d > 0, t / c > 0. () A bgger value of dscourages securty nformaton sharng and technology nvestments,.e., s / < 0 and t / < 0. Proposton 4() suggests that nvestng n securty nformaton s more valuable to larger frms, because the margnal return to nvestment s drectly related to the volume of sales of the frms. Ths concluson s consstent wth the well-known result that a monopolst benefts more from cost-reducng nnovatons than a frm competng n a duopoly, gven that t can extract a hgher proporton of the surplus from the market. 24 Because nformaton sharng and technology nvestment act as strategc complements, ths ncreased securty nvestment also leads to hgher securty nformaton sharng by the larger frm. The result stated n Proposton 4() mples that hgher demand-sde spllovers promote hgher levels of nformaton sharng and technology nvestment. Increased spllovers shft the demand curve outward, whch enable frms to ncrease ther prces and, as a result, ther profts. Smlarly, ncreased cost spllovers mply that the margnal cost of nvestment declnes, thus provdng greater ncentves for the frm to ntensfy securty nvestments and nformaton sharng. Note that the latter result s mpled by our assumpton that the cost of nvestng n securty nformaton s ndependent of the frm s volume of sales. In 4, we demonstrate that cost spllovers have an opposte effect to that descrbed n the above proposton when the cost of nvestment s volume dependent. Ths opposng effect was also derved n Gordon et al. (2003). As ponted out earler, the results reported n Proposton 4() rely on the exstence of postve demand spllovers that lead to some nformaton sharng at the equlbrum. Snce n our model spllovers exst only f frms communcate wth each other, the nvestment n securty technology s ndependent of the values of d and c when d < 0 (.e., t/ d = t/ c = 0). Proposton 4() evaluates the parameter, whch measures the adverse mplcatons of the compettor s 24 Bascally, the extent of ncentves to nvest n technology and share nformaton s a functon of the degree of concentraton of frms n the market. As the number of frms n the ndustry decreases, the margnal beneft from the technology nvestment and nformaton sharng ncreases.

11 Gal-Or and Ghose: The Economc Incentves for Sharng Securty Informaton 196 Informaton Systems Research 16(2), pp , 2005 INFORMS securty nvestment on the demand ntercept of a gven frm. Accordng to ths part, bgger values of dscourage technology nvestments and nformaton sharng. Ths result s qute ntutve, as bgger values of mply lower volumes of sales and, as explaned before, reduced ncentves to nvest Socal Welfare We now consder the case that the ISA dons the role of a federally funded socal planner. From the demand expressons, one can derve the nverse demand functons n terms of prces such that p = F q q j. Let q 1 = q 2 = q denote the equlbrum quantty determned by the market. Focusng on a symmetrc envronment, where the socal planner sets t 1 = t 2 = t, s 1 = s 2 = s, and F 1 q q = F 2 q q = F q q, socal welfare can be wrtten as follows: where SW = 2 = 2 q 0 q 0 F q q dq 2f t c ts a + B q b 1 b 2 dq 2f t c ts (9) B = t 1 + d ts g s s (10) In Appendx A, we show that the socal welfare maxmzng level of nformaton sharng s hgher than the soluton to B/ s = 0. Ths last condton mples that the drect net margnal beneft of nformaton sharng on each frm s demand s equal to zero. Usng Equaton (10), ( g ) = 0 (11) B s = dt + g s s j When each frm maxmzes ts own profts under a Nash equlbrum, t chooses the extent of nformaton sharng to satsfy / s = 0. Hence the optmal level of nformaton chosen at the market equlbrum, s NE satsfes the followng condton: ( ) 2b1 g d t + g = 0 (12) b 2 s s j Because 2b 1 /b 2 > 1, t follows from comparng Equaton (12) wth (11), that for a fxed level of securty technology nvestment, the socally optmal level of nformaton shared s hgher than that chosen under the Bertrand-Nash market equlbrum where frms are engaged n ndvdual proft maxmzaton. Next, we consder the case where the ISA coordnates the choces of ts members, n terms of ther securty technology nvestments and extent of nformaton sharng, to maxmze jont ndustry profts. In spte of ths coordnaton on the choce of s and t, we assume that the ISA s prohbted from facltatng prce coordnaton among ts members. Prces are stll gven, therefore, by Equaton (21) (n Appendx A), whch at the symmetrc equlbrum reduces to p = a + B 2b 1 b 2 Because q = b 1 p, jont ndustry profts can be expressed as follows: JP = = 2b 1 a + B 2 2b 1 b 2 2 2f t c ts The ISA chooses s and t to maxmze the above payoff functon. The optmzaton wth respect to s and t yelds the condtons, respectvely. JP t JP s = 4b 1 a + B B 2b 1 b 2 2 s 2 ct f = 0 (13) y j [ f = 4b 1 a + B 2b 1 b 2 2 B t 2 t + c s f y j ] = 0 (14) A comparson of Equatons (13) and (14) wth (27) and (28) (from Appendx A) mples that maxmzng socal welfare yelds hgher levels of sharng and securty technology nvestment than that chosen under jont proft maxmzaton. A smlar comparson of Equatons (13) and (14) wth (12) and (29) (n Appendx A), yelds that jont proft maxmzaton yelds hgher levels of sharng and securty nvestment than that obtaned at the market equlbrum. In Proposton 5, we summarze the comparson of the extent of nformaton sharng and technology nvestment under the three regmes dscussed above: welfare maxmzaton, jont proft maxmzaton, and ndvdual proft maxmzaton. Proposton 5. () Socal welfare at the symmetrc Bertrand equlbrum s hgher wth securty nformaton sharng than wth no sharng. () When, the level of securty nformaton sharng and securty technology nvestment that are socally optmal are hgher than those selected by an ISA whose

12 Gal-Or and Ghose: The Economc Incentves for Sharng Securty Informaton Informaton Systems Research 16(2), pp , 2005 INFORMS 197 objectve s to maxmze jont ndustry profts. Moreover, a jont proft maxmzng ISA chooses hgher levels of nformaton sharng and technology nvestment than those selected at the market equlbrum, when frms are engaged n ndvdual proft maxmzaton. The comparson presented n Proposton 5 can be explaned by recallng the dfferent objectves of the socal planner, the jont proft maxmzng ISA, and the ndvdual frms. Whle the ISA s objectve s to maxmze total ndustry profts, the socal planner ams to maxmze the sum of the consumer and producer surplus. Hence, the jont proft maxmzng ISA mplements lower levels of technology nvestment and securty nformaton sharng than the socal planner, because t does not ncorporate the added beneft to consumers from enhanced technology nvestments. The reason the jont proft maxmzng ISA wshes to mplement hgher levels of nformaton sharng and securty technology nvestment than frms that choose these decson varables ndependently, stems from the fact that ndvdual frms do not fully nternalze the postve externalty that the nvestment confers on ther compettors. Hence, ths decreases the margnal return from nformaton sharng and technology nvestment. Once agan, t s mportant to note that the comparson conducted n Proposton 5 depends on our assumpton that d > 0. Wth negatve demand spllovers, a socal planner may also wsh to prevent any nformaton sharng among frms f the extent of adverse demand spllovers s relatvely bg, n comparson to the extent of postve cost spllovers. From Equaton (27) n Appendx A, t follows that f the magntude of d (when negatve) s relatvely bg n comparson to the magntude of c, a socal planner wll choose s = s j = 0, smlar to frms that act as Nash compettors. The result reported n Proposton 5 mples that the government should encourage ndustry partcpants to cooperate n settng ther securty nvestments and nformaton sharng levels. Even f ther coordnaton does not result n socally optmal levels of nvestment and sharng, t stll yelds an mprovement over the outcome attaned n the absence of coordnaton. Ths concluson s vald, however, only f members of the ISA do not use those coordnaton actvtes as a vehcle to collude on prces. If formaton of the jont proft maxmzng ISA facltates such colluson, the members may rase prces above the Bertrand- Nash level and, consequently, reduce socal welfare. Whereas prces at the Bertrand-Nash equlbrum are equal to p NE = a + B / 2b 1 b 2, prce under colluson s the monopoly prce p JP = a + B / 2 b 1 b 2. For a fxed level of securty technology nvestment, the hgher prces selected under colluson result n reduced quanttes demanded by consumers, snce q JP = a+b /2 < b 1 a+b / 2b 1 b 2 = q NE. Gven that quanttes at the Bertrand-Nash equlbrum q NE fall short of the socally optmal level of producton q SW, the further declne of quanttes because of colluson n prcng reduces socal welfare. Ths ponts out the need for legslaton, whch would allow an ISA to choose levels of securty nformaton sharng but prevent members from colludng n prces. Our result that nformaton sharng s socal welfare enhancng s also consstent wth the fndngs of Gordon et al. (2003) who post that at the Nash equlbrum, a small ncrease n expendtures on nformaton securty by ether frm would ncrease socal welfare. They also pont out that the socally optmal expendture levels for each frm are greater than the Nash equlbrum levels. However, they hghlght that ths may not hold true for both frms smultaneously, f there s asymmetry among frms n terms of IT securty productvty. 3. Sequental Entry Analytcal modelers have recognzed that the qualtatve nsghts regardng market equlbra often depend on the sequence n whch frms n an ndustry choose ther strateges. Whle the smultaneous mode of conduct s more common n fragmented ndustres, there are numerous examples where one frm acts as a leader and others act as followers n a gven ndustry. Frms may understandably be reluctant to share senstve propretary nformaton on securty practces, ntrusons, and actual crmes wth ether government agences or compettors. To many frms, nformaton sharng s a rsky proposton wth less than clear benefts. Specfcally, concerns have been rased that a frm s nformaton could be subject to the Freedom of Informaton Act, or face potental lablty concerns for nformaton shared n good fath (Dacey 2003b). These actons could potentally jeopardze a frm s

13 Gal-Or and Ghose: The Economc Incentves for Sharng Securty Informaton 198 Informaton Systems Research 16(2), pp , 2005 INFORMS market share or customer base. Ths may be especally true when some frms are more lkely to be poneerng n ther approach to dsclosng crtcal nformaton whle others adopt a wat and watch polcy. 25 It may be nterestng, therefore, to compare the amount of securty nformaton sharng and technology nvestment when frms jon an ISA n a sequental manner, wth the case when they make ther choces smultaneously. Hence, we consder a scenaro where an ncumbent frm has already commtted to sharng nformaton and nvestng n technology, antcpatng the entry and smlar sharng behavor of another frm. In Stage 1, the ncumbent chooses s t, and n Stage 2, the entrant chooses s j t j. In Stage 3, both frms choose prces p j smultaneously. Wth sequental choces, the FOCs for frm (ncumbent) are as follows: G = d ds H = d dt = 2b 1 p s + 2b 1 p s j s j s + 2b 1 p t j t j s = 0 (15) = 2b 1 p t + 2b 1 p t j t j t + 2b 1 p s j s j t f t = 0 (16) Note, however, that the FOCs for the follower wll be smlar to those n the smultaneous mode, gven by Equatons (5) and (6). Proposton 6. The optmal amount of shared securty nformaton and securty technology nvestment by frm (ncumbent) wll be hgher n the sequental mode than n the smultaneous mode, provded that. Comparng FOCs gven by Equatons (15) and (16) wth (5) and (6), mples that wth sequental entry, each FOC of the leader ncludes an addtonal postve term that reflects the Stackelberg effect. Ths effect occurs because the leader ncorporates the mplcaton of ts own nvestment t and sharng s on the choce of the levels of nvestment t j and sharng s j made subsequently by the follower. The leader 25 Startng wth October 2000, there were only 277 members who had joned InfraGard. By early January 2001, 518 enttes had joned. As of February 2003 InfraGard members totaled more than 6,700 (Dacey 2003a). knows, n partcular, that such a precommtment to ncrease the securty technology nvestment or shared securty nformaton wll nduce the entrant to do the same. 26 Because ncreased nformaton sharng and technology nvestment leads to softenng of prce competton, both frms profts wll be strctly hgher n the sequental mode than n the smultaneous mode game. Proposton 6 suggests that securty nformaton sharng and securty technology nvestment are ndeed hgher n the former than n the latter mode, leadng to hgher profts because of further allevaton of prce competton Impact of Volume-Related Costs Many frms beleve that ncreased effcency may be attaned by outsourcng the nformaton securty functon. Hence, some frms have outsourced ther securty and network management to an external entty lke a managed securty servces provder (MSSP). Ths entty engages n modulaton of securty resources and servces, dependng on control/varablty. 28 Durng the course of outsourcng, an MSSP often provdes dfferent levels of qualty of securty servce (QoSS) based on the sze of the frm. Gven that the payment to the MSSP may depend on the frm sze, t would be approprate to modfy our model by ncludng some addtonal technology costs, whch are affected by the volume of sales. Even f the frm manages ts own securty, as demand and the correspondng IT nfrastructure grows, so would costs related to nstallaton of addtonal servers, QoSS lcense fees, dynamc securty servce agreements, 26 By choosng a hgher level of s t, the leader moves n a drecton that s favorable for both frms, and thus convnces the entrant to follow sut. Ths, n turn, results n mproved opportuntes for tact colluson. 27 It s also possble to consder the scenaro n whch technology nvestments t t j are chosen frst and smultaneously by frms, followed by nformaton-sharng levels n the penultmate stage s s j, and prces p j n the last stage. Even n ths scenaro, hgher levels of technology nvestment and nformaton sharng arse n equlbrum, compared to the smultaneous mode game consdered n the prevous secton. Proof of ths s avalable from the authors upon request. 28 Examples of varant securty nclude the length of encrypton keys, assurance level of remote executon envronment, ntensty level of boundary controllers lke IDS, frewall, etc.

14 Gal-Or and Ghose: The Economc Incentves for Sharng Securty Informaton Informaton Systems Research 16(2), pp , 2005 INFORMS 199 ncreasng utlzaton of assocated securty weapons lke frewalls, ntruson detecton systems (IDS), vrtual prvate networks, content flters, access control systems, etc. In ths secton, we analyze the mpact of sales volume-related costs of technology on frms optmal sharng and nvestment strateges. Havng consdered cost spllovers on fxed costs, we now consder only spllovers on securty technology costs, whch are nfluenced by the volume of sales. We model the new margnal cost functon as c ˆ t j s j t and assume that > 0, > 0. The parameter ˆ s the volume-related cost sde spllover from nformaton sharng. In ths new envronment, the frst-stage proft equaton n reduced form s = b 1 c ˆ t j s j t 2 f t where, for smplcty, we assume the nonexstence of fxed cost spllovers (.e., c = 0). Desgnatng the term c ˆ t j s j t = F the FOCs can now be wrtten as: H = d dt G = d = 2b ds 1 F = 0 (17) s ( p = 2b 1 F F ) f t t t = 0 (18) From condtons (17) and (18), we can assess how cost sde spllovers mpact frms ncentves to share nformaton and nvest n technology. We formally show the followng: Proposton 7. When the costs of securty technology nvestment are affected by the volume of sales, and there are volume-related cost sde spllovers as captured by the parameter ˆ, () An ncrease n ˆ has ambguous mplcatons on the propensty to share securty nformaton or nvest n securty technology for both frms. () Volume-related spllovers reduce ncentves to share nformaton n comparson to an envronment, where no such spllovers exst. Changes n the spllover parameter ˆ ntroduce two countervalng effects. An ncrease n ˆ makes frm s compettor more effcent by reducng ts unt cost c ˆ t s. Ths enables j to prce more aggressvely. If frm ncreases ts level of nformaton shared, t further ncreases the cost effcency of the compettor, whch acts to the dsadvantage of the frm. Because the mproved cost effcency precptates further prce competton, both frms respond strategcally by reducng ther levels of nformaton sharng. On the other hand, an ncrease n ˆ ncreases the proft margn of each frm, thus provdng greater ncentves for ncreased nvestment n technology and nformaton sharng. In Appendx A, we demonstrate that the relatve sze of the above-mentoned effects depends on the rato of the two parameters measurng demand and volume-related cost spllovers, d /ˆ. The smaller ths rato, the bgger the former effect, mplyng that ncreased volume-related cost spllovers reduce the ncentves to share nformaton. It may also be nterestng to nvestgate what happens to the slope of the nformaton-sharng reacton functons. We demonstrate that the nformatonsharng reacton functon, s / s j, s not necessarly ncreasng, unlke n the case when there are no volume-related costs of nvestng n securty technology. In partcular, the sgn of the slope of ths reacton functon s determned by the sze of the parameter ˆ. For small values of ˆ, s / s j > 0, and for large, s / s j < 0. Thus, only f volume-related cost spllovers are suffcently small, nformaton sharng by one frm nduces the other frm to share more nformaton. Whle a hgher level of nformaton sharng fosters greater opportuntes for tact colluson, as derved n earler sectons, t also leads to a more effcent compettor who faces lower varable costs. Such a compettor tends to prce more aggressvely. When the value of ˆ s suffcently bg, the latter effect s sgnfcant, thus reversng the result we have derved n the absence of volume-related cost spllovers. Volume-related spllovers costs yeld, therefore, predctons that are more consstent wth the free-rdng behavor descrbed n Gordon et al. (2003) or n the R&D lterature (d Aspremont and Jacquemn 1988, Kamen et al. 1992) Ths result also corresponds well wth Gordon et al. (2003) who pont out that whether or not nformaton sharng results n an ncreased level of securty depends on the nature of the probablty securty breach functon. Bascally, what drves ther result s the relatve sze of the frm s margnal beneft from an addtonal dollar of nformaton securty expendture, at dfferent levels of securty nvestment.

15 Gal-Or and Ghose: The Economc Incentves for Sharng Securty Informaton 200 Informaton Systems Research 16(2), pp , 2005 INFORMS 5. Implcatons, Concluson, and Extensons The U.S. federal government has encouraged the formaton of ISACs, wth the goal of helpng protect crtcal nfrastructure assets that are largely owned and operated by the prvate sector. Ths has been wtnessed n ndustres such as bankng and fnance, IT, chemcals, ol and gas, electrcty, etc. The underlyng assumpton s that such centrally coordnated nformaton-sharng organzatons would facltate the algnment of goals for both the prvate sector and the federal government, whch, n turn, would mprove the securty of cyber nfrastructure assets. However, all sectors do not have a fully establshed ISAC, and n those sectors that do, there s mxed partcpaton. Specfcally, fve recently revewed ISACs showed dfferent levels of progress n mplementng the PDD 63 suggested actvtes. 30 Hence, the government felt the mportance to dentfy economc ncentves to encourage the desred nformaton-sharng behavor n IT securty (Dacey 2003a). We develop a model to nvestgate the benefts to frms from jonng such securty nformaton-sharng allances. Our results pont out that f nformaton sharng among members of the allance had suffcently large postve mplcatons on the demand facng the frms, there are, ndeed, strong economc ncentves for frms to engage n sharng securty nformaton. Increase n securty nformaton sharng may yeld two benefts for the frms: a drect effect, whch ncreases demand and a strategc effect, whch allevates prce competton. These ncentves become stronger wth ncreases n the frm sze and the degree of competton. Because such allances can gve rse to postve spllover effects, we nvestgate ther mpact on sharng and securty nvestment levels. Importantly, we demonstrate that the nature of the securty technology cost functon plays a pvotal role n determnng whether spllovers are benefcal or detrmental to frms ncentves to jon the ISA. We also pont out that jonng the ISA may not be benefcal to the frm f t loses ts compettve advantage n the marketplace, when competng aganst a rval whose product s perceved to be more secure by 30 These were the IT, telecommuncatons, energy, water, and electrcty ISACs. consumers. To support the exstence of ncentves for nformaton sharng, the extent of postve demand spllovers should be suffcently large to more than offset ths adverse mplcaton on the compettve poston of the frm. 31 We fnd that an ncrease n securty nformaton sharng and securty technology nvestment levels lead to hgher socal welfare, compared to the no-sharng regme. However, the equlbrum levels vary dependng on whether an ISA enacts the role of a socal planner or a jont proft maxmzer. The levels of securty nformaton sharng and technology nvestment obtaned under a market equlbrum fall short of those that maxmze socal welfare. Even when the members of an ISA coordnate ther nformaton sharng and technology nvestment decsons to maxmze jont ndustry profts, the extent of sharng and nvestment falls short of socally desrable levels. Jont proft maxmzaton yelds, however, hgher levels of sharng than those obtaned at the market (Bertrand-Nash) equlbrum, mplyng that coordnaton among frms on technology securty should actually be encouraged by the federal government. 32 Even f ther coordnaton does not result n socally optmal levels of technology nvestment and nformaton sharng, t stll yelds an mprovement over the outcome attaned n the absence of coordnaton. Our model shows that when frms face volumerelated costs, ncreased spllover effects do not necessarly encourage frms to share securty nformaton. In our analyss, we have only consdered symmetrc cost sde spllovers, mplyng that both frms are equally effcent n utlzng the shared securty nformaton n reducng ther margnal costs of technology nvestment. In future research, we plan to extend the model to allow for asymmetres among frms n utlzng the cost sde spllover beneft. A prelmnary nvestgaton ndcates that f frms dffer n ther ntrnsc ablty to utlze the shared nformaton, the more effcent frm may have stronger ncentves to undernvest n securty technology and have lower ncentves to share nformaton, compared to the less 31 The comparson of the parameters and d as expressed n the Assumpton 1 of our model. 32 ISAs should not be allowed to restran trade by restrctng output, coordnatng prces, or otherwse nhbtng competton, on whch anttrust laws generally focus.

16 Gal-Or and Ghose: The Economc Incentves for Sharng Securty Informaton Informaton Systems Research 16(2), pp , 2005 INFORMS 201 effcent frm. The total effect of a change n the spllover parameter s not drven by the drect effect of ths change alone, but also by the compettor s reacton to t. Ths opens up the possblty of ndrect freerdng behavor by the more effcent frm. Gordon et al. (2003) also pont out such a possblty n ther model. ISACs do not seem to have well-desgned ncentves to prevent frms from free rdng. Addtonally, frms that jon such allances are often concerned about provdng compettve advantage to other member frms. Thus, there s a possblty that even after enterng an allance, frms mght renege on sharng securty breach nformaton wth other member frms. To mtgate such concerns, the Chemcal Industry Cyber-Securty Informaton Sharng Network has put n place standards for authentcaton and verfcaton of the securty nformaton beng shared. Whle PDD 63 encouraged the creaton of ISACs, t left the actual desgn and functon of the ISACs to be determned by the prvate sector n consultaton wth the federal government (Dacey 2003a). A sgnfcant mplcaton of our model s that rgorous emprcal studes of the structure and actvtes of such nformaton-sharng organzatons are needed. These studes would not only determne the actual levels of nformaton sharng occurrng among members of ISACs, but could provde deep nsghts nto the approprate ncentves that may be requred to facltate such sharng, wthout causng excessve prce ncreases. 33 These ncentves may nclude varous publc polcy tools related to tax benefts, subsdes, or specfc legslaton protectng frms from anttrust actons. In addton, emprcal studes could address the role of government nterventon n the form of optmal ncentves or subsdes to prevent frms from renegng on ther nformaton-sharng commtments. Although markets dffer n a number of ways, we consder only a lmted number of market characterstcs n our research. For nstance, n our socal welfare analyss, we focus on only one ndustry. In realty, a securty breach n a crtcal nfrastructure ndustry, such as bankng, may adversely affect producers and consumers n other ndustres. Ideally, 33 Dacey (2003b) outlnes some actual levels of nformaton sharng and reportng (to the Natonal Infrastructure Protecton Center) occurrng n these ISACs. a socal welfare functon should recognze such crossndustry spllover effects. Another lmtaton of our model s that we mplctly assume that whatever securty nformaton a frm s wllng to share, t shares t truthfully. However, n the absence of addtonal ncentves, truthtellng may not be an equlbrum outcome as has been shown by Zv (1993) n the context of trade assocatons. 34 Despte these lmtatons, we beleve that our model addresses an mportant ssue, and hope that the proposed approach may be used as a startng pont for addtonal research n ths area. Acknowledgments The authors are grateful to semnar partcpants at the 2005 Internatonal Industral Organzaton Conference, 2003 Workshop on Economcs and Informaton Securty, Henz School of Publc Polcy, and Tepper School at Carnege Mellon Unversty for useful suggestons. They also thank Ross Anderson, John Caulkns, Anthony Dukes, Ramayya Krshnan, and Uday Rajan for helpful comments. Fnally, the authors thank the assocate edtor and two anonymous referees for ther substantve suggestons, whch have mproved ths paper. Appendx A. Proofs Dervaton of Beneft Functon Assume that the utlty of a representatve consumer when consumng q 1 and q 2 unts of the two products s U q 1 q 2 = r 1 q 1 + r 2 q 2 d 1q d 2q zq 1q 2 + Y p 1 q 1 p 2 q 2 where d j >z and the last bracketed term s the consumer s utlty from the consumpton of other products. Then, U = r q j d j q j zq p j = 0 j = 1 2 j (19) j Hence the margnal utlty from consumng product j ncreases wth r j and declnes wth the quantty that the consumer buys of product j as well as the quantty he buys of the competng product. The parameter r j reflects the consumer s apprecaton of j s product, whch s nversely related to hs expectatons concernng securty breaches that frm j mght experence. From (19), we get the followng two equatons: q 1 = d 2r 1 zr 2 d 1 d 2 z 2 d 2 p 1 d 1 d 2 z 2 + zp 1 d 1 d 2 z 2 q 2 = d 1r 2 zr 1 d 1 d 2 z 2 d 1 p 2 d 1 d 2 z 2 + zp 2 d 1 d 2 z 2 34 We thank an anonymous referee for pontng ths out. (20)

17 Gal-Or and Ghose: The Economc Incentves for Sharng Securty Informaton 202 Informaton Systems Research 16(2), pp , 2005 INFORMS Defne a + B = d jr zr j d 1 d 2 z 2 b 1 = d j d 1 d 2 t 2 b 2 = Hence, from the defnton of B, t follows that z d 1 d 2 t 2 g s s j = a + t t j + d s j t j d jr zr j d 1 d 2 z 2 For smplcty, assume that the consumer s apprecaton of product, as measured by r, depends on s but s ndependent of the value of s j. Hence r / s < 0 but r / s j = 0. As well, assume that ths apprecaton declned at an ncreasng pace when s ncreases, thus 2 r / s 2 < 0. As a result, g s = d j r / s d 1 d 2 z > 0 g = 2 s d t j + z r j/ s j j d 1 d 2 z 2 Hence g / s j < 0f d t j < z r j / s j / d 1 d 2 z 2. As well, g / s > g / s j by our assumpton that d j >z. 2 g s 2 = d j 2 r / s 2 d 1 d 2 z 2 2 g s 2 j > 0 = z 2 r j / s 2 j d 1 d 2 z 2 < 0 2 g s s j = 0 Snce z<d j, 2 g / s 2 > 2 g / sj 2. The above specfcaton yelds all the restrctons we have mposed on the leakage costs functon g s s j. Proof of Proposton 1. From the proft functon of frm, we frst derve the reduced form verson of frm s proft functon gven by Equaton (4). From Equatons (1) and (3), the proft functon of frm s =p q f t y j =p a b 1 p +b 2 p j +B f t y j mplyng that d =a dp 2b 1 p +b 2 p j +B The optmal prce s then p = a b 1 p + b 2 p j + B /b 1. Ths then mples that q = b 1 p. Hence = q p f t y j = b 1 p 2 f t y j From Equaton (4), the FOC for the second-stage decson varable; that s, the prce leads to the followng reacton functon: p p j = a + b 2 p j + B 2b 1 By solvng these two equatons smultaneously, we get the followng optmal prces: p = 2b 1a + b 2 a j + 2b 1 B + b 2 B j 4b1 2 (21) From Equaton (21), we then have = 2b 1 + b 2 d s t 4b1 2 > 0 j = 1 2 j The above nequalty holds snce <1 and b 1 >b 2. From (21), we also have = 2b 1 d s j + b 2 t j 4b1 2 Under Assumpton 1, the above s postve. Dfferentatng further the optmal prce w.r.t. s yelds = 2b 1 g / s + b 2 g j / s + b 2 d t s 4b1 2 (22) Evaluatng the above dervatve at s = 0 mples that / s s =0 > 0 and evaluatng the above dervatve at s = s j = 1 mples that / s s =s j =1 < 0 from Assumpton 2. As well, snce 2 g / s s j 0, the dervatve / s s strctly ncreasng n s j. Hence, f / s s =s j =1 < 0, t follows that / s s =1 < 0 for any value of s j < 1 as well. By our assumpton that 2 g / s 2 > 2 g j / s 2, t follows that / s s a strctly decreasng functon of s. Hence, there exsts s c 0 1, where / s = 0, and the proposton follows. Proof of Lemma 1. The proof for the frst part follows from Equatons (5), (6), and (22). The proof for the second part s embedded n the followng proof of Proposton 2. Proof of Proposton 2. () Because we do not get closed-form solutons for the frst-stage decson varables, we adopt the mplct functon approach to present our results and gan nsghts. We want to perform comparatve statcs of the frm s decson varables s and t w.r.t. that of the second frm decson varables; say, s j. Upon total dfferentaton of Equatons (5) and (6), we get the followng set of equatons: 2 p ds s p dt s t + 2 p ds s s j = 0 (23) j H ds s + H dt t + H ds s j = 0 j = 1 2 j (24) j The set of two smultaneous equatons for each frm leads us to the followng soluton for the dervatves ds /ds j and dt /ds j : ds 2 p ds j 1 s s j = M dt H ds j s j where M = 2 p s 2 H s 2 p s t H t

18 Gal-Or and Ghose: The Economc Incentves for Sharng Securty Informaton Informaton Systems Research 16(2), pp , 2005 INFORMS 203 Here, H s j p = 2b 2 p 1 + 2b t s 1 p 2 f j t s c t j j t y j H p = 2b 2 p s 1 + 2b s t 1 p t s ( ) H 2 p 2 p = 2b t 1 + 2b t 1 p 2 f t 2 t 2 From the expresson for the optmal prces gven n the Proof of Proposton 1, we derve the followng: 2 p s 2 2 p = b 2 d t s 4b1 2 > 0 = 2b 1 2 g / s 2 + b 2 2 g j / s 2 4b 2 1 < 0 To satsfy the second-order condtons and ensure global concavty, the determnant of M must be postve and H / t < 0. Further n equlbrum, / s = 0, mplyng that H / s > 0 snce 2 p / t s > 0. As well, we proceed to prove that the followng expresson s postve: = 2b 1 d t j g / s j + b 2 g j / s j s j 4b1 2 From the FOC p j / s j = 0, we have that gj = b ( ) 2 g s j 2b 1 s d t j j Hence s j = 2b 1 d t j g / s j + b 2 /2b 1 b 2 g / s j b 2 d t j 4b 2 1 = dt j g / s j > 0 2b 1 Next, from Equaton (21), we show that 2 p t s j =0 and 2 p = 2b 1 2 g / s s j b 2 2 g j / s s j 0 s s j 4b1 2 where the last nequalty follows snce 2 g / s s j 0. Hence H / s j > 0 snce 2 f / t y j 0. The above dervatves help us establsh the comparatve statcs results wth respect to s j. (), () In a smlar manner, total dfferentaton of Equatons (5) and (6) wth respect to t j yelds ds 2 p dt j 1 s t j = M dt H dt j t j It s easy to show that 2 p / s t j = 0 and H t j p = 2b 2 p 1 + 2b t j t 1 p t t c s j j 2 f t y j Snce 2 p / t t j = 0 and 2 f / t y j 0, a suffcent condton for H / t j > 0 s that / t j > 0. Further, = 2b 1 d s j + b 2 t j 4b1 2 Hence the above s nonnegatve as long as d s j + b 2 / 2b 1. By requrng that, we guarantee that / t j > 0 for both frms. As a result, H / t j s postve for both frms, and reacton functons are upward slopng w.r.t. t j (.e., s / t j > 0 and t / t j > 0). Note that the condton s stronger than necessary snce H / t j can be postve even when / t j < 0. Proof of Proposton 3. () Smlar to the Proof of Proposton 2, upon total dfferentaton of Equatons (5) and (6), we get the followng set of equatons: 2 p ds s p dt s t + 2 p db s b 1 = 0 (25) 1 H ds s + H dt t + H db b 1 = 0 (26) 1 The set of two smultaneous equatons for each frm yelds ds 2 p db 1 1 s b 1 = M dt H db 1 b 1 H p = 2p p b + 2b 2 p 1 t 1 + 2b b 1 t 1 p b 1 t Now = 2b 1 + b 2 d s t 4b1 2 = 2 4b 1p a + B b 1 4b1 2 < 0 2 p = 2 4b2 1 8b 1 2b 1 + b 2 d s t b 1 4b1 2 < 0 2 The above expressons mply that H < 0 b 1 In addton, 2 p / s b 1 = 2 g / s < 0. As a result, the comparatve statcs wth respect to b 1 are determned unambguously (.e., s / b 1 < 0, t / b 1 < 0). () For the comparatve statcs wth respect to b 2, we need to establsh the sgns of H / b 2 and 2 p / s b 2. Here, H p = 2b 2 p b 1 + 2b 2 b 2 t 1 p where b 2 t = a j + B j b 2 4b b 2p 4b1 2 > 0

19 Gal-Or and Ghose: The Economc Incentves for Sharng Securty Informaton 204 Informaton Systems Research 16(2), pp , 2005 INFORMS Smlarly, from (21), the expressons for the dervatves of the equlbrum prces evaluated at the symmetrc equlbrum are gven as follows: = 2b 1 + b 2 d s t 4b1 2 > 0 2 p = ds t b 2 4b b 2 2b 1 + b 2 d s 4b1 2 2 = 4b 1b 2 + 4b1 2 + ds 4b1 2 2 Under the assumpton that, the above second dervatve s postve. In addton, 2 p s b 2 = dt g j / s 4b b 1 g / s b 2 g j / s + b 2 d t 2b 2 4b1 2 > 0 2 because at the equlbrum, the second term vanshes from Equaton (22). The comparatve statcs wth respect to b 2 are mpled by the above dervatves. Note, once agan, that the assumpton s stronger than necessary, snce H / b 2 can be postve even when 2 p / t b 2 s negatve. Proof of Proposton 4. Proof of Proposton 4 s smlar to 2 and 3 above, and hence t s not repeated for brevty. We only show the relevant expressons. H a H a j = 2b 1 a = 2b 1 a j 2 p + 2b t 1 p t a 2 p + 2b t 1 p t a j Here, / a = 2b 1 / 4b 2 1 and / a j = b 2 / 4b 2 1. Ths mples that Hence and () Now a t = 2 p a j t = 0 H a H a j = 2b 1 a t > 0 = 2b 1 a j t > 0 H p = 2b 2 p 1 + 2b d d t 1 p t d = 2b 1s j t j + b 2 t s d 4b1 2 2 p = b 2t s d 4b1 2 > 0 2 p = b 2s t d 4b1 2 > 0 Hence s / d > 0, t / d > 0. In a smlar manner, t can be shown that s / c > 0, t / c > 0 snce [ ] H 2 f = t c t y j s j > 0 j () H = 2b 2 p 1 + 2b t 1 p t where = 2b 1t j + b 2 t 4b1 2 < 0 2 p t = b 2 4b1 2 < 0 2 p s = 0 The above nequaltes mply that s / < 0 and t / < 0. Proof of Proposton 5. Solvng for the nverse demand functons from (1) and (3), p = b 1a + b 2 a j b 1 q + b 2 q j + b 1 B + b 2 B j b1 2 At the symmetrc equlbrum we have a + B q p = b 1 b 2 where B = t 1 + d ts g s s. Hence, total welfare s equal to SW = q 0 2 a + B q dq 2f t b 1 b c ts 2 where q s the quantty at the market equlbrum. Takng the dervatve w.r.t. s, the optmal s SW s gven by the soluton to SW = ( q 2 s s 0 2 q b 1 b 2 0 ) dq 2f t c ts = 0 a + B q b 1 b 2 ( ) B a+b q q dq +2 s b 1 b 2 s 2 ct f y j =0 by usng Lebntz theorem. At the symmetrc equlbrum, q = b 1 p = b 1 a + B / 2b 1 b 2 and q / s = b 1 / 2b 1 b 2 B/ s, where B/ s = d t g / s + g / s j. Hence, we can wrte ths equaton as SW s [ b1 a + B 3b = 2 1 2b 2 2b 1 b 2 2 b 1 b 2 ] B s 2 ct f y j = 0 (27) Because the last term s always postve, t follows that for a fxed t, s SW s bgger than the value satsfyng

20 Gal-Or and Ghose: The Economc Incentves for Sharng Securty Informaton Informaton Systems Research 16(2), pp , 2005 INFORMS 205 B/ s = 0. When B/ s = 0, d t g / s + g j / s = 0. Recall from (22) that n the market equlbrum the condton, whch determnes the optmal amount of sharng, s gven by d t 2b 1 /b 2 g / s + g j / s = 0. Snce 2b 1 >b 2, t follows that for a fxed t, s NE s smaller than the value satsfyng B/ S = 0. Hence s NE <s SW. In a smlar manner, dfferentatng SW wth respect to t as above, we obtan SW = ( q ) a + B q 2 dq 2f t t t 0 b 1 b c ts 2 By usng Lebntz theorem and then rearrangng terms, we obtan the followng FOC for t ( b 1 3b 1 2b 2 a + B B f 2b 1 b 2 2 b 1 b 2 t + t c s f ) = 0 (28) y j where B/ t = 1 + d s. The soluton to ths equaton determnes the optmal level of securty technology nvestment. Compare ths to the optmal level of technology nvestment under the frms ndvdual proft maxmzaton that solves the followng equaton: 2b 1 p = f t t At the symmetrc equlbrum, p = a + B / 2b 1 b 2 and / t = 2b 1 + b 2 d s / 4b1 2. Hence the FOC at the market equlbrum reduces to 2b 1 a + B 2b 1 + b 2 d s 2b 1 b 2 4b 2 1 f t = 0 (29) When, t can be shown that 3b 1 2b 2 2b 1 +b d s > 2 b 1 b 2 2b 1 + b 2 d s. Hence, a comparson of Equatons (28) and (29) mples that for a fxed level of s, the socally optmal level of technology nvestment t SW exceeds that obtaned at the market equlbrum under ndvdual proft maxmzaton, t NE. When both s and t are chosen optmally, the above nequaltes are renforced snce s and t are strategc complements when. From Equatons (13) and (14), we have the followng: JP = 4b [ ( )] 1 a + B g s 2b 1 b 2 2 d t + g 2 s s c t f = 0 j y j (30) JP = 4b [ 1 a + B 1 + d s f 2 + t 2b 1 b 2 2 t c s f ] = 0 y j (31) A comparson of (30) wth Equatons (12, 27) and (31) wth Equatons (28) and (29) when, mples that the securty technology nvestment and securty nformatonsharng levels under jont proft maxmzaton les n between socal welfare maxmzaton and the market (Bertrand-Nash) equlbrum. Hence, t follows that t NE < t JP <t SP and s NE <s JP <s SP. Proof of Proposton 6. The proof follows from comparng Equatons (15) and (16) wth Equatons (5) and (6), respectvely. The addtonal terms n Equatons (15) and (16) are the Stackelberg effects and prove the result. Snce / s j s j / s >0 and when, / t j t j / t >0at the levels of smultaneous mode game, to get to the optmum, s s j and t t j must be hgher. Proof of Proposton 7. () The optmal prce n ths case s gven by p = 2b 1 a + B + b 2 a j + B j + 2b1 2F + b 1 b 2 F j 4b1 2 j = 1 2 j We frst derve the relevant expressons here. B t Next, F = 0 s = 1 B j = t d s B j = s d t gj s F s j = ˆ t j t F j s = ˆ t t j B s = g s F t = c ˆ t j s j t F j t = ˆ s t j As well, = 2b 1 g / s + b 2 d t g j / s b 1 b 2 ˆ t t j s 4b1 2 Comparng ths to Equaton (22), t s mmedate that spllovers on the margnal cost sde reduce wllngness to share compared to spllovers on the fxed cost sde. () Next, we have the followng: = 2b 1 + b 2 d s + 2b1 2 c ˆ s j t j t b 1 b 2 ˆ s t j t 4b1 2 ˆ = 2b2 1 t js j t + b 1 b 2 t s t j 4b1 2 F ˆ = s jt j t From the FOCs (17) and (18), we can derve the followng set of smultaneous mplct equatons: ds 2 p d ˆ 1 s = M ˆ dt H d ˆ ˆ where M = 2 p s 2 H s 2 p s t H t