Investment Secrecy and Competitive R&D

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1 BE J. Econ. nal. Polcy 2016; aop Letter dt Sengupta* Investment Secrecy and Compettve R&D DOI /beeap bstract: Secrecy about nvestment n research and development (R&D) can promote greater technologcal change and hgher socal welfare n compettve ndustres. In a duopoly where each frm has prvate nformaton about ts actual producton technology (or cost) and frms engage n cost-reducng R&D wth uncertan outcomes pror to engagng n prce competton, the equlbrum outcome when frms do not observe the R&D nvestment chosen by the rval (nvestment secrecy) yelds hgher nvestment, socal welfare, and ndustry proft compared to the outcome when R&D nvestment levels of frms are publcly observable. Government nterventon to secure dsclosure of R&D nvestments may be counterproductve; trade secret laws that protect prvacy of nformaton related to R&D nputs or nvestment may be helpful. Keywords: Cost-reducng technology, Duopoly, Incomplete nformaton, Prce competton, Secrecy, Strategc nvestment 1 Introducton Frms mprove ther producton technology through a varety of means, many of whch are unobservable to the outsde world. Ths s, n partcular, true for a very sgnfcant proporton of nnovatons and other producton effcency gans that arse through learnng, nternal research and development (R&D), and accumulaton of organzatonal captal. s many of these gans are not patentable, frms prefer to retan prvacy of nformaton about ther actual cost and technology structure. More nterestngly, t s dffcult for exstng rvals, potental compettors, and other stakeholders n the ndustry to readly acqure nformaton about efforts and nputs expended n the R&D process of a frm. In compettve markets, the absence of observablty of R&D nvestment or *Correspondng author: dt Sengupta, Department of Economcs, uburn Unversty 0341 Haley Center, uburn, L , US, E-mal: azs0074@auburn.edu Brought to you by uburn Unversty Man Campus uthentcated azs0074@auburn.edu author's copy

2 2. Sengupta efforts undertaken by other frms s lkely to nfluence the strategc ncentve to nvest, the extent of actual technologcal mprovements, and the eventual market outcomes. Ths leads to an mportant queston about the effect of prvacy of such nformaton on technologcal change and socal welfare. If such secrecy s not socally desrable, then there would be a case for publc polcy to dscourage secrecy and promote sharng and dsclosure of nformaton about R&D nvestments made by the frms. Ths paper attempts to analyze the potental mpact of secrecy of the level of R&D nvestment made by the frms n a market characterzed by prvacy of nformaton about the actual cost structure of the frms. e., ther actual producton technology. My paper draws on the semnal work of Gal-or (196) who fnds that frms strategcally competng n prces do not have any ncentve to dsclose nformaton about ther own cost of producton. In ths paper, I assume that frms keep ther fnal outcome of process nnovaton secret and prmarly focus on the role of (exogenously gven) secrecy of strategc R&D nvestment. Moreover, n contrast to ths paper, the exstng lterature has largely focused on ssues related to the observablty of cost or R&D outcomes. Thomas (1997) examnes the ncentve for costreducton by a sngle frm n an ndustry where frms dffer n ther ntal cost and shows that ths unlateral ncentve for cost-reducton s hgher when nformaton about actual producton cost s prvately held. In partcular, the paper analyzes an ex ante symmetrc homogenous good duopoly where frms engage n process nnovaton (that reduces producton cost) and prce competton. The frms smultaneously decde whether to nvest n costreducton and after ths, they compete n prces. The realzed cost-reducton s uncertan and depends on the amount of nvestment. Each frm observes ts own realzed producton cost outcome pror to prce settng but remans unaware of the actual outcome of the R&D nvestment made by ts rval. I compare the ncentve to nvest n cost-reducton and the market outcome generated n ths extensve form wth the secrecy of nvestment to the equlbrum outcome of an alternatve extensve form where the level of R&D nvestment s publcly observed before prce settng. The realzed cost. e., the outcome of R&D s assumed to be prvate nformaton n both extensve forms. The man result of the paper s the equlbrum outcome under secrecy of R&D nvestments yelds hgher socal welfare than publc observablty of (or nformaton sharng about) nvestment. Further, secrecy may yeld hgher total amount R&D nvestment and hgher expected proft for frms. One mplcaton of ths s that there may not be any case for publc polcy to encourage nformaton sharng arrangements among competng forms about R&D nvestments. Further, there s some beneft from the protecton of nformaton about expendtures, nputs or efforts gong nto frms R&D processes Brought to you by uburn Unversty Man Campus uthentcated azs0074@auburn.edu author's copy

3 Investment Secrecy 3 through trade secret laws 1 and deterrence of compettve ntellgence gatherng actvtes 2 related to R&D nvestment or nputs. The paper s organzed as follows. Secton 2 descrbes the model. In Secton 3, I dscuss the prcng and nvestment outcomes under ncomplete nformaton when R&D nvestment s secret and when t s publcly observable. 2 The Model I consder an olgopolstc market wth two ex ante dentcal frms that compete n prces and produce a physcally homogenous product. The producton technology of each frm can be of two potental types: hgh-cost (H) and low-cost (L): Each frm produces at constant unt cost. The unt producton cost of a hgh-cost type (defned by c H ) s greater than that of a low-cost type (defned by c L ). e., 0<c L < c H. There s a unt mass of rsk neutral consumers n the market. Consumers have unt demand. e., each consumer buys at most one unt of the good. Each consumer s wllng to pay V for a unt produced by ether frm. I assume that V > c H. Frms are ntally endowed wth hgh-cost technology. e., each frm ncurs a unt producton cost of c H. Frms can nvest n R&D of a new cost-reducng technology. However, the outcome of the nvestment s uncertan, and the probablty of success s postvely related to the cost of nvestment. The cost of nvestment s gven by μ where the R&D effcency parameter,, can be nterpreted as the maxmum possble cost of nvestment that a frm can ncur and μ 2½0, 1Š = 1, 2 s the nvestment or alternatvely can be nterpreted as the probablty of successful R&D. In partcular, a frm successfully nstalls the lowcost technology wth probablty μ and remans the hgh-cost type wth probablty μ. I assume that 0 < < 3. In the frst stage, the frms smultaneously decde how much to nvest (vz., μ ) 4. It s evdent that the more a frm nvests n cost-reducng technologcal R&D, the hgher s the probablty of beng successful. e., becomng a lowcost type frm. I consder two possble scenaros after the frms decde on ther R&D nvestment n the frst stage. (1) The nvestment decsons become publcly 1 In the US, state governments choose to adopt convenently modfed versons of the Unform Trade Secret cts (1979). 2 See Bagnol and Watts (2015) among others. 3 If > then frms do not nvest n the equlbrum under ncomplete nformaton. 4 lternatvely, one can thnk that the frms choose the probablty of successful nvestment n cost-reducng technology. e., μ. Brought to you by uburn Unversty Man Campus uthentcated azs0074@auburn.edu author's copy

4 4. Sengupta observable but the frms reman unaware of the fnal outcome of the nvestment made by the rval frms; n the rest of the paper, I refer to ths as the ncomplete nformaton wth observable nvestment. The alternatve scenaro s where (2) the nvestment decson of each frm remans prvate knowledge (secret) and thus, a frm nether observes the rval s nvestment decson nor the fnal outcome of the rval s nvestment; ths s referred as the ncomplete nformaton wth unobservable nvestment. I denote the nvestment outcomes and the ex ante expected profts under ncomplete nformaton wth observable nvestment as well as wth unobservable nvestment wth superscrpt IO and IU respectvely. The realzatons of the producton technology after nvestment are ndependent across frms, and there s no spll over. In the next stage, frms choose prces smultaneously. Fnally consumers observe the prces charged by the frms, decde whether to buy, and from whch frm to buy. 3 Observablty vs Secrecy fter the strategc nvestment decsons n the frst stage, a frm gets to know the actual outcome of ts own nvestment n the cost-reducton, but does not learn anythng about the rval s R&D outcome. Therefore, when the frms smultaneously choose prce of ther product they are not aware of each other s margnal cost of producton. e., a frm does not know whether the rval has successfully adopted the low-cost technology. To begn wth, I solve the second stage (ncomplete nformaton) subgame where frms choose prces smultaneously wth the prvate knowledge of ther own producton technology 5. Wthout any loss of generalty, I assume that μ μ, = 1, 2 where. e., frm s more lkely to successfully nstall the new low-cost technology than frm. Lemma 1 (Prce equlbrum under ncomplete nformaton): The hgh-cost type charges a prce equal to ts own unt producton cost ðp H = c H Þ and the lowcost type randomzes over an nterval p L 2 μ ch + μ c L, c H wth probablty dstrbutons F ðpþ = ð μ Þ μ μ μ ðp c L Þ and F ðpþ = 1 μ ð μ Þ ðp c L Þ 5 Spulber (1995) and Routledge (2010) consder Bertrand prce competton under asymmetrc nformaton about rval s cost when frms face downward slopng market demand. Brought to you by uburn Unversty Man Campus uthentcated azs0074@auburn.edu author's copy

5 Investment Secrecy 5, =1,2 where and μ μ. The ex ante expected profts are π = μ ð μ Þ and π = μ ð μ Þ. [1] Proof: Frst, note that there does not exst any Bayesan prce equlbrum n pure strateges. The reason s as follows. The low-cost type has compettve advantage over the hgh-cost type snce V c L > V c H ; thus, f the nvestng frm becomes low-cost type t enoys market power and steals all busness n the state when the rval (nvestng frm) remans hgh-cost type, but also has an ncentve to undercut the rval n case t s of low-cost type too (. e., the rval has adopted the low-cost technology successfully). In the unque prce equlbrum, the lowcost type randomzes prce over an nterval p, c H to balance these ncentves. If μ > μ, the low-cost type of frm has a mass pont on the upper bound; n other words, frm has hgher probablty of chargng the upper bound (c H )of the prce dstrbuton than frm does. Further, frm of low-cost type charges the upper bound (c H ) when t beleves that the rval has remaned a hgh-cost type wth probablty μ. Therefore, the equlbrum proft of the low-cost type frm s π L = μ ðch c L Þ for any prce p 2 p, c H. Note that the low-type of frm earns the same proft ðπ L Þ, but there s no mass pont 6 on the upper bound (c H ) for frm. lso, f μ = μ then there s no mass pont on the upper bound of low-cost type of ether frm. The low-cost type charges p only when the rval s of hgh-cost type for sure; ths mples that π L = p c L. Ths yelds the lower bound of the mxed strategy prce support p = μ ch + μ c L. t any prce p 2 μ ch + μ c L, c H the low-cost type frm can sell to the entre market f ether the rval s of hgh-cost type or t s not undercut by the low-cost rval. Thus, the low-cost frm earns expected proft of the drty type. e., π L = μ ðch c L Þ; ths mples that the proft of the low-cost type of frm s μ ðp cl Þ + ð F ðpþþμ ðp c L Þ = π L = μ ðch c L Þ where μ (n the left-hand sde) s the probablty that the rval of frm remans hgh-cost type and ð F ðpþþμ (n the left-hand sde) mples that though the rval frm has become low-cost type but t does not undercut the 6 Ths essentally means that snce frm has a lower probablty of beng successful n adoptng the low-cost technology compared to ts rval frm, frm charges the upper bound of the prce nterval (. e., c H ) wth zero probablty. Brought to you by uburn Unversty Man Campus uthentcated azs0074@auburn.edu author's copy

6 6. Sengupta frm. e., does not charge a prce below p; smlarly, the proft of the low-cost type of frm s μ ðp cl Þ + ð F ðpþþμ ðp c L Þ = π L = μ ðch c L Þ. Thus, I get F ðpþ = 1 μ μ ðp c L Þ and F ðpþ = μ μ μ μ ðp c L Þ. Note that F ðpþ = F ðpþ f μ = μ. The hgh-cost type charges ts own margnal cost and earns zero proft n the equlbrum. e., π H = 0. I calculate the expected profts of frm and frm as and π = μ π L + ð μ Þπ H = μ μ ðch c L Þ π = μ π L + μ πh = μ μ ðch c L Þ respectvely, = 1, 2 where and μ μ. frm earns a strctly postve expected proft because of ts strctly postve nvestment. Moreover, the expected proft of the frm wth hgher nvestment depends on the probablty of falure of the rval wth lower nvestment, but not the vce versa; because the low-cost type of the frm wth hgher as well as lower nvestment earn the same expected proft over the (same) prce nterval. Note that the Bayesan prcng equlbrum s the same rrespectve of the observablty of the frms strategc nvestment decsons. Frst, I consder the case where the strategc nvestment decsons become observable. In the frst stage, frm chooses μ to maxmze expected proft gven that rval frm has chosen μ : ( max μ μ ½ð μ Þ Š s.t. 0 μ μ max = maxðπ μ μ μ Þ = max μ μ μ ðch c L Þ s.t. μ μ 1 The followng proposton descrbes the Bayesan Nash nvestment equlbrum under ncomplete nformaton wth observable nvestment. [2] Proposton 1: Under ncomplete nformaton wth observable nvestment, frms choose μ IO =1 and μ IO = 1 2, =1, 2 where n the Bayesan Nash nvestment equlbrum. Brought to you by uburn Unversty Man Campus uthentcated azs0074@auburn.edu author's copy

7 Investment Secrecy 7 Proof: I evaluate the best response functon of each frm (. e., gven μ the best possble nvestment frm can make) and then fnd the Nash equlbrum of the nvestment game. Suppose arg max μ π μ = μ * and * =max μ π μ.forthe frstpartofeq.[2] 1 μ f μ μ * = f μ 2 > 1 [3] 2 >: μ μ ðch c L Þ f μ 1 2 * = ½ Š 2 f μ 4 > 1 2 >: [4] Observe that for any μ μ,theex ante expected proft of frm ð Þ s maxmzed when μ = 2 1.However,whenμ 1 2 then the relevant ex ante expected proft functon of frm s gven by the second part of eq. [2]. e., = μ ð μ Þ. In ths case, gven that μ μ and μ 2 1 the proft maxmzng value of μ s equal to the value of μ. Consder the second part of eq. [2]. = 1 f 0 μ < 1 μ * 2,1 f μ = 1 [5] >: = μ f < μ 1 μ ðch c L Þ > 0 f 0 μ < 1 * = 0 f μ = 1 μ μ ðch c L Þ >: < 0 f < μ 1. [6] The last part of eq. [5] can be explaned by the smlar argument as that of the frst part of eq. [3]. To fnd the best response functon of frm for any gven μ, I compare the derved expected profts of frm n eqs [4] and [6]. Brought to you by uburn Unversty Man Campus uthentcated azs0074@auburn.edu author's copy

8 . Sengupta 4 2 Note that ð μ Þ > μ ð μ Þ whch means that f 0 μ 2 1 the best response of frm s μ * = 1. lso ½ðcH clþ Š2 ð μ Þ 4 for μ ððch clþ + Þ2 4ðc H c whch mples that μ * LÞ 2 =1 f 2 1 μ ð + Þ 2 4. However, ð 2 μ Þ ½ Š 2 4 for μ ððch clþ + Þ2 4 ; thus, best response of frm s μ * 2 2 = 1 2 f ð + Þ 2 μ 1 To summarze, the reacton functon of frm under ncomplete nformaton wth observable nvestment s gven by μ IO! 1 f0 μ ððc 2 H c L Þ + Þ 4 2 μ =! 1 2 f ð + Þ 2 >: 4 2 μ 1, =1,2 where. Two asymmetrc 7 Bayesan Nash equlbra of the nvestment game under ncomplete nformaton wth observable nvestment are μ IO =1, μ IO = 1 2 [] whch yeld the followng ex ante expected profts for frm and frm [7] Y IO =, YIO 2 = ½ Š 2. [9] 4 Fgure 1 depcts the reacton functons of the frms (denoted by eq. [7]). In the asymmetrc Bayesan Nash equlbra (represented by E 1 and E 2 ), one of the frms chooses nvestment such that t becomes low-type wth probablty one ð.e., μ IO =1Þ; alternatvely the frm nvests maxmum possble amount (). Whereas the other frm nvests less, remans hgh-cost type wth a strctly postve probablty, and earns less proft. Both frms make strctly postve nvestment to generate uncertanty about the cost structure and thus, n turn, 7 It s easy to prove why symmetrc equlbrum does not exst. ssume that μ = μ = ~μ. Gven μ = ~μ, frm has a strctly postve ncentve to devate to μ > ~μ snce frm earns hgher expected proft f t decdes to nvest more than ts rval. Brought to you by uburn Unversty Man Campus uthentcated azs0074@auburn.edu author's copy

9 Investment Secrecy 9 (0, 1), (0, 0) (1, 0) Fgure 1: Equlbrum under ncomplete nformaton wth observable nvestment. earn strctly postve expected proft. Further, ncrease n cost dfferental ncreases market power and proftablty of the low-cost type whch n turn creates hgher strategc ncentve to nvest. Fnally, I study the equlbrum nvestment behavor when the nvestment n cost-reducng technology remans prvate knowledge. In other words, a frm knows ts own type but s unaware of both the nvestment and the actual outcome of the rval. Note that n ths multstage mperfect nformaton game, the nature of prcng equlbrum outcomes s smlar to that of the ncomplete nformaton one dscussed n Lemma 1. Proposton 2: Under ncomplete nformaton wth unobservable nvestment, frms choose μ IU = μ IU =, =1, 2 where n the Bayesan Nash nvestment equlbrum. Proof: Suppose μ = μ = μ s a Nash equlbrum. Gven μ = μ, f frm devates to μ μ then the rval frm does not observe ths devaton and beleves that frm has chosen μ. Thus, the low-cost type of frm randomzes over a prce nterval p 2½ð μþ c H + μc L, c H Š and earns ð μþ. If t devates to μ, the ex ante expected proft of frm. e., π = μ π L + ð μ Þπ H, s gven by π = μ ð μþ. Brought to you by uburn Unversty Man Campus uthentcated azs0074@auburn.edu author's copy

10 10. Sengupta The expected proft from devaton s maxmzed at = 1 f 0 μ < 1 μ 2½0, 1Š f μ = 1 >: = 0 f 1 μ > 1 Smlarly, f μ = μ I can fnd the proft from devaton for frm and the value of μ that maxmzes the expected proft from devaton. Thus, nether frm has no ncentve to devate f μ IU = μ IU = μ = 1. In ths case, the ex ante expected proft of each frm s π IU = π IU =. Next, I check whether μ = 1 and μ = 0 s a Nash equlbrum. In ths case, p = p = c H, π = ½ Š and π = 0. Gven μ = 1, f frm devates. e., μ > 0 then t earns strctly postve proft; further, ths expected proft from devaton s maxmzed at μ = 1. Therefore, I can conclude that μ = 1 and μ =0 s not a Nash equlbrum. From the above propostons, one can make the followng observatons: (1) When the nvestment decsons reman secret, both frms engage s symmetrc nvestment behavor n the equlbrum unlke the case where nvestment s observable. e., μ IO = 1 2 where 6¼. μ IU = μ IU = μ IO =1, =1, 2 (2) The ex ante expected proft earned by each frm under secrecy s hgher than that of under observable nvestment. e., π IU π IO =1, 2 ðch clþ f 2 < (3) The aggregate (or ndustry level) nvestment n R&D under secrecy s hgher compared to no secrecy (about the nvestment behavor) when 3 <. (4) The aggregate (or ndustry level) ex ante expected proft under secrecy s hgher 3 7 <. (5) Socal surplus s maxmzed when a frm charges ts own margnal cost. Thus, the expected total surplus s equal to Brought to you by uburn Unversty Man Campus uthentcated azs0074@auburn.edu author's copy

11 Investment Secrecy 11 μ μ + μ μ + μ μ V cl + μ μ V ch μ + μ whch s maxmzed at μ S = μ S =, = 1, 2 where. Observe that the frm s equlbrum nvestment behavor under secrecy maxmzes the socal surplus. However, needless to say that the ncomplete nformaton equlbrum wll be less desrable for the consumers as consumer surplus s defntely lower under the ncomplete nformaton compared to the socally optmal one. 4 Concluson I fnd that the ex ante total expected proft of the ndustry as well as the socal welfare are hgher when strategcally competng frms keep ther R&D nvestments n cost-reducng technology secret compared to the case when such nformaton s publc observable. Ths mples that the government nterventon to secure dsclosure of R&D nvestments may be counterproductve and the trade secret laws that protect prvacy of nformaton related to R&D nputs or nvestment may be conducve to nnovaton. References Bagnol, M., and S. Watts Compettve Intellgence and Dsclosure. RND Journal of Economcs 46: Gal-or, E Informaton Transmsson Cournot and Bertrand Equlbra. Revew of Economc Studes 53:5 92. Routledge, R Bertrand Competton wth Cost Uncertanty. Economcs Letters 107: Spulber, D Bertrand Competton When Rvals Costs re Unknown. Journal of Industral Economcs 43:1 11. Thomas, C Dsncentves for Cost-Reducng Investment. Economc Letters 57: Brought to you by uburn Unversty Man Campus uthentcated azs0074@auburn.edu author's copy