Information Acquisition and Disclosure: the Case of Differentiated Goods Duopoly

Transcription

1 Informtion Acquisition nd Disclosure: the Cse of Differentited Goods Duopoly Snxi Li Jinye Yn Xundong Yin We thnk Dvid Mrtimort, Thoms Mriotti, Ptrick Rey, Wilfried Snd-Zntmn, Frnces Xu nd Yongsheng Xu for their helpful comments. Of course, ll errors re our own. Toulouse School of Economics. Emil: School of Bnking nd Finnce, University of Interntionl Business & Economics. Emil: Toulouse School of Economics. Emil: 1

2 Abstrct We study the incentive of duopoly to cquire nd disclose informtion on the unknown privte costs. First, firms cn precommit or not to full shring or full concelment disclosure regime. Then in the first stge they decide whether to exert n effort to cquire informtion respectively. In the second stge, they disclose or concel their cquired costs informtion ccording to different disclosure regimes they precommitted. If they cnnot or do not precommit to prticulr regimes, they shre or concel their costs informtion cquired in the first stge voluntrily nd strtegiclly. In the finl stge firms compete on the product mrket s pir of differentited duopoly. We exmine ech corresponding impct on the firms profits, the consumer surplus, nd the socil totl surplus, under different regimes. We find tht under differentited good s quntity competition, the informtion cquisition benefits both firms nd consumers; yet informtion disclosure hurts the consumer surplus, though it benefits both the firms nd the socil welfre. The strtegic informtion disclosure regime lwys gives firms the strongest incentive to cquire informtion; Moreover, it my even involve n inefficient over-investment on informtion cquisition especilly when the mrket s demnd potentil is extremely lrge. Under price competition, the informtion cquisition benefits firms nd consumers; yet the informtion disclosure is detrimentl to both consumer surplus nd firms profit. Key words: Informtion cquisition; Informtion disclosure; S- trtegic informtion disclosure; Cournot competition JEL clssifiction: D8; D83; L13; L40

3 1 Introduction A firm tht introduces new product on mrket does not lwys know its production cost t the time of mking its production decision. 1 The firm cn perform R&D on its potentil technology to lern it. Doing so is both costly nd risky. It is costly, becuse the firm needs to invest in the cquisition of relevnt informtion. An investment in informtion cquisition is risky, since it my fil to generte the desired informtion. Yet the more time, effort nd money is spent on the reserch, the more likely the firm gets to know the production cost of this new product beforehnd. We exmine incentives of firms in duopoly to cquire nd disclose informtion bout their unknown privte production costs. There re lso ppers which studied informtion shring on privte costs, yet they ssume the informtion is exogenously determined, e.g., Vives 1984, This pper endogenizes the informtion structure nd tkes one step further by studying the informtion gthering stge nd the interction between informtion gthering nd disclosure. In our model, ech firm produces differentited product nd fces stochstic technology. The rndom shock tht determines ech firm s cost function is different nd independent from tht of its rivl. Ech firm gets to observe its privte unit cost signl if its R&D effort succeeds. We consider different disclosure regimes for the informed firms, nmely, full shring, full concelment, or strtegic disclosure bsed on their informtion cquired in the R&D phse. Before exerting efforts, firms know the corresponding disclosure regime tht they will obey fter their R&D results come out. The previous literture on informtion shring without informtion cquisition in oligopolistic mrkets nlyzes the incentives of firms tht precommit to prticulr informtion shring rules, e.g. by estblishing trde ssocition. Typiclly, two extreme informtion disclosure regimes re compred: full informtion shring, nd no pooling of informtion full concelment. Gl-Or 1985 shows, even if the firms re llowed to use prtil informtion shring, the optiml shring rule is full disclosure or full concelment depending on the chrcteristics of the competition Cournot or Bertrnd nd the products substitutes or complements. Nturlly, in this pper when we tke one step further to consider the informtion cquisition phse, we cn n- 1 For instnce, when firm fces to produce or not brnd-new good with potentilly high mrket demnd, it will hve to set up the fctory production cpcity ccording to the expecttion of its own cost nd the mrket s environment. Even if the firm will lern its cost informtion during the specific production process ex post, they cnnot chnge their production in the short run, e.g., they cnnot fire their employees or increse their production cpcity immeditely. 3

4 lyze the two precommitment regimes: full disclosure nd full concelment. However, if firms cnnot precommit to informtion disclosure rule ex nte, the decision to disclose or not informtion is endogenous. In this cse, firms shre or concel voluntrily nd strtegiclly depending on wht kind of privte informtion they cquired in R&D. So, in the lnguge of industril orgniztion modeling, the firms ply three-stge gme in the strtegic disclosure regime cse. In stge 1 they decide whether to exert n effort to cquire informtion respectively. In stge they shre or concel their costs informtion cquired in stge 1 ccording to different disclosure regimes. In stge 3 firms compete on the product mrket s pir of differentited good duopoly. In contrst with erlier literture, e.g., Gl-Or 1985, Novshek nd Sonnenschein 198 nd Jnsen 008, where uncertinty is bout n unknown common demnd intercept, the uncertinty in the present pper is bout unknown privte costs. With n uncertin demnd, by exerting efforts, ech firm observes privte signl of prmeter of the model, which ffects everyone s pyoff function in the sme wy. This is clled common vlue problem in the literture. While with uncertin costs, by exerting effort, ech firm observes privte signl of prmeter which is different for ech firm. And this environment is clled privte vlues problem. We ssume tht the disclosed informtion is verifible, i.e., tht firm cnnot lie or untruthfully report its type if it shres with its rivl fter being informed. This ssumption is consistent with some empiricl findings.,3 Our pper finds tht the informtion bout the own nd rivl s production costs is lwys beneficil to firm, nd the vlue is non-decresing with the substitutbility of two goods on the mrket. More specificlly, we cn decompose the vlue of informtion into three prts: 1 the vlue of lerning own cost; the vlue of knowing the rivl s cost; 3 the vlue of shring own cost to the rivl. 4 So, if the informtion cquisition cost is very low, then ech firm hs full incentive to exert efforts to investigte production cost, whether or not it shlls its privte informtion with its rivl; when R&D becomes costly, informtion cquisition hppens only if informtion Doyle nd Snyder 1999 find tht US cr mkers nnouncements of production plns re informtive, nd not mere chep tlk, since they ffect mrket outcomes. Genesove nd Mullin 1999 mde relted observtion on US sugr cne refiners prticipting in the Sugr Institute trde ssocition between 198 nd The pper finds no indiction tht the ssocition s members were mking untruthful reports: truth-telling is the outcome of the informtion reveltion gme. 3 The truth-telling problem of informtion shring bout privte cost in oligopoly/duopoly my be the next step of reserch. 4 We find tht firm s profit function is convex in the rivl s output level, so mking the ltter contingent on the own cost is ex nte vluble. 4

5 shring is possible. Moreover, in the full disclosure regime, the two firms my prefer to commit n R&D coopertion in the phse of informtion cquisition, nd then they cn compete non-coopertively on the product mrket. An interesting point is: the existence of n R&D legue greement is not necessrily n indiction of collusion between firms on the mrket competition. In the equilibrium under strtegic informtion disclosure regime, due to the equilibrium belief under unrveling effect, 5 more informtion bout unknown cost my be cquired nd disclosed before the mrket competition phse thn in the equilibrium under mndtory informtion disclosure regime, especilly when the informtion cquisition cost is quite high. Regrding the consumer surplus nd the socil welfre, we find: the informtion gthering benefits the consumer, but the shring between the firms erodes some benefits on consumer surplus. The intuition is: informtion cquisition benefits the firms profits under resonble R&D cost, nd thus increses the equilibrium production, which enhnces the consumer surplus; yet, informtion shring lets the firms coordinte their production bsed on the reveled cost informtion, which hurts the consumer surplus. While the informtion cquisition nd disclosure lwys benefit the totl socil surplus, nd the benefits increse with the product substitutbility. So, we find tht the socilly efficient R&D cost threshold is even higher thn the firms coopertive one. At lst, when the mrket demnd intercept is extremely high, some over-investment on informtion cquisition my hppen in the strtegic informtion disclosure regime. In short, when we consider quntity competition Cournot, llowing firms to shre informtion hs two effects on consumer surplus. On the one hnd, s previous literture pointed out, there is negtive direct effect. Given informtion structure, llowing informtion shring between firms hs negtive effect positive effect on the consumer surplus profits of the firms. However, on the other hnd, there is positive indirect effect of shring informtion. This is due to the fct tht the incentives of cquiring informtion re lrger when firms re llowed to shre informtion. The higher investments by firms tht shre informtion hve positive effect on the consumer surplus. When we consider price competition Bertrnd, firms hve no incentive to engge in greement to shre informtion full disclosure regime is dominted. Firstly, full shring greement will give less incentive to cquire informtion. Secondly, given informtion structure, firms prefer not shre their informtion. But under some cses when R&D cost is higher, strte- 5 Milgrom 1981, Milgrom nd Roberts

6 gic disclosure regime is prefered, becuse it gives the strongest incentive to cquire informtion. This pper is orgnized s follows. Section describes the model. Section 3 derives the equilibrium in different informtion shring regimes: full disclosure, full concelment, nd strtegic disclosure, respectively. Section 4 investigtes the impcts on the consumer nd welfre. Section 5 nlyzes price competition. Section 6 concludes. The model A mrket consists of two firms, ech producing differentited product. The mrket demnd is liner, nmely p i = x i γx j with i, j {1, } nd 0 γ 1. 1 Prmeter γ cptures the degree of product substitutbility. x ij is the production quntity of firm i j. If γ = 1, then goods re homogeneous, i.e., the mrket is pure Cournot duopoly; while if γ = 0, then firms supply to independent mrkets, i.e., ech firm is monopoly. Firms re risk-neutrl. The technology for production is stochstic but it exhibits constnt return to scle, c i = θ i x i where θ i f θ i on [ 0, θ ], i = 1,. The process of θ i is independent with tht of θ j. We ssume tht > θ γ, which will lter on ensure interior solutions, i.e., x i, x j > 0 for ny reliztion of the cost pir θ i, θ j nd ny informtion disclosure structure. 6 In the first stge, firms cn lern their unit costs by cquiring informtion. Firms choose n investment of informtion cquisition, r i [0, 1] for firm i, simultneously nd respectively. With probbility r i firm i observes its own cost θ i ; but with probbility 1 r i the firm lerns nothing nd continues holding the prior f over its own cost when mking its production decision. The success of i nd j s R&D informtion cquisition 7 investment is independent with ech other. A firm s informtion cquisition behvior is not observble by its rivl. Firm i only expects tht its rivl invests r j in 6 Condition comes from the fct tht the worst reliztion of θ i, θ j is profitble on behlf of firm i, i.e., θ i = θ nd i hs to disclose it to j, while θ j = 0 nd i knows it; by imposing θ i = θ, θ j = 0 into Lemm 4 nd Lemm 1, we cn get tht the profit π i in this cse is still strictly positive under. 7 Henceforth, we cll nd interpret informtion cquisition s R&D too, since the investment is bout new product line development. 6

7 informtion cquisition. We ssume tht if firm i decides to disclose, then θ i is hrd informtion to the public, i.e., it cnnot mnipulte θ i. The costs of informtion cquisition re liner: ηr i > 0 for i = 1,. After the informtion cquisition stge, n informed firm discloses or concels its privte cost ccording to different informtion shring regimes. We consider three informtion shring regimes respectively: full concelment, full disclosure, nd strtegic disclosure. These different regimes constitute three different scenrios/gmes since we ssume tht firms precommit to regime before they invest in R&D in the first stge. Full concelment mens tht, firms gree on not shring or cnnot shre e.g., technologiclly the informtion is not trnsmissible their cost informtion in the second stge, respectively, if they lerned in the first stge. Full disclosure mens tht, in the second stge firms gree on shring the cost informtion respectively or it cn be observed by the rivl utomticlly so long s the firm lerned it in the first stge. Strtegic disclosure llows the firm to voluntrily disclose or concel its cost informtion lerned in the first stge. So the full concelment nd full disclosure regimes serve s the two extreme benchmrks of the informtion disclosure problems. Under strtegic disclosure, firm i is sure tht firm j hs successfully lerned θ j only if j discloses it before they compete on the product mrket; otherwise firm i is not sure whether firm j filed to cquire θ j or successfully lerned it but did not disclose i.e., conceled it. If n informed firm i chooses shring, it cn only send the messge θ i since the informtion is verifible. However, if n informed firm chooses to concel its privte cost, then it sends the uninformtive messge [ 0, θ ], which is the sme s the messge sent by n uninformed firm. Firms mke their disclosure decisions simultneously. The first purpose of the pper is to investigte nd compre the different equilibrium R&D intensity in different informtion disclosure regimes, s Jnsen 008 did when the pir of duopoly fces uncertin common demnd. In the finl stge, firms simultneously choose their output levels x i, i.e. firms re differentited Cournot competitors. Firm i s expected profit cn be written s: 8 π i x i ; E fj x j, ϑ i = x i γe fj x j ϑ i x i. 3 8 From this profit expression, we cn lso interpret θ ij in n lterntive wy: is the common demnd intercept on the two mrkets, while θ ij cn be regrded s the individul mrket demnd shock specific to firm i j; in this cse, we ssume tht the product cost of both firms is zero, s Vives 1990, where the firms exogenous common nd privte demnd shocks re considered seprtely nd respectively, while ll the production cost is normlized t zero. This explntion brodens the ppliction of our model, since ll the subsequent nlysis nd conclusions concerning privte cost R&D re lso vlid to the individul mrket demnd shock investigtion. 7

8 where E fj x j is i s equilibrium expecttion over j s strtegy, nd the subscript f j represents i s equilibrium belief over j s type nd E fj is the expecttion opertor over the distribution f j ; we notice tht f j my be different from the prior f since it s the updted posterior fter the informtion cquisition r j nd disclosure decisions/regimes; ϑ i equls either θ i if firm i is informed, or E f θ if firm i is not informed, where E f is the expecttion opertor over f on [ 0, θ ]. Since both firms fce liner mrket demnd, it s strightforwrd to obtin tht π i = x i. The following lemm pplies nd comes from the firm s profit mximiztion. Lemm 1 π i E fj x j, ϑ i = x i E fj x j, ϑ i, i = 1,, where x i E fj x j, ϑ i nd π i E fj x j, ϑ i denote the output level nd expected profits of firm i in the mrket competition phse under the informtion structure ϑ i nd equilibrium belief E fj x j, respectively. Proof. The first order condition of mximizing 3 with respect to x i gives the optiml output of firm i under E fj x j, ϑ i : x i E fj x j, ϑ i = γe f j x j ϑ i. 4 Insert 4 bck into 3, we cn get the conclusion. 3 The Equilibrium under Different Regimes Before nlyzing the three regimes, full concelment, full disclosure, nd strtegic disclosure, respectively, we chrcterize the mrket competition e- quilibrium under r i = r j = 0, i.e., neither R&D effort in the first stge, so no one hs the cost informtion during production phse no informtion to shre or concel, nd the pyoffs re only expected on the prior f over [ 0, θ ]. Lemm In the continution gme in which no firm exerted R&D investment, i.e., no one hs the cost informtion during mrket production, the equilibrium output level is: Proof. In the ppendix. x i = x j = E fθ + γ. 5 8

9 Then, by Lemm 1, we know tht the expected profit, i.e., the pyoff under no R&D is Eπ ri =r j =0 = πf, f = E fθ + γ, 6 where f, f denotes the continution gme in which r i = r j = 0, i.e., firms hold their prior beliefs bout production costs. 3.1 Full Concelment Regime First, we consider the regime in which firms cnnot or do not shre informtion in the second stge. This regime serves s one extreme benchmrk of the informtion cquisition nd disclosure problem. Firms precommit or know nd obey full concelment before they mke their R&D investment decisions. The considertion of this benchmrk will help the decomposition of the vlue of informtion the decomposition will be complete in the next two subsections. So, in this subsection, we sk the question: wht is the net vlue of R&D under precommitted no informtion shring? Before nswering, we look t the following lemm. Lemm 3 For ny informtion-disclosure choice of firm i, so long s firm j does not disclose, then firm i is indifferent whether firm j knows it own type θ j. Since other informtion-disclosure choices pper in the subsequent subsections, we put the proof of this lemm in the ppendix. The key property behind Lemm 3 is the linerity of the best response with respect to the rivl s type, which is result of constnt return to scle setting. So fter Lemm 3, the ex nte profit of firm i exerting r i is: r i E f π c θ i, f + 1 r i πf, f ηr i, 7 where E f represents the expecttion over the prior f on θ i since the decision of r i is before the stge of mrket profits reliztion, nd the superscript c stnds for concelment. By 7 nd Lemm 3, we see tht the ex nte pyoff is independent of r j, which tells us tht the R&D extent is unilterl decision rther thn n interctive gme, under precommitted full concelment regime. From the linerity of r i in 7, we cn infer tht the R&D decision depends on the reltive mgnitude between the vlue of knowing own type θ i nd the full R&D cost η, nd there is no equilibrium where 0 < r i < 1 except in knife-edge cse. The following proposition confirms this nd depicts E f π c θ i, f. 9

10 Proposition 1 E f π c θ i, f = E f θ +γ σ θ. The informtion cquisition equilibrium under full concelment regime is: r i = r j = 1 Resp. 0 if η < Resp. > 1 4 σ θ, where σ θ is the vrince of f over [ 0, θ ]. If η = 1 4 σ θ knife-edge cse, then ny r i, r j [0, 1] cn be the equilibrium. Proof. In the ppendix. By Proposition 1 nd 67, if the informtion is conceled in stge, then the net gin of informtion cquisition, i.e., the vlue of lerning own type, is 1 4 σ θ, which is independent of the mrket structure γ, nd of the R&D strtegy of the rivl. The vlue of informtion in this subsection under informtion concelment comes from the intuition: the liner demnd, constnt return to scle, nd Lemm 1 give convex profit function over the firm s own cost, so, when there is lot of vrince in θ i, then, ex nte, it s vluble for the firm to hve the informtion on θ i t the production stge. 3. Full Disclosure Regime Now we consider the regime in which firms hve to disclose its cost type informtion if successfully lerned to the rivl fter the R&D stge. Full disclosure serves s nother extreme benchmrk compred to full concelment of the informtion disclosure problem. We sk: hs firm more or less incentive to invest in cost informtion cquisition if precommitting to disclosure, compred to concelment regime? And in this subsection we will complete the decomposition of the vlue of informtion bout the costs θ i, θ j. First, we look t the following lemm of equilibrium mrket outputs of pir of informed θ i, θ j under full shring, which is the stndrd Cournot competition result. Lemm 4 If firms know their own nd rivls per-unit production costs θ i, θ j, respectively, during the mrket competition phse, then, the equilibrium outputs re: x d i θ i, θ j = where the superscript d stnds for disclosure. + γ θ i γθ j 4 γ, i, j = 1,, 8 Proof of Lemm 4. In the ppendix. If firm i expects the rivl s R&D effort r nd exerts r i, there re ltogether four kinds of continutions during mrket competition: both R&Ds succeed, 10

11 with probbility r i r; i cquires nd discloses θ i but j fils, with probbility r i 1 r; j succeeds but i fils, with probbility r 1 r i ; both fil, with probbility 1 r i 1 r. So the pyoff ex nte profit of r i bsed on the belief r is: r i ref,f π d θ i, θ j + 1 r E f π d θ i, f +1 r i re f πf, θ j + 1 r πf, f ηr i, 9 where the superscript d stnds for disclose since s long s firm knows its own type, the rivl knows it too by mndtory shring under this regime; the subscript f, f before π d θ i, θ j represents the joint expecttion over θ i nd θ j ; while the subscript f before π d θ i, f Resp. πf, θ j represents the expecttion over θ i Resp. θ j. By 9, unlike the full concelment regime, now the R&D decisions become n interctive gme since the rivl s strtegy r enters the pyoff function of i; but the following proposition will tell us tht r i nd r re seprted in 9, which implies tht there will be still no equilibrium with 0 < r i < 1 except for knife-edge cses. From Lemm 1, we know tht π d θ i, θ j = x d i θ i, θ j, where the quntity is given by Lemm 4. And Proposition chrcterizes π d θ i, f, πf, θ j nd the equilibrium under full disclosure regime. Proposition If the firms commit to shre informtion in the second stge, then: i E f,f π d θ i, θ j = E f θ +γ + 4+γ σθ. 4 γ ii E f π d θ i, f = E f θ +γ + 4σ θ. 4 γ iii E f πf, θ j = E f θ +γ + γ σθ. 4 γ iv the informtion cquisition equilibrium is: when η < Resp. > 4σθ, r 4 γ i = r j = 1 Resp Proof of Proposition. In the ppendix. We see tht the cost threshold of full informtion cquisition under full disclosure regime η < 4σ θ is less stringent thn tht under full concelment regime η < σ θ 4 γ 4, so precommitted disclosure rule cn led to more informtion cquisition. By referring to prt i of Proposition nd Proposition 1, we cn decompose the net gin of both full R&Ds r i = r j = 1 on i s ex nte profit γ into three prts: 1 the vlue of knowing the rivl s type, σθ ; the 4 γ vlue of lerning own type, σ θ 4 from Proposition 1; 3 the vlue of shring 9 If η = 4σ θ 4 γ knife-edge cse, then ny r i, r j [0, 1] cn be the equilibrium. 11

12 own type to the rivl, 4 4 γ 1 4 σ θ. All these three kinds of vlue of informtion come from: the profit function of firm i is convex function of both its own cost θ i nd its rivl firm j s cost θ j. So knowing its own cost nd the rivl s cost is vluble. Besides, from n ex nte point of view, firms prefer to disclose informtion to its rivl even if the ltter discloses nothing becuse i s profit function is lso convex in the rivl s output, x j, mking x j contingent on own θ i is ex nte vluble too. Moreover, the vlue of knowing the rivl s type prt 1 nd the vlue of shring own type prt 3 depends on nd increses with the mrket linkge γ. But plyer is only willing to py the sum of prt nd prt 3, i.e., 4σ θ 4 γ, since prt 1 of vlue comes from the decision of the rivl, which is free lunch. This implies tht, when 4σ θ 4 γ < η < 4+γ σ θ 4 γ the sum of three prts gin, there would be n efficiency loss due to the noncoopertive R&Ds, i.e., prisoners dilemm. The following corollry pplies. Corollry 1 Under full disclosure regime, the pyoffs in the first stge R&D 4σ θ 4 γ gme cn be bstrcted s Tble 1. When < η < 4+γ σθ, the R&D 4 γ interction is prisoners dilemm gme, i.e., the non-coopertive equilibrium is r i = r j = 0, but the coopertive optimum is r i = r j = 1 if the plyers cn collude in R&D. Tble 1: The First Stge R&D Gme under Full Disclosure Regime I r = 1 N r = 0 I r = 1 N r = 0 [ E f θ +γ + 4+γ σ θ 4 γ η, [ E f θ +γ + 4σ θ 4 γ η, E f θ +γ + 4+γ σ θ 4 γ η] E f θ +γ + γ σ θ [ E f θ +γ + γ σθ, 4 γ E f θ +γ + 4σ θ η] 4 γ [ E f θ +γ, E f θ +γ ] 4 γ ] Proof of Corollry 1. If defining the ction I investment by r = 1, nd the ction N no investment by r = 0, respectively, then the first stge gme cn be depicted by mtrix N, N, N, I, I, N, I, I s in Tble 1, where the pyoffs cn be obtined by inserting the corresponding combintions r i = r = 0, r i = 0, r = 1, r i = 1, r = 0, r i = r = 1 into 9. Regrding Tble 1 s sttic norml form, then clerly when 4σ θ 4 γ < 1

13 η < 4+γ σθ, it s prisoners dilemm gme, i.e., I is the dominted strtegy 4 γ so N, N is the equilibrium, but I, I is the mutully beneficil profile. The intuition is: the rivl s R&D genertes positive externlity on i s profit prt 1: σθ, but this mount will not support the non-coopertive γ 4 γ R&D since it s up to the decision of j nd the two firms ctions, r i, r j re seprted. So from point of view of joint profits, it s vluble to exert both 4σ θ R&Ds when η exceeds, but lower thn 4+γ σθ, i.e., to support joint 4 γ 4 γ R&Ds by the ex post externlities. Overll, the totl net gin of informtion cquisition nd shring is 4+γ σ θ 4 γ, which is incresing in γ; when γ = 0, i.e., two independent mrkets, we see tht the mount 4+γ σ θ 4 γ degenertes to 1 4 σ θ nd coincides with the net vlue of informtion in the full concelment regime, tht is to sy, when the two goods re more substitutble, firms hve incentive to do R&D nd to pre-commit to shre the result. Figure 1 illustrtes the decomposition of the totl vlue of informtion cquisition nd shring globlly when γ evolves from 0 to 1. The verticl distnce between the horizontl solid line nd the horizontl xis represents the vlue of knowing own type ; the verticl distnce between the long dshed curve nd the horizontl solid line is the vlue of shring own type to the rivl ; while the verticl distnce between the dot-dshed curve nd the long dshed curve represents the vlue of knowing the rivl s type. Figure 1 is bout here On the other hnd, Figure 1 expresses different mximum thresholds of R&D cost tht firm is willing to fford under different regimes/situtions. The horizontl solid line, 1 4 σ θ, is the threshold under full concelment. The 4σθ long dshed curve,, represents the threshold under full disclosure. 4 γ When η is lrger thn this threshold, but not too high less thn 4+γ σθ, 4 γ the prisoners dilemm rises: though the unique equilibrium in the noncoopertive R&D gme is r i = r j = 0; while r i = r j = 1 is the Preto dominnt lloction becuse of the vlue of knowing the rivl s type, which γ benefits from the rivl s R&D under full disclosure, σθ. If there exists n 4 γ exterior commitment device to cooperte in the R&D phse, e.g., to sign the promise of R&D investment on top of the disclosure greement, nd if its fulfillment is protected nd monitored by lw, then the coopertive optimum r i = r j = 1 cn be relized. This conveys n interesting nd importnt indiction on rel mrkets: the duopoly fcing individul uncertinties my 13

14 incline to cooperte on R&D, which my be mutully beneficil to their future products competition. 3.3 Strtegic Disclosure Now we relx the previous two extremes disclosure regimes in the second stge nd llow n informed firm to strtegiclly decide whether to disclose or concel its cost informtion to the rivl contingent on the cost type it lerned. We cll this strtegic disclosure regime without precommitted disclosure rule. Given n informed type θ i, is it willing to disclose? Wht does the disclosure incentive depend on? We hve the following importnt lemm which is useful to derive the R&D equilibrium under strtegic disclosure. Lemm 5 If i knows its cost θ i, s in 3 nd Lemm 1, denote f i s the prior/posterior/equilibrium belief tht j holds for θ i, then no mtter the informtion-disclosure choice of j, θ i is willing to disclose if nd only if θ i < E fi θ i, which is j s expecttion on θ i under f i, where i, j = 1,. Proof. In the ppendix. We notice tht f i f j my differ from the symmetric prior s the very beginning, f, since it my be the posterior/equilibrium belief tht j i holds. Before chrcterizing the R&D equilibrium, we investigte the continution fter symmetric informtion cquisition r, r. 10 Then the following proposition pplies. Proposition 3 Given the symmetric ctions in the first stge r, r: if r > 0, then there exists unique θ r E f θ, θ ] such tht n informed θ i discloses if nd only if θ i < θ r, where θ r > 0 nd θ 1 = θ, lim r = r 0 θ E f θ. Proof. In the ppendix. First, if r i = r j = 1, then the unrveling effect leds to full shring even if the disclosure is voluntry, i.e., the unique continution equilibrium is full disclosure, nd the belief supporting full disclosure is tht ny unobservble/conceled rivl s cost is regrded s the type θ, e.g. see Milgrom 1981, Milgrom nd Roberts 1986, nd Okuno-Fujiwr et l So in this cse, the lower bound of concelment is θ, i.e., θ 1 = θ. 10 This pper concentrtes nd restricts to the symmetric equilibri. Recll tht we set the R&D extent, r i, r j, is not observble by the rivl, which simplifies the nlysis nd rules out those rbitrry nd non-symmetric continutions with 0 r i, r j 1. 14

15 Second, if the continution comes from 0 < r i = r j < 1, then we know tht the existence of uncertinty bout one s own type probbility 1 r my destroy the unrveling effect, i.e., firms cn credibly concel unfvorble news by hiding to be uninformed, see e.g. Frrell Hence, there exists threshold θ E f θ, θ such tht ll the informed types smller Resp. lrger thn θ will disclose Resp. concel. θ stisfies ech type s disclosure/concelment incentive in Lemm 5, i.e., E fθ = θ, where f is the posterior distribution over [ 0, θ ] of n unobservble type: the informed but conceled θ i lrger thn threshold θ with probbility r, plus the uninformed with probbility 1 r, s illustrted by Figure. By Byes rule, fcing n unknown type of the rivl, the updted equilibrium belief contins informed but conceled types with probbility r1 F θ nd uninformed types with probbility 1 r 1 rf θ. 1 rf θ Figure is bout here When r i = r j = 0, θ r hs no definition t r = 0, but by the continuity of θ, we cn write lim = Ef θ see the proof of the proposition in the r 0 θ ppendix, i.e., plyers do not updte the prior belief f when fcing n unknown type of the rivl fter r i = r j = 0. The uniqueness of θ with respect to r nd θ r > 0 tells us tht the more R&D exerted in the first stge, the more informtion will be disclosed before the mrket competition. After chrcterizing the complete continution equilibrium in the disclosure stge by Proposition 3, we know tht there re ltogether six possibilities during mrket competition phse if exerting r i nd expecting rivl s r: 1 i is informed, discloses, nd cn observe θ j ; i is informed, discloses, but cnnot observe θ j ; 3 i is informed, concels, nd cn observe θ j ; 4 i is informed, concels, nd cnnot observe θ j ; 5 i is not informed nd cn observe θ j ; 6 i is not informed nd cnnot observe θ j. The corresponding probbility nd i s pyoff expected profits of ech cse re in Tble. The clcultion of π 1 i to π 6 i in Tble is in the ppendix; E f,f before π i in the tble is the joint expecttion over θ i nd θ j on their corresponding supports in different cses, respectively. Therefore, i s ex nte expected pyoff 15

16 Tble : Six Informtion Structures of Firm i during Mrket Competition under Strtegic Disclosure Regime Cse Probbility π i 1 r i r F θ E fθi θi< θ,fθj θj< θ θ i γθ j +γ 4 γ θ θ r i F 1 rf E fθi θ i < θ θ i γ θ +γ 4 γ θ θ 3 r i rf 1 F E fθ i θ i > θ,fθ j θ j < θ θ i γθ j + γ θ i θ +γ 4 γ 4 γ θ θ + γ 4 r i 1 F 1 rf E θ fθi θ i > θ θ i +γ θ 5 1 r i rf E fθ j θ j < θ E f θ γθ j γ θ E f θ +γ 4 γ 4 γ θ 6 1 r i 1 rf E f θ γ θ +γ 4 γ of exerting r i with expecting the rivl s r is: θ [ θ θ ] r i {F rf π 1 i + 1 rf π i θ [ θ θ ] + 1 F rf π 3 i + 1 rf π 4 i } θ θ + 1 r i {rf π 5 i + 1 rf π 6 i } 10 ηr i The following proposition depicts the equilibrium in the R&D stge under strtegic disclosure regime. Proposition 4 If we restrict to the symmetric equilibri r i = r j = r, then: i When η < 4σ θ +η 4 γ 1 4σ θ + γ θ E f θ E f θ γ θ E f θ, r = 1 4 γ 4 γ +γ 44 γ is n R&D equilibrium, nd both firms will fully disclose the informtion they lerned since θ 1 = θ. ii When η > 4σ θ +η 4 γ 0 4σ θ +1 F E 4 γ f θ E fθ i θ i >E f θ π c θ i, f π d θ i, f, where F is the c.d.f. of f, π c θ i, f is the profit of n informed but conceled θ i fcing n uninformed j, π d θ i, f is the profit of n informed nd disclosed θ i fcing n uninformed j, then, r = 0 is n R&D equilibrium, i.e., no informtion cquired or disclosed, nd both firms get the profit E f θ +γ. 16

17 4σθ iii If η 0 > η 1, then, when + η 4 γ 1 < η < 4σ θ + η 4 γ 0, there exists n r 0, 1 being the R&D equilibrium, 11 nd the informtion disclosure rule will follow Proposition 3 nd θ 4σθ r; if η 0 < η 1, then, when + η 4 γ 0 < η < r 0, 1. 4σ θ 4 γ + η 1, there exists t lest three equilibri, r = 0, r = 1, nd n Proof. In the ppendix. From the proof of Proposition 4, η 1 > 0, so the upper bound of full R&D r = 1 in the voluntry disclosure regime is higher thn tht of mndtory disclosure, nd the firms will shre ll the informtion they lerned to the rivl too. Hence, there is no necessity to regulte the firms to shre informtion forcibly since the mrket result relizes it utomticlly even when the informtion cquisition cost is higher thn the threshold of the full disclosure 4σθ regime. 4 γ The reson tht the firms exert more R&D effort under strtegic disclosure regime thn tht of full disclosure regime prt i of Proposition 4 is: deviting from r i = 1 to r i < 1 will not chnge firm j s equilibrium belief firm j thinks r i = 1 nd θ i = θ, which mens tht, if firm i lerns θ i, it will disclose it truthfully; if firm i knows nothing, it will be perceived s θ i = θ. This concern drives the R&D more ggressive, compred to the full disclosure regime. Prt ii of Proposition 4 sttes tht the threshold of no R&D r = 0 under strtegic disclosure regime is lso higher thn tht of full disclosure regime. The explntion is: deviting from r i = r j = 0 for firm i, i.e. setting r i > 0 will be profitble becuse there exists strtegic vlue of cost informtion. The strtegic vlue comes from the fct tht firm i cn both hide unfvorble informtion effectively nd disclose fvorble one by setting r i > 0. So t η = 4σ θ where the R&D cost is equl to the vlue of 4 γ informtion under full disclosure regime, incorporting this strtegic vlue η 0 will definitely mke R&D more profitble. In the cse of η 0 > η 1, if the full R&D r = 1 is not supportble η > 4σθ + η 4 γ 1, then prtil R&D r < 1 equilibrium my rise till η > 4σ θ 4 γ + η 0. When η 0 < η 1, both r = 1 nd r = 0 re equilibri if 4σ θ 4 γ + η 0 < η < 4σ θ + η 4 γ 1, then the coordintion problem between the firms my rise. η 1 my be lrger or smller thn η 0, which depends on the distribution 11 There my exist multiple equilibri for r 0, 1. We hve not proved or disproved the uniqueness. 17

18 of θ, i.e., the prior f. 1 So in the sense of informtion cquisition nd disclosure extent, the s- trtegic disclosure regime domintes mndtory disclosure or concelment, given tht the firms ply non-coopertive R&D gme. But from Corollry 1, under the full disclosure regime, when 4σ θ 4 γ < η < 4+γ σθ, if the firms 4 γ cn collude or the stte or industry union hs n exterior power to commit mutully the full R&D behvior of ech firm, then the efficient coopertive informtion cquisition cn be relized. In this cse, which regime, full disclosure or strtegic disclosure, will explore nd disclose more informtion? It depends on the reltive mgnitude of their upper bound thresholds of full R&D r = 1, i.e., γ σ θ 4 γ versus η 1. 4 Welfre Anlysis In this section, we first develop the consumer surplus, nd investigte the vlue nd impct of informtion cquisition of the firms on the industry profits, the consumer surplus, nd the socil totl welfre, which is the joint firm-consumer surplus. We lso exmine the impct of informtion shring between the firms on the consumer nd the society. 13 Second, we nlyze the upper bound of full R&D r = 1 threshold under the strtegic disclosure regime, to see whether this regime promotes n efficient R&D towrd socil optimum when the industry commitment device on R&D is bsent, or it involves n over-investment on R&D when the cost is socilly inefficient η extremely high. We ssume tht the liner demnd system 1 is obtined from the optimizing behvior of representtive consumer which mximizes U x i, x j p i x i p j x j, where U x i, x j = x i + x j γx i x j 1 x i + x j. 11 In 11, γ represents the substitutbility discount on the totl consumption mount of i nd j. Consumer surplus CS in terms of quntities is CS x i, x j = 1 x i + x j + γxi x j, 1 1 The intuition for which one η 0 or η 1 is lrger is not very cler for the moment. 13 Since the firms will fully disclose the informtion lerned in full R&D r = 1 equilibrium under either strtegic or mndtory disclosure regime, we cn only focus on full shring. 18

19 which is lso equl to U x i, x j p i x i p j x j nd cn be regrded nd clculted s the verge sum of two consumer surplus in the two mrkets. 14 If there is no R&D investment r i = r j = 0, then, using Lemm 1 nd, one cn derive the socil surplus when r = 0: EW r=0 = CS r=0 + Eπ r=0 13 = 3 + γ x f, f = 3 + γ E fθ + γ. If the firms lerned the cost informtion, the socil totl surplus cn be denoted s: EW r=1 = EU x i, x j E θ i x i E θ j x j η = ECS r=1 + Eπ r=1 η. 14 Then we clculte the impcts on expected CS nd W of informtion cquisition, with respect to disclosure nd concelment. Proposition 5 The vlue of informtion to the consumer nd socil surplus is: i If the informtion is conceled in the second stge, ECS r=1 CS r=0 = 1 4 σ θ; EW r=1 EW r=0 = 3 4 σ θ η. ii If the informtion is disclosed in the second stge, which is decresing in γ; which is incresing in γ. ECS r=1 CS r=0 = 4 3γ 4 γ σ θ, EW r=1 EW r=0 = 1 γ 4 γ σ θ η, 15 Proof. In the ppendix. According to these results, when γ = 0, i.e., two independent mrkets, the vlue of informtion net gin of R&D investment in i nd ii coincides, 14 The surfce below the inverse demnd curve nd bove the price. 19

20 tht is to sy, there is no extr vlue or hurt of informtion shring to the firm, consumer nd socil surplus, respectively, if the two goods re not relted. When γ > 0, shring informtion benefits the firms mutully, while the consumer is hurt. And this hurt is incresing in γ, i.e., the vlue of informtion to the expected consumer surplus declines more under disclosure when γ increses from 0 to 1. Though the consumer dislikes the disclosure of informtion, the vlue of informtion itself to the consumer surplus is n- evertheless lwys positive, i.e., to cquire informtion is lwys beneficil to the consumer. The intuition why the consumer prefers firms to cquire informtion but prefers them not to disclose it is: informtion cquisition will increse the equilibrium production therefore will enhnce the consumer surplus. Yet informtion shring between firms hs detrimentl effect to consumer surplus becuse firms could coordinte their production bsed on the reveled production costs. If they disclose their production costs, their production will be negtively correlted. Forbidding disclosure will brek up this negtive correltion nd increse the totl production, hence increse consumer surplus. Besides, the more substitutble re the products, the more effective re their coordintion on the production. Hence, under full disclosure regime or the full R&D equilibrium under strtegic disclosure regime, the informtion vlue on consumer surplus is decresing with γ. The benefits of informtion shring to the firms profits surpss the loss on the consumer surplus, so on behlf of socil welfre, informtion disclosure is lwys vluble nd the net socil gin increses with the substitutbility of the two mrkets. Figure 3 illustrtes ll these effects on the firm s profit, the consumer s surplus nd the socil welfre, respectively, when γ evolves from 0 to 1. Figure 3 is bout here On behlf of socil surplus, socilly efficient R&D cost threshold is lrger thn the firms coopertive gme result compring Proposition 5 with Corollry The short dotted curve in Figure 1 represents the socilly efficient R&D cost upper bound nd the following corollry specifies its vlue. Figure 1 lso tells us tht ll kinds of R&D full threshold is non-decresing in γ, i.e., when the mrkets re more relted with ech other, the informtion R&D becomes more vluble to the firms nd the society. 15 Even the coopertion between the firms cnnot fford R&D η > 4+γ σ θ, from 4 γ Proposition nd Corollry 1, the consumer funding for R&D to cquire production costs for the firms is socilly efficient. 0

21 Corollry R&D is socilly efficient Resp. inefficient if η < Resp. > 1 γ 4 γ σ θ. Proof. Esily obtined from 15. The interesting point is: when 4+γ σθ < η < 1 γ σ 4 γ 4 γ θ, powerful industry union which cn commit the informtion shring nd coopertive R&D will not do the R&D since the joint net gin on profits cnnot fford the costs, but it s still vluble to extrct tx or pyment from the consumer to support the firms R&Ds on behlf of the socil surplus; to relize this socil efficiency when η is very high, we need mechnism to collect funds from the consumer through tx, for instnce. But when η > 1 γ σ 4 γ θ, ny R&D even prtil R&D is not worth doing. We remember tht if the stte or the industry union lets the mrket be do not regulte the pre-commitment of disclosure, i.e., the two firms ply voluntry strtegic disclosure nd cquisition gme, then the full R&Ds cn be even more esily obtined. But whether the strtegic R&D threshold is welfre enhncing, we should compre it with the socilly efficient upper bound 1 γ σ 4 γ θ. Corollry 3 The upper bound of full R&D threshold under strtegic disclosure regime is lrger thn tht of the socil efficient threshold if nd only if > E f θ + γ θ E f θ + + γ σ θ 4 γ γ θ E f θ 16 nd γ > 0. Proof. In the ppendix. First, when γ = 0, η 1 = 0, the upper bound of R&D cost threshold under strtegic disclosure regime coincides with other two regimes, which is 1 4 σ θ. It is definitely lower thn the socil efficient upper bound 3 8 σ θ when the two mrkets re independent. But when γ > 0, if 16 holds, then the strtegic disclosure regime my involve some inefficient on behlf of socil surplus R&D when its cost η is 1 γ extremely high, i.e., σ 4 γ θ < η < 4σ θ + η 4 γ 1. We lso notice tht this stisfction of 16 my hppen especilly when the mrket demnd potentil the demnd intercept is extremely lrge; in this cse, the incentive for strtegic R&D cn be very strong nd cn endure very high η. The intuition is: the prty who devites from r = 1 is frid of being treted s the highest cost type; when the mrket s potentil demnd is quite lrge, the firms my over-invest in R&D for their mrket competition. 1

22 5 Concluding Remrks In this pper, we tke one step further to study the incentive to gther informtion nd thus endogenize the informtion structure on the privte cost informtion trnsmission in differentited duopoly model. We restrict out ttention to three informtion shring regimes: full concelment, full disclosure, nd strtegic disclosure. The min findings re s follows. The rnking of the three regimes with respect to the incentive to cquire informtion is: strtegic disclosure full disclosure full concelment. If firms re subject to precommit the informtion shring regimes before cquiring informtion, i.e., full disclosure or full concelment, then they prefer the full disclosure regime under which more informtion is cquired; moreover, on top of this, they prefer the coopertion in the informtion gthering phse even if they hve to compete nd cnnot collude on the production mrket. In other words, precommitting to prticulr disclosure regime nd even cooperting on informtion gthering re not indictors of collusion on production mrkets. If firms cn not precommit to prticulr regimes, then fter informtion gthering, firms will choose to disclose informtion strtegiclly, i.e. disclose fvorble informtion lower cost while concel unfvorble informtion higher cost. Firms will tke this strtegic effect into ccount when they try to infer their competitor s cost using Byes rule. When there exists prtil informtion cquisition, we prove tht given the probbility of informtion gthering, there exists unique cutoff vlue of cost under Resp. bove which cost informtion is disclosed Resp. conceled. We lso show tht the incentive to cquire informtion under strtegic regime is the strongest mong the three. Two forces come into effect: the fer of being treted s the highest cost type when deviting from r i = r j = 1; nd the strtegic vlue of deviting from r i = r j = 0. Both effects enhnce the incentive to gther more informtion compring to the full disclosure cse. Regrding the welfre, consumers benefit from informtion gthering, yet prefer the firms to concel their informtion fter gthering it. Becuse under complete informtion, the production of the two firms will be negtively correlted, so forbidding informtion disclosure will brek up this correltion nd enhnce the totl production. The society s whole prefers to disclose the informtion tht the firms cquired. On behlf of the consumer surplus, full concelment regime is preferred if the cost of cquiring informtion is low; if is high, the consumers will prefer strtegic disclosure regime. On behlf of the firms nd the socil welfre, full concelment regime is dominted. If the stte, the society, or the firms themselves hve commitment device to mutully cooperte on the R&D ctivity, then the full

23 disclosure regime my be preferred. But, if firms cn not cooperte on R&D, nd the informtion cquisition cost is sufficiently high, the strtegic disclosure regime my be preferred. At lst, strtegic disclosure regime my involve n over-incentive to gther informtion with respect to the socilly efficient level, when the mrket s demnd potentil is quite lrge. We model the mrket competition phse s Cournot gme. As robustness test, we provide the price Bertrnd competition structure nd ll its prllel results in the ppendix. Specil points of Bertrnd competition re: full disclosure regime is dominted from perspective of both firms nd consumers; yet when R&D cost is high enough, strtegic disclosure regime is preferred compring to full concelment regime, becuse the former give strongest incentive to cquire informtion. 3

24 6 Appendix. Proof of Lemm. From 3, the expected profit of firm i is Eπ i x i, x j = x i γx j E f θx i. 17 First order condition gives the rection function: x i x j = E fθ γx j. Similrly, x j x i = E f θ γx i. The equilibrium is determined by the intersection of the two rection functions: x i = x j = E fθ + γ. 18 Proof of Lemm 3. There re three informtion-disclosure choices of firm i: i i is informed nd discloses θ i ; ii i is informed but concels θ i ; iii firm i is not informed nd bsed on the prior f i. With respect to ech informtion-disclosure choice of firm i, given tht firm j does not disclose, i.e., i cnnot observe θ j, there re two possibilities of firm j: j is not informed nd bsed on the prior f j ; b j is informed but concels θ j. So it suffices to prove tht on behlf of firm i s profit, the combintion of i nd is equivlent to the combintion of i nd b, the combintion of ii nd is equivlent to the combintion of ii nd b, nd, the combintion of iii nd is equivlent to the combintion of iii nd b, respectively. i-: The first order conditions of firm i nd j mximizing their profits in the mrket competition phse in this informtion structure re: x i = γx j θ i ; x j = γx i E fj θ j. The equilibrium quntity of x d i θ i, f j, where the superscript d stnds for disclosure nd the second rgument f j mens tht j is not informed, is determined by the intersection of two response functions, i.e., i-b: x d i θ i, f j = + γ θ i γe fj θ j 4 γ. 19 4

25 The first order condition of firm i is x i = γe f j x j θ j θ i. Since firm j knows its own type, its best response is x j θ j = γx i θ j. So E fj x j θ j = γx i E fj θ j, which cn be put into the response of x i to determine x d i θi, E fj x j : x d i θi, E fj x j = + γ θ i γe fj θ j 4 γ = x d i θ i, f j. 0 So the equilibrium quntities in i- nd i-b coincide. By Lemm 1, we know tht π d i θ i, f j = x d i θ i, f j = x d i θi, E fj x j = π d i θi, E fj x j. ii-: Compred to i-, the first order condition for i does not chnge but tht for j chnges since now θ i is conceled: x i = γx j θ i ; x j = γe f i x i θ i E fj θ j. 1 Tking expecttion on both sides of x i, we hve E fi x i θ i = γx j E fi θ i. Tking this into ccount, x φ j f j, E fi x i = + γ E f j θ j γe fi θ i 4 γ = E fθ + γ, where the superscript φ stnds for not informed. Substituting this into the best response of i in 1, we get x c i θ i, f j = + γ E fθ + γ θ i, 3 where the superscript c stnds for concelment. ii-b: Compred to ii-, both first order conditions for i nd for j chnge since on behlf of j, the informtion on θ j becomes precise, but on behlf of i, x j becomes uncertin, so the best responses become: x i = γe f j x j θ j θ i Tking expecttion on both sides of both, we hve E fi x i θ i = γe f j x j θ j E fi θ i ; x j = γe f i x i θ i θ j. 4 ; E fj x j θ j = γe f i x i θ i E fj θ j. 5 5

26 The intersection in 5 determines E fj x j θ j = By 4, we cn get x c i + γ E f j θ j γe fi θ i 4 γ = E fθ + γ. θi, E fj x j = + γ E fθ + γ θ i. 6 which is exctly the sme s 3, the quntity in ii-. So by Lemm 1, πi c θ i, f j = x c i θ i, f j = x c i θi, E fj x j = π c i θi, E fj x j. iii-: By Lemm, when neither i nor j is informed, x φ i f i, f j = x φ j f j, f i = E fθ + γ. iii-b: This is the symmetric cse s with ii-, so we just chnge i, j in : x φ i fi, E fj x j = + γ E f i θ i γe fj θ j 4 γ = E fθ + γ. 7 By Lemm 1 gin, π φ i f i, f j = x φ i f i, f j = x φ i fi, E fj x j = π φ i fi, E fj x j. Proof of Proposition 1. By Lemm 1, π c θ i, f = x c i θ i, f, which hs been depicted by 3 in the proof of Lemm 3: x c i θ i, f = + γ E fθ + γ So before observing θ i, the profit of i is + γ E f π c θ i, f = E E fθ f θ i + γ θ i. 8 = 1 E f θ 4 E fθ + + γ = E fθ + γ σ θ = πf, f σ θ. 6 γ + γ 4 E f θ