The Effects of Information on Strategic Investment and Welfare

Transcription

1 The Effects of Informaton on Strategc Investment and Welfare Jacco J.J. Thjssen Kuno J.M. Husman Peter M. Kort October 2003 Abstract A model s consdered where two frms compete n nvestng n a rsky project. At certan ponts n tme the frms obtan mperfect nformaton about the proftablty of the project. We mpose that nvestng frst can be benefcal because a Stackelberg advantage, and thus a hgher market share, s obtaned. On the other hand, nvestng as second mples that one can beneft from an nformaton spllover generated by the nvestment of the other frm. Consequently, n equlbrum there s ether a preempton stuaton or a war of attrton. In case no nvestment takes place durng the war of attrton, ths war of attrton can turn nto a preempton stuaton. One counterntutve result s that welfare can be negatvely affected by sgnals becomng more nformatve or by occurrng more frequently. Furthermore, smulatons ndcate that duopoly leads to hgher welfare than monopoly when sgnals are less nformatve, whereas the opposte holds f there s more or better nformaton. Keywords: Uncertanty, Strategc nvestment, Imperfect nformaton, Welfare. JEL codes: C61, D43, D81. Dolf Talman s acknowledged for many nsprng dscussons and metculous proof-readng. Jan Boone and Thomas Sparla are thanked for helpful comments. The usual dsclamer apples. Department of Economcs, Trnty College, Dubln, Ireland. Centre for Quanttatve Methods, Endhoven, The Netherlands. Correspondng author. Department of Econometrcs & Operatons Research and CentER, Tlburg Unversty. P.O. Box LE Tlburg, The Netherlands. E-mal: Kort@uvt.nl, and Department of Economcs, UFSIA, Unversty of Antwerp, Antwerp, Belgum. 1

2 1 Introducton Two man forces that nfluence a frm s nvestment decson are uncertanty about the proftablty of the nvestment project and the behavour of potental compettors, havng an opton to nvest n the same project. In ths paper the nfluence of uncertanty and competton on the strategc consderatons of a frm s nvestment decson and the resultng welfare effects are nvestgated. The framework we use here assumes mperfect nformaton that arrves stochastcally over tme. As to the project only two states are possble: ether the project s proftable or t yelds a loss. Frms have an dentcal belef n the project beng proftable. Ths belef s updated over tme due to nformaton that becomes avalable va sgnals that arrve accordng to a Posson process. The sgnal can ether be good or bad: n the frst case t ndcates that the project s proftable, whereas n the latter case nvestment yelds a loss. However, the sgnals may not provde perfect nformaton. Wth an exogenously gven fxed probablty the sgnal gves the correct nformaton. For smplcty, t s assumed that the sgnals can be observed wthout costs. They can be thought of for example as arsng from meda or publcly avalable marketng research. As an example of the duopoly model wth sgnals, consder two soccer scouts who are consderng to contract a player. In order to obtan nformaton on the player s qualty both scouts go to matches n whch the wanted player plays. If he performs well, ths can be seen as a sgnal ndcatng hgh revenues, but f he performs poorly, ths s a sgnal that the nvestment s not proftable. Ths nduces an opton value of watng for more sgnals to arrve and hence gettng a better approxmaton of the actual proftablty of the project. On the sde of the economc fundamentals underlyng the model t s assumed that there are both a frst mover and a second mover advantage. The frst mover effect results from a Stackelberg advantage obtaned by the frst nvestor. The second mover advantage arses, because after one of the frms has nvested, the true state of the project becomes known to both frms. The frm that has not nvested yet benefts form ths n that t can take ts nvestment decson under complete nformaton. In ths paper t s shown that, dependng on the pror belefs on the proftablty of the project and the magntudes of the frst and second mover advantages, ether a preempton game or a war of attrton arses. The latter occurs f the nformaton spllover exceeds the frst mover Stackelberg effect. In the reverse case a preempton game arses. Even both types of games may occur n the same scenaro: n a war of attrton there exsts a postve probablty that no frm undertakes the nvestment. Then t may happen f enough good sgnals arrve that at a certan pont n tme the frst mover outweghs the nformaton spllover, mplyng that a 2

3 preempton game arses. It s shown that at the preempton pont two thngs can happen n equlbrum. Frstly, one frm can nvest whle the other frm frst wats to get the nformaton spllover before t decdes whether to nvest or not. In ths case the resultng market structure s a Stackelberg one. Secondly, both frms can nvest smultaneously, thus resultng n e.g. a Cournot market. n that case both frms prefer a symmetrcal stuaton n the output market above acceptng the nformaton spllover together wth the Stackelberg dsadvantage that s obtaned upon nvestment by the compettor. In ths paper we show that the presence of nformaton streams and uncertanty concernng the proftablty of a new market leads to hybrd welfare results. We nvestgate the mpact of nformaton on expected ex ante welfare. For the monopoly case we fnd that welfare may n fact be decreasng n the quantty and qualty of the sgnals. Ths s manly due to the fact that when sgnals appear more frequently over tme, or provde more relable nformaton, the opton value of watng for more nformaton ncreases, whch leads to nvestment at a later date, lowerng consumer surplus. Ths result may extend to the duopoly case. One would expect that compettve pressure together wth better nformaton leads to earler nvestment and thus to hgher expected consumer surplus. There s, however, an opposte effect closely lnked to the market structure. In equlbrum there s a certan probablty that the actual outcome s a Stackelberg equlbrum. If ths s the case and the market turns out to be bad there s only one frm that looses the sunk nvestment costs (namely the leader), whle the follower wll not nvest at all. There s also a probablty that the market ends up n a Cournot equlbrum wth smultaneous nvestment at the preempton pont. If the market turns out to be bad n ths case there are two frms that loose the sunk nvestment costs. When more nformaton s avalable, the nformaton spllover s less valuable. Ths mples that a Cournot market wll arse wth a hgher probablty when the qualty of nformaton rses. In that case the resultng downward pressure on expected producer surplus (losng twce the sunk nvestment costs nstead of once) mght outwegh the ncrease n expected consumer surplus. Secondly, smulatons ndcate that for low levels of quantty and qualty of the sgnals a duopoly yelds sgnfcantly hgher levels of expected welfare. The ntuton behnd ths result s straghtforward. When the nformaton stream s poor n both quantty and qualty, the opton value of watng for a monopolst s low. Snce for competng frms ths value s already low due to competton, the standard deadweght loss argument apples here. We also fnd, however, that wth hgh levels of quantty and qualty of the sgnals, monopoly leads to sgnfcantly hgher welfare levels than a duopoly. Ths s because of two reasons. Frstly, duopoly stmulates 3

4 preempton whch s bad for welfare because a sgnfcant value of watng exsts n case the expected nformaton gan per unt of tme s large. Secondly, the possblty of smultaneous nvestment n a preemptve duopoly has a negatve effect on expected producer surplus, because there exsts a possblty that the project turns out to be bad. These effects are larger than the ncrease n expected consumer surplus. Most of the lterature on optmal nvestment deals wth the effects of ether uncertanty or competton. The real opton theory concerns tself wth nvestment decsons under uncertanty (cf. Dxt and Pndyck (1996)). In ths lterature nature chooses a state of the world at each pont n tme, nfluencng the proftablty of the nvestment project. The problem s then to fnd an optmal threshold level of an underlyng varable (e.g. prce or output value of the frm), above whch the nvestment should be undertaken. A recent contrbuton n ths area dealng wth technology adopton s Alvarez and Stenbacka (2001) who nclude the opportunty to update the technology wth future superor versons. In the strategc nteracton lterature a number of models have been developed, dealng wth dfferent stuatons such as patent races and technology adopton. In general, a dstncton can be made between two types of models. Frstly, there are preempton games n whch two frms try to preempt each other n nvestng (cf. Fudenberg and Trole (1991)). The equlbrum concept used n such games s developed n Fudenberg and Trole (1985). Another class s the war of attrton, whch s frst ntroduced by Maynard Smth (1974) n the bologcal lterature and later adopted for economc stuatons (cf. Trole (1988)). Orgnally, the war of attrton descrbes two anmals fghtng over a prey. In an economc context one can thnk of two frms consderng adoptng a new technology. Both know that for one frm t would be optmal to nvest, but nether wants to be the frst to nvest, snce watng for an even newer technology would be better. The equlbrum concept used n ths type of game s ntroduced n Hendrcks et al. (1988). The lterature combnng both aspects s small ndeed, see Grenader (2000) for a survey. A frst attempt to combne real opton theory wth tmng games was made n Smets (1991). Husman (2001) provdes some extensons to ths approach and apples ths framework to technology adopton problems. Recent contrbutons nclude, e.g., Boyer et al. (2001) and Weeds (2002). Ths paper extends the strategc real optons lterature n the drecton of mperfect nformaton. Jensen (1982) was the frst to ntroduce uncertanty and mperfect nformaton n a one-frm-model dealng wth technology adopton. The present paper uses an nformaton structure that s smlar and whch s dscussed extensvely n Thjssen et al. (2003) for the one frm case. In Mamer and McCardle (1987) the mpact on the tmng of nnovaton of costs, speed and qualty of nformaton 4

5 arrvng over tme s studed for a one-frm model as well as a duopoly. However, due to an elaborate nformaton structure, Mamer and McCardle (1987) dd not obtan explct results. Hoppe (2000) consders a duopoly framework n whch t s a pror uncertan whether an nvestment project s proftable or not. The probablty wth whch the project s proftable s exogenously gven, fxed and common knowledge. As soon as one frm nvests, the true proftablty of the project becomes known. Ths creates nformatonal spllovers that yeld a second mover advantage. The observaton that a game of technology adopton under uncertanty s ether a preempton game or a war of attrton dates back to Jensen (1992a). However, where Jensen (1992a) examnes a two-stage adopton game, the present paper provdes an extenson of these results to the case of an nfnte horzon contnuous tme framework. Moreover, as has been mentoned before, n our framework both types of games can occur wthn the same scenaro. The equlbrum concept that we use s dscussed n detal n Thjssen et al. (2002). The present paper s related to Décamps and Marott (2000) who also consder a duopoly model where sgnals arrve over tme. Dfferences are that n Décamps and Marott (2000) only bad sgnals exst and that sgnals are perfectly nformatve. Ths means that after recevng one sgnal the game s over snce the frms are sure that the project s not proftable, whle n our framework t could stll be possble that the project s good. In Décamps and Marott t holds that, as long as no sgnal arrves, the probablty that the project s good contnuously ncreases over tme and the frms are assumed to be asymmetrc, whch also nduces uncertanty regardng the players types, whereas we consder dentcal frms. Furthermore, Décamps and Marott apply the Bayesan equlbrum concept, whereas n our model ths s not the case. Another mplcaton s that a coordnaton problem between the two frms that occurs n our framework s not present n Décamps and Marott (2000). Ths coordnaton problem concerns the ssue of whch frm wll be the frst to nvest n the preempton equlbrum. Another duopoly paper where nformaton arrves over tme s Lambrecht and Perraudn (2003). There, the nformaton relates to the behavour of the compettor: each frm has a certan belef about when the other frm wll nvest and ths belef s updated by observng the other frm s behavour. The paper s organsed as follows. In Secton 2 the model s descrbed. Then, n Secton 3 we analyse the model for the scenaro that the frm roles,.e. leader and follower, are exogenously determned. In Secton 4 the exogenous frm roles are dropped and the model s analysed for the case where the frms are completely symmetrc. In Secton 5 a welfare measure s ntroduced and welfare effects are dscussed. Fnally, Secton 6 concludes the paper. 5

6 2 The Model We consder a stuaton n whch two dentcal frms have the opportunty to nvest n a project wth uncertan revenues. Tme s contnuous and ndexed by t [0, ). The project can ether be good (denoted by H), leadng to hgh revenues, or bad (denoted by L), leadng to low revenues. From the pont of vew of strategc behavour there ar two possbltes. Let τ 0 denote the frst pont n tme where nvestment takes place. If there s exactly one frm nvestng at tme τ ths frm s called the leader. The other frm then automatcally becomes the follower. In our model ths pattern of nvestment leads to Stackelberg competton. A second possblty s that both frms nvest at tme τ, leadng to Cournot-Nash competton. After nvestment has taken place by at least one frm t s assumed that the state of the project becomes mmedately known to both frms. Hence, n the case where there s a leader and a follower there s an nformaton spllover from the leader to the follower, whch creates a second mover advantage. In that case, the follower decdes on nvestment mmedately after the true state of the project s revealed. It s assumed that ths does not take any tme. So, f one frm nvests at tme τ 0, the follower wll ether nvest at tme τ as well or not at all. We dstngush ths case from the case of smultaneous nvestment where both frms also nvest at the same tme τ 0, but wthout one of the frms havng the second mover advantage. 1 That s, n case of smultaneous nvestment, at the tme of nvestment both frms are uncertan as to the true state of the project. In case the project s good the leader s revenue equals UL H > 0, whereas f the project s bad the leader s revenue equals UL L = 0. The sunk costs of nvestment are gven by I > 0. If the project s good, the follower wll mmedately nvest as well and gets revenue UF H > 0. The follower wll also ncur the sunk costs I. It s assumed that UL H > U F H > I. Hence, there s a frst mover advantage f the project turns out to yeld a hgh revenue and nvestment s proftable for both frms. If the project s bad the payoff for the follower equals UF L = U L L = 0. So, f the project s bad the follower observes ths due to the nformaton spllover and thus refrans from nvestment. Ths mples that n case of a bad project, only the leader ncurs a loss that s equal to the sunk costs of nvestment. To see who s n the best poston, the leader or the follower, the magntudes of the frst and second mover advantages 1 The assumpton that the follower reacts mmedately mght seem unrealstc, but s not very restrctve. If for example there s a tme lag between nvestment of the leader and the follower ths only has an nfluence on the payoffs va extra dscountng by the follower. The mportant pont s that the game ends as soon as one frm has nvested, because then the decson of the other frm s made as well. The fact that actual nvestment may take place at a later date s rrelevant for the qualtatve analyss. 6

7 have to be compared. If both frms nvest smultaneously and the project turns out to be good, both receve UM H > 0, where U F H < U M H < U L H. The revenues can be seen as an nfnte stream of payoffs πj dscounted at rate r (0, 1),.e. U j = 0 e rt πj dt = 1 r π j, = H, L, j = L, M, F. Example 1 llustrates ths framework. Example 1 Consder a new market for a homogeneous good. Two frms have the opportunty to enter the market, that can be ether good or bad. Let market demand be gven by P (Q) = Y Q for some Y > 0 f the market s good (H) and by P (Q) = 0 f the market s bad (L). The cost functon s gven by C(q) = cq, for some 0 c Y. It s assumed that f the frms nvest they engage n quantty competton. If the market turns out to be bad, then the acton to take s not to produce,.e. UL L = U F L = U M L = 0. Suppose that there s one frm that nvests n the market frst. Ths frm then s the Stackelberg leader. 2 In case the market s good the follower solves the followng proft maxmsaton problem: 1 q F 0 max r q F [P (q L + q F ) c], where r s the dscount rate. Ths yelds q F = Y c q L 2. Usng ths reacton, the leader maxmses ts stream of profts. Solvng the correspondng maxmsaton problem yelds q L = Y c 2, whch results n q F = Y c 4, and the payoffs U L H (Y c)2 = 8r and (Y c)2 =, respectvely. In case both frms nvest smultaneously, the Cournot- U H F 16r Nash outcome prevals. Straghtforward computatons yeld U H M U H L > U H M > U H F.3 (Y c)2 = 9r. Note that It s assumed that both frms have an dentcal belef p [0, 1] n the project beng good. Ths belef s assumed to be common knowledge. If the leader nvests at a pont n tme where the belef n a good project equals p, the leader s ex ante expected payoff equals L(p) = p(u H L I) + (1 p)( I) = pu H L I. The follower only nvests n case of a good project. Therefore, f the leader nvests when the belef n a good project equals p, the ex ante expected payoff for the follower equals F (p) = p(u H F I). 2 It s assumed that frms can only set capacty once, thereby fxng the producton level forever. Ths resolves the commtment problem mentoned n Dxt (1980). 3 The assumpton of an nfnte Stackelberg advantage may seem to be hghly restrctve and unrealstc. For our framework, however, ths assumpton s not essental. The man pont s that t should be the case that the frst mover has a hgher dscounted present value f the market s good. Ths could also be establshed by a temporary Stackelberg advantage. 7

8 In case of smultaneous nvestment at belef p, each frm has an ex ante expected payoff that equals M(p) = pum H I. Defne by p M the belef such that the ex ante expected proft for the follower equals the ex ante expected proft of smultaneous nvestment,.e. p M s such that F (p M ) = M(p M ). Note that, when p p M, both frms wll always nvest smultaneously,.e. before the true state of the project s known, yeldng payoffs L(p) f p < p M, l(p) = M(p) f p p M, for the leader and F (p) f p < p M, f(p) = M(p) f p p M, for the follower. A graphcal representaton of these payoffs s gven n Fgure 1. U H M I M(p) payoff l(p) f(p) 0 I 0 p P p M 1 p Fgure 1: Payoff functons. At the moment that the nvestment opportunty becomes avalable, both frms have an dentcal pror belef about the project yeldng hgh revenues, say p 0 (0, 1), whch s common knowledge. Occasonally, the frms obtan nformaton n the form of sgnals about the proftablty of the project. These sgnals are observed by both frms smultaneously and are assumed to arrve accordng to a Posson process wth parameter µ > 0. Informaton arrvng over tme wll n general be heterogeneous regardng the ndcaton of the proftablty level of the project. We dstngush two types of sgnals: a sgnal can ether ndcate hgh revenues (an h-sgnal) or low 8

9 revenues (an l-sgnal). A sgnal revealng the true state of the project occurs wth the common knowledge probablty λ > 1 2, see Table 1.4 h H λ 1 λ L 1 λ λ Table 1: Condtonal probabltes of h- and l-sgnals. Let n denote the number of sgnals and let g and b be the number of h-sgnals and l-sgnals, respectvely, so that n = g + b. Gven that at a certan pont n tme n sgnals have arrved, g of whch were h-sgnals, the frms then calculate ther belef n a good project n a Bayesan way. Defne k = 2g n = g b so that k > 0 (k < 0) ndcates that more (less) h-sgnals than l-sgnals have arrved. After defnng the pror odds of a bad project as ζ = 1 p 0 p 0, t s obtaned from Thjssen et al. (2003) that the (condtonal) belef n a good project s a functon of k and s gven by p(k) = l λ k λ k + ζ(1 λ) k. (1) Note that the nverse of ths functon gves the number of h-sgnals n excess of l-sgnals that s needed to obtan a belef equal to p: 3 Exogenous Frm Roles k(p) = log( p 1 p ) + log(ζ) log( λ 1 λ ). (2) Before we turn to the case where t s endogenously determned whch frm nvests frst, we now look at the smpler case of exogenous frm roles. There are two symmetrc cases, namely one beng that only frm 1 s allowed to be the frst nvestor and the other beng ts symmetrc counterpart. Suppose that only frm 1 s allowed to be the frst nvestor. Then frm 1 does not need to take nto account the possblty that frm 2 preempts. Frm 2 can choose between the follower role,.e. watng to ncur the second mover advantage, and nvestng at the same tme as frm 1,.e. wthout watng for the true state of the project to become known. These two cases lead to dfferent forms of competton f the project turns out to be proftable. In the frst case a Stackelberg equlbrum arses, whereas n the latter case a Cournot 4 Wthout loss of generalty t can be assumed that λ > 1, snce f the converse holds we can 2 redefne the h-sgnals to be l-sgnals and vce versa. Then a sgnal agan reveals the true state of the project wth probablty 1 λ > 1. If λ = 1 the sgnal s unnformatve and, consequently, the 2 2 value of watng dsappears. 9

10 equlbrum s to be expected. Frm 1 should nvest at the pont n tme at whch ts belef n a good project exceeds a certan threshold. In case of the Stackelberg equlbrum t holds that, analogous to Thjssen et al. (2003), that ths threshold belef, denoted by p L, s gven by where and Ψ = 1 p L = Ψ(UL H (3) /I 1) + 1, β(r + µ)(r + µ(1 λ)) µλ(1 λ)(r + µ(1 + β λ)), β(r + µ)(r + µλ) µλ(1 λ)(r + µ(β + λ)) β = r + µ 2µ ( r µ + 1)2 4λ(1 λ). Hence, as soon as p exceeds p L, the leader nvests. Then, the follower mmedately decdes whether or not to nvest, based on the true state of the project that s mmedately revealed after the nvestment by the leader. Note that p L wll not be ht exactly, snce the belef p(k) jumps alongsde wth the dscrete varable k. Hence, the leader nvests when p = p( k L ), where k L = k(p L ). The above story only holds f p( k L ) < p M. If the converse holds, frm 1 knows that frm 2 wll not choose the follower role, but wll nvest mmedately as well yeldng UM H nstead of U L H f the project turns out to be good. Then a Cournot equlbrum arses and the threshold n ths case s equal to 1 p L = Ψ(UM H /I 1) + 1. Note that snce U H L > U H M t holds that p L > p L. When p 0 s contaned n the regon (p M, 1], both frms wll mmedately nvest, yeldng for both a dscounted payoff stream UM H I f the project s good, and I f the project s bad. Lke n the Cournot equlbrum, here too the belef s such that the follower prefers to receve the smultaneous nvestment payoff rather than beng a follower, mplyng that t takes the rsk of makng a loss that equals the sunk costs of nvestment when the project value s low. 4 Endogenous Frm Roles Let the frm roles now be endogenous, whch mples that both frms can be the frst nvestor. Defne the preempton belef, denoted by p P, to be the belef at whch the leader value equals the follower value,.e. where L(p P ) = F (p P ) (cf. Fgure 1). Ths gves p P = I U H L U H F + I. (4) 10

11 Note that p P < p M. As soon as p reaches p P (f ever), both frms want to be the leader and try to preempt each other, whch erodes the opton value of watng. It does not vansh completely, however, snce L(p P ) > 0. Ths ndcates that the net present value of the nvestment of the preemptor s stll postve. Furthermore, defne k P = k(p P ). For the analyss an mportant part s played by the postonng of k L, whch can be smaller or larger than k P. Snce k s monotoncally ncreasng n p, from (3) and (4) t follows that k L > k P Ψ < U H L U H F U H L I. (5) Note that f k L > k P then k L k P. The rght-hand sde of the second nequalty n (5) can be seen as the relatve prce that the follower pays for watng to obtan the nformaton spllover. Snce Ψ decreases wth λ and (n general) wth µ (see Thjssen et al. (2003)), Ψ ncreases wth the value of the nformaton spllover. For f Ψ s low, the qualty and the quantty of the sgnals are relatvely hgh. Therefore, f a frm becomes the leader t provdes relatvely less nformaton to ts compettor for low values of Ψ compared to when Ψ s hgh. So, expresson (5) mples a comparson between the frst mover advantage and the second mover advantage. In what follows we consder the two cases k L k P and k L < k P. 4.1 The Case Where the Leader Advantage Outweghs the Informaton Spllover Suppose that k L k P. In ths case frms start to duel over the leader role as soon as k = k P, whereas an exogenously assgned leader would wat untl k = k L. Ths mples that frms try to preempt each other n nvestng n the project. We apply the equlbrum concept ntroduced n Fudenberg and Trole (1985), whch s extended for the present settng nvolvng uncertanty n Thjssen et al. (2002), to solve the game. In Appendx A a bref revew of the approprate strategy and equlbrum concepts can be found. The applcaton of ths equlbrum concept requres the use of several stoppng tmes. Defne for all startng ponts t 0 0, T t 0 P = nf{t t 0 p t p P } and T t 0 M = nf{t t 0 p t p M }, where p t p(k t ) and k t s the number of h-sgnals n excess of l-sgnals at tme t. Note that T t 0 M T t 0 P a.s. for all t 0 0. In what follows we consder three dfferent startng ponts, namely p t0 p M, p P p t0 < p M and p t0 < p P. If p t0 p M the value of smultaneous nvestment s greater than or equal to the value of beng the second nvestor. If the nequalty s strct ths mples that no frm wants to be the follower and hence that both frms wll nvest mmedately. If p t0 = 11

12 p M frms are ndfferent between beng the follower and smultaneous nvestment. 5 Next, let p P p t0 < p M be the startng pont of the game. Both frms try to preempt n ths scenaro, snce the value for the leader s hgher than the value for the follower. Ths mples that n a symmetrc equlbrum 6 each frm nvests wth a postve probablty. Here both frms want to be the frst nvestor, snce the expected Stackelberg leader payoff s suffcently hgh. Equvalently, the belef n a good project s suffcently hgh for takng the rsk that the project has a low payoff to be optmal. On the other hand, f the frms nvest wth postve probablty, the probablty that both frms smultaneously nvest s also postve. Ths would lead to the smultaneous nvestment (Cournot-Nash) payoff. However, snce t 0 < T t 0 M ths payoff s not hgh enough for smultaneous nvestment as such to be optmal. We conclude that there s a trade-off here between gettng the hgh payoff as a leader or a low payoff that s nfluenced by the rsk of nvestng n a bad project as a leader, the lower payoff of beng the follower, and the lower payoff of (a suboptmal) smultaneous nvestment. As s proved n Proposton 1 below, the probablty that a frm nvests equals L(p) M(p) L(p) 2M(p)+F (p). Hence, ths probablty decreases wth the dfference between the leader and the smultaneous nvestment payoff. Ths happens because f ths dfference s large the frms wll try to avod smultaneous nvestment by lowerng ther nvestment probablty. From Thjssen et al. (2002) t s known that t s optmal f one of the two frms nvests as soon as the preempton regon s reached. The equlbrum strateges are such that the probablty that at least one frm nvests equals one. 7 Snce mmedately after nvestment by the leader the follower decdes on nvestment, the game ends exactly at the pont n tme where the preempton regon s reached. Agan, the poston of p L s of no mportance, snce the leader curve les above the follower curve, mplyng that both frms wll try to become the leader. The last regon s the regon where p t0 < p P. As long as t 0 t < T t 0 P, the leader curve les under the follower curve, and snce n ths case k L k P, p L has not been 5 Note that whether or not p M > p L s rrelevant. For suppose that p M p L. Then no frm would be wllng to wat untl p L s reached, because of the sheer fear of beng preempted by the other frm. 6 Snce the frms are dentcal, a symmetrc equlbrum seems to be the most plausble canddate. See Thjssen et al. (2002) for a more elaborate dscusson of ths pont. 7 Note that the probablty of smultaneous nvestment at T t 0 P s strctly postve, even f t0 < T t 0 P. Ths happens because the preempton pont wll not be ht exactly due to the dscontnuty of the stochastc process governng the evoluton of p. In the standard game theoretc real optons lterature (e.g. Weeds (2002)) one uses a less complcated equlbrum concept and smply assumes that the probablty of smultaneous nvestment at the preempton pont equals zero. Such an assumpton would be unjustfed here. 12

13 reached yet. Hence, no frm wants to be the leader and both frms abstan from nvestment untl enough h-sgnals have arrved to make nvestment more attractve than watng. Formally, the above dscusson can be summarsed n a consstent α-equlbrum. Ths equlbrum concept for game theoretc real optons models s descrbed n detal n Thjssen et al. (2002). The strateges used n these tmng games consst of a cumulatve dstrbuton functon G t 0 ( ), where G t 0 (t) gves the probablty that frm has nvested before and ncludng tme t t 0, and an ntensty functon α t 0 ( ). The ntensty functon serves as an endogenous coordnaton devce n cases where t s optmal for one frm to nvest but not for both. In coordnatng frms make a trade-off between succeedng n nvestng frst and the rsk of both nvestng at the same tme. For detals, see Appendx A. Proposton 1 If Ψ U L H U F H UL H I, then a symmetrc consstent α-equlbrum s gven by the tuple of closed-loop strateges ( (G t 1, αt 1 ), (Gt 2, αt 2 )), where for = 1, 2 t [0, ) 0 f s < TP t, G t L(p T t ) M(p T t ) (s) = P P L(p T t ) 2M(p T t )+F (p T t ) f TP t s < T M t, P P P 1 f s TM t, 0 f s < TP t, α(s) t L(p T t ) F (p T t ) = P P L(p T t ) M(p T t ) f TP t s < T M t, P P 1 f s TM t. For a proof of ths proposton, see Appendx B. (6) (7) 4.2 The Case Where the Informaton Spllover Outweghs the Leader Effect Suppose that p L < p P. Now the problem becomes somewhat dfferent. Let t 0 0. For t > T t 0 P the game s exactly the same as n the former case. The dfference arses f t t 0 s such that p t [p L, p P ). In ths regon t would have been optmal to nvest for the leader n case the leader role had been determned exogenously. However, snce the leader role s endogenous and the leader curve les below the follower curve, both frms prefer to be the follower. In other words, a war of attrton (cf. Hendrcks et al. (1988)) arses. Two asymmetrc equlbra of the war of attrton arse trvally: frm 1 nvests always wth probablty one and frm 2 always wth probablty zero, 13

14 and vce versa. However, snce the frms are assumed to be dentcal there s no a pror reason to expect that they coordnate on one of these asymmetrc equlbra. We know that the game ends as soon as T t 0 P s reached. Note, however, that before ths happens p L can be reached several tmes, dependng on the arrval of h- and l-sgnals. There s a war of attrton for k K = { k L,..., k P 1}. To keep track of the ponts n tme where a war of attrton occurs, defne the followng ncreasng sequence of stoppng tmes: T t 0 1 = nf{t t 0 p t = p L }, T t 0 n+1 = nf{t > T t 0 n k K : p t = p(k)}, n = 1, 2, 3,..., wth the correspondng levels of h-sgnals n excess of l-sgnals k n = k(p t T 0 ). Note that n s the number of sgnals that have n arrved up untl and ncludng tme T t 0 n snce the frst tme the war of attrton regon has been reached. To fnd a symmetrc equlbrum we argue n lne wth Fudenberg and Trole (1991) that for each pont n tme durng a war of attrton the expected revenue of nvestng drectly exactly equals the value of watng a small perod of tme dt and nvestng when a new sgnal arrves. 8 The expected value of nvestng at each pont n tme depends on the value of k at that pont n tme. Let k t K for some t t 0. Denotng the probablty that the other frm nvests at belef p(k t ) by γ(k t ), the expected value of nvestng at tme t equals V 1 (p t ) = γ(k t )M(p t ) + (1 γ(k t ))L(p t ). (8) The value of watng for an nfntesmal small amount of tme equals the weghted value of becomng the follower and of both frms watng,.e. V 2 (p t ) = γ(k t )F (p t ) + (1 γ(k t ))Ṽ (p t), (9) where Ṽ (p) s the value of watng when nether frm nvests. Let γ( ) be such that V 1 ( ) = V 2 ( ). To actually calculate γ(k) for all k K, we use the fact that only for certan values of p the probablty of nvestment needs to be calculated. These probabltes are the belefs that result from the sgnals,.e. for the belefs p such that p = p(k), k K. For notatonal convenence we take k as dependent varable nstead of p. For example, we wrte V (k) nstead of V (p(k)). To calculate the solated atoms the probabltes of nvestment n the war of attrton, γ( ), the value of watng Ṽ ( ) needs to be determned. It s governed by the followng equaton: Ṽ (k) =e rdt {(1 µdt)ṽ (k) + µdt[p(k)(λv 1(k + 1) + (1 λ)v 1 (k 1))+ + (1 p(k))(λv 1 (k 1) + (1 λ)v 1 (k + 1))]}. (10) 8 It mght seem strange that a frm then also nvests when a bad sgnal arrves. Note, however, that t s always optmal for one frm to nvest n the war of attrton regon. The probablty of nvestment s most lkely lower for lower values of p. 14

15 Eq. (10) arses from equalzng the value of Ṽ (k) to the value an nfntesmally small amount of tme later. In ths small tme nterval, nothng happens wth probablty 1 µdt. Wth probablty µdt a sgnal arrves. The belef a frm has n a good project s gven by p(k). If the project s ndeed good, an h-sgnal arrves wth probablty λ, and an l-sgnal arrves wth probablty 1 λ. Vce versa f the project s bad. If a sgnal arrves then nvestng yelds ether V 1 (k + 1) or V 1 (k 1). After lettng dt 0 and substtutng eqs. (1) and (8) nto eq. (10) t s obtaned that Ṽ (k) = µ [ λ k+1 + ζ(1 λ) k+1 ( γ(k + 1)M(k + 1) + (1 γ(k + 1)) r + µ λ k + ζ(1 λ) k L(k + 1) ) + λ(1 λ) λk 1 + ζ(1 λ) k 1 λ k + ζ(1 λ) k ( γ(k 1)M(k 1) + (1 γ(k 1))L(k 1) )]. Substtutng eq. (11) nto eq. (9) yelds, after equatng eqs. (9) and (8) and rearrangng: where (11) a k γ(k) + b k = (1 γ(k))(c k γ(k + 1) + d k γ(k 1) + e k ), (12) a k =M(k) L(k) F (k), b k =L(k), c k = µ λ k+1 + ζ(1 λ) k+1 ( ) M(k + 1) L(k + 1), r + µ λ k + ζ(1 λ) k d k = µ λ)λk 1 r + µ λ(1 + ζ(1 λ) k 1 ( ) M(k 1) L(k 1), λ k + ζ(1 λ) k e k = µ ( λ k+1 + ζ(1 λ) k+1 r + µ λ k + ζ(1 λ) k L(k + 1) + λ(1 λ) λk 1 + ζ(1 λ) k 1 λ k + ζ(1 λ) k L(k 1) To solve for γ( ) note that f k < k L, no frm wll nvest, snce the opton value of watng s hgher than the expected revenues of nvestng. Therefore γ( k L ) = 0. On the other hand, f k k P the frms know that they enter a preempton game,.e. γ( k P ) = G t (T P t ), where Gt (T P t ) can be obtaned from Proposton 1. Note that t s possble that k P = k M. Then the game proceeds from the war of attrton drectly nto the regon where smultaneous nvestment s optmal. Ths happens f TM t = T P t. In ths case the expected payoff s governed by M( ). For other values of k, we have to solve a system of equatons, where the k-th entry s gven by eq. (12). The complete system can be wrtten as ). dag(γ)aγ + Bγ = b, (13) 15

16 for approprately chosen matrces A and B, and vector b. The system of equatons (13) cannot be solved analytcally. However, for any specfc set of parameter values, a numercal soluton can be determned. The followng lemma shows that a soluton always exsts. The proof can be found n Appendx C. Lemma 1 The system of equatons (13) has a soluton. Furthermore, γ(k) [0, 1] for all k K. Defne n t = sup{n T t 0 n t} to be the number of sgnals that has arrved up untl tme t t 0. In the followng proposton a symmetrc consstent α-equlbrum s gven. Proposton 2 If Ψ > U L H U F H UL H I, then a consstent α-equlbrum s gven by the tuple of closed-loop strateges ( (G t 1, αt 1 ), (Gt 2, αt 2 )), where for = 1, 2 t [0, ) 0 f s < T t 1 ns γ(k n) n ( G t n=n t 1 γ(k n) n =n t 1 γ(kn ) ) f T1 t s < T P t, (s) = ( 1 G t (TP t )) L(p T P t ) M(p T t ) P L(p T t ) 2M(p T t )+F (p T t ) f TP t s < T M t, P P P 1 f s TM t, or s > T P t 0 f s < TP t, α(s) t L(p T t ) F (p T t ) = P P L(p T t ) M(p T t ) f TP t s < T M t, P P 1 f s TM t. and H, (14) (15) The proof of Proposton 2 can be found n Appendx D. An llustraton of the case where the second mover advantage outweghs the frst mover advantage can be found n the followng example. Example 2 Consder a stuaton whose characterstcs are gven n Table 2. For U H L = 13.3 r = 0.1 U H F = 13 µ = 2 U H M = 13.2 λ = 0.7 I = 2 p 0 = 0.5 Table 2: Parameter values. ths example the preempton belef equals p P = The mnmal belef that an exogenous leader needs to nvest optmally s gven by p L = Usng eq. (2) ths 16

17 mples that a war of attrton arses for k {1, 2}. Solvng the system of equatons gven n (13) yelds the vector of probabltes wth whch each frm nvests n the project. It yelds γ(1) = and γ(2) = From ths example one can see that the probablty of nvestment ncreases rapdly and s substantal. Both frms know that, gven that the project s good, t s better to become the leader. So, as the belef n a good project ncreases, both frms nvest wth hgher probablty. 5 Welfare Analyss Welfare effects resultng from nvestment under uncertanty have been reported by e.g. Jensen (1992b) and Stenbacka and Tombak (1994). In both papers the tmng of nvestment does not depend on the arrval of sgnals. In these papers the uncertanty comprses the tme needed to successfully mplement the nvestment,.e. the tme between nvestment and the successful mplementaton of the nvestment s stochastc. The models n Jensen (1992b) and Stenbacka and Tombak (1994) allow for the crtcal levels to be explct ponts n tme. In our model, the crtcal level s not measured n unts of tme but measured as a probablty,.e. a belef. To perform a welfare analyss, however, t s necessary to ncorporate the tme element n the model. For smplcty we only consder preempton cases (p 0 < p P < p L ). The resultng equlbrum mples that as soon as k P s reached, at least one frm nvests and the game ends. We analyse two questons relatng to welfare that, at frst sght, are expected to have obvous answers. Frst, we nvestgate f more and/or better nformaton leads to hgher levels of expected ex ante welfare. Secondly, we analyse f competton (n duopoly) s better from a socal welfare pont of vew than monopoly. Gven the belef n a good project p [p P, p M ), the probablty of smultaneous nvestment, denoted by b(p), s gven by (cf. (7) and (17)): b(p) = L(p) F (p) L(p) 2M(p) + F (p). Let CSM l denote the dscounted value of consumer surplus f the project s l {L, H} and smultaneous nvestment takes place. Furthermore, let CSS H and CSL denote the nfnte dscounted stream of consumer surplus n the Stackelberg equlbrum f the project s good, and the nfnte dscounted stream of consumer surplus f the project s bad and one frm nvests, respectvely. If the crtcal number of h-sgnals n excess of l-sgnals s gven by k 0 wth frst passage tme t, the expected dscounted total surplus f the project gves hgh 17

18 revenues s gven by ES H (k, t) =e rt[ b(p(k))(2u H M + CS H M) + ( 1 b(p(k)) ) (U H L + U H F + CS H S ) 2I whereas f the project gves a low revenue the expected total surplus equals ES L (k, t) = e rt[ b(p(k))(csm L 2I) + ( 1 b(p(k)) ) ] (CS L I). The expected total surplus wth crtcal level k and frst passage tme t s then gven by W (k, t) = p(k)es H (k, t) + (1 p(k))es L (k, t). To ncorporate the uncertanty regardng the frst passage tme through k, we defne the ex ante expected total welfare W (k) to be the expectaton of W (k, t) over the frst passage tme through k. That s, W (k) = IE k ( W (k, t) ) = 0 W (k, t)f k (t)dt, where f k ( ) s the probablty densty functon (pdf) of the frst passage tme through k. ], (16) The pdf of the frst passage tme through k 0 s gven n the followng proposton, the proof of whch can be found n Appendx E. Proposton 3 Let k 0 = 0 a.s. The probablty densty functon f k ( ) of the frst passage tme through k 0 s gven by for all t 0. Here, f k (t) = λk +ζ(1 λ) k ( ) k/2 k 1+ζ λ(1 λ) t I k(2µ λ(1 λ)t)e µt, I ρ (x) = l=0 1 ( x ) 2l+ρ, l!γ(l + ρ + 1) 2 s the modfed Bessel functon wth parameter ρ and Γ( ) denotes the gamma functon. In the remander, let CS mon and W mon denote the present value of the nfnte flow of consumer surplus and the ex ante expected total surplus, respectvely, n the case of a monopolst. The crtcal level of nvestment for the monopoly case s obtaned from Thjssen et al. (2003). We use the economc stuaton descrbed n Example 1,.e. a new market model wth affne demand and lnear costs. Consder the parametrzaton as gven n Table From Example 1 we can conclude that

19 Y = 5 r = 0.1 c = 2 p 0 = 0.4 I = 5 Table 3: Parameter values. the monopoly prce s gven by P mon = Y +c 2, the prce n case of smultaneous nvestment equals P M = Y +2c 3, and the prce n the Stackelberg case s gven by P S = Y +3c 4. Gven that the market s good, the flow of consumer surplus s then represented by Y P P P 1 (p)dp = 1 2 (Y P P ) 2, where P P s the equlbrum prce. Hence, CSmon H = 0 e rt 1 2 (Y P mon) 2 (Y Pmon)2 dt = 8r. Smlarly, CSM H = (Y P M ) 2 6r, CSS H = (Y P S) 2 32r, and CSmon L = CSM L = CSL = 0. We want to analyse the effect of the quantty and qualty of nformaton on welfare n both the monopolstc and the duopoly case. Frst, consder the case where λ = 0.6 and µ vares from 2 up to 5. Calculatons lead to Fgure 2. As can Welfare monopoly duopoly µ Fgure 2: Welfare as a functon of µ. be seen from the fgure, one cannot derve a clear-cut result sayng that competton s better than monopoly or vce versa. Ths s caused by the dscreteness of the nvestment threshold. In the duopoly case a Stackelberg equlbrum arses for all values of µ, whle the nvestment threshold always equals k d = 1. From (4) one can see that p P s ndependent of both µ and λ and that k(p) s ndependent of µ. Hence, k d cannot dffer for varyng values of µ. As µ ncreases welfare mproves, because more nformaton s (n ths case) better. The jump n the curve for welfare under monopoly occurs because at µ 3 the nvestment threshold k m jumps from 1 to 2. Ths happens snce k m s ncreasng n µ, whch mples that k m exhbts upward jumps for some values of µ, whle t s constant otherwse. As soon as there 19

20 s a jump, the monopolst wats longer, whch reduces both the rsk of nvestng n a bad market as well as expected consumer surplus. From the above t becomes clear that the latter effect domnates, mplyng that the ntuton that more nformaton s always better cannot be sustaned. Secondly, we analyse the effect of the qualty of nformaton on welfare by takng µ = 4 and by lettng λ vary from 0.55 to 0.8. Ths yelds Fgure 3. The jumps occur Welfare monopoly duopoly λ Fgure 3: Welfare as a functon of λ. due to the dscreteness of the nvestment threshold just as before. We wll descrbe monopoly and duopoly separately to get some feelng for the dfferent effects at work. Frst, let us consder the monopoly case. At λ 0.575, k m jumps from 1 to 2, whch accounts for the drop n welfare. For the remander of the doman, an ncrease n λ reduces the rsk of nvestment whle the market s bad and accelerates nvestment, whch results n ncreasng expected consumer and producer surplus and thus n hgher welfare levels. In the duopoly case there are more effects. The jump at λ 0.57 occurs snce k d jumps from 2 to 1 (although p P remans constant), snce less sgnals are needed to reach p P. Ths s good for expected consumer surplus, hence the ncrease. For λ between 0.57 and 0.635, a Stackelberg or a Cournot equlbrum arses. Welfare decreases over ths range snce for ncreasng λ the probablty of smultaneous nvestment at the preempton pont ncreases monotoncally. 9 In case of smultaneous nvestment both frms do not wat for the outcome of the other frm s nvestment. Hence, they both nvest wthout knowng beforehand the state of the market. Ths mples that n case of a bad market the sunk nvestment costs s lost twce for the whole market. Therefore, the loss (due to sunk nvestment costs) n case the mar- 9 Ths s not an analytcal result. The probablty of smultaneous nvestment can also decrease wth ncreasng λ. 20

21 ket turns out to be bad s ncreasng n λ whch has a negatve effect on welfare. From λ onwards, a Cournot equlbrum arses where both frms always nvest smultaneous. Hgher λ means that sgnals are more relable. Therefore, the probablty of smultaneous nvestment n a bad market s smaller, whch ncreases expected producer surplus and thus enhances expected welfare, although the welfare level s lower than under monopoly. A fnal remark concerns the range where λ s n between 0.55 and Here k m = 1 and k d = 2,.e. n a monopolstc market nvestment takes place at an earler date than n a duopoly, gven an dentcal sample path of the nformaton process. Ths s due to the fact that the dscounted value of the project s hgher for a monopolst than for a frm that faces competton. Ths hgher dscounted value has a dampenng effect on the watng tme. From these examples two observatons can be made. Frstly, more or better nformaton does not always lead to hgher welfare. Ths s manly due to opposng effects nfluencng the expected producer surplus. Expected consumer surplus n general ncreases n the qualty and quantty of nformaton. An excepton arses n the monopoly case where the threshold level k m can jump upwards. Ths happens because of the fact that the ncrease n the value of watng delays nvestment, whch s bad for consumer surplus. In the duopoly case there s another effect regardng the qualty of nformaton. In a range where both a Stackelberg and a Cournot-Nash equlbrum can occur the probablty of jont nvestment at the preempton pont can ncrease, f nformaton gets qualtatvely better. Ths has a negatve nfluence on producer surplus, snce f the market turns out to be bad both frms wll lose the sunk costs I. The magntude of these sunk-costs mght not offset the ncrease n expected consumer surplus due to earler nvestment. The second observaton s that t s not clear whether a monopolstc or an olgopolstc market structure s desrable from an ex ante socal welfare perspectve. To get a better nsght n ths problem, consder an example wth Y = 60, c = 20, I = 500, p 0 = 0.4 and r = 0.1. We take µ [0.5, 4] and λ [0.6, 0.9] and compare welfare for monopoly and duopoly. Ths s depcted n Fgure 4. From the fgure one gets the mpresson that bad nformaton (.e. low µ and low λ) seems to favour a duopolstc structure, whereas good nformaton (.e. hgh µ and hgh λ) seems to favour a monopolstc market structure. To test ths hypothess we smulate the model. In each run we sample (Y c) U[5, 50], where U denotes the unform dstrbuton and I U[ 1 4 U F H, 3 4 U F H]. The nterest rate s set to r = 0.1 and the pror belef n a good market at p 0 = 0.4. We sample 1000 nstances of bad nformaton wth µ L U[0.5, 1.5] and λ L U[0.6, 0.7], and 1000 nstances of good nformaton wth µ H U[3, 4] and 21

22 W mon >W duo λ W duo >W mon µ Fgure 4: Regons of hgher welfare (monopoly or duopoly) for dfferent (µ, λ)- combnatons. W mon (W duo ) denotes welfare n the monopoly (duopoly) case. λ H U[0.8, 0.9]. Ths leads to four seres of smulated expected ex ante welfare levels for monopoly and duopoly, Wmon, L Wduo L, W mon, H and Wduo H. Snce we hypothesse that IE(Wduo L ) > IE(W mon) L and IE(Wmon) H > IE(Wduo H ), we test the null-hypotheses H 0 : IE(Wduo L W mon) L 0 and H 0 : IE(Wmon W H duo H ) 0. Usng standard asymptotcally normal tests, both null-hypotheses are rejected at 5%. 10 So, we fnd evdence that a duopoly leads to a sgnfcantly hgher level of expected ex ante welfare than monopoly f the nformaton s relatvely bad, whereas the reverse holds f nformaton s relatvely good. Intutvely, one can see that f nformaton s bad, the value to wat for a monopolst s very low. Therefore, he wll nvest soon. On the other hand, n the duopoly case, although the preempton level may be reached soon, the probablty of jont nvestment s low and ths dampens the negatve preemptve effect on expected producer surplus. If nformaton s good, frms are more lkely to smultaneously nvest whch s bad for expected producer surplus. So, n expectaton the preempton effect hurts more f nformaton s good. Moreover, the value of watng ncreases when sgnals become more valuable, or occur more frequently. In the monopoly case ths value of watng s fully taken nto account, whereas n a duopoly frms stll ntend to nvest quckly to preempt ther rval. In the above analyss only the preempton case s consdered. From a mathematcal pont of vew the advantage of consderng the preempton case s that one knows that the game stops as soon as the preempton level s reached. Ths allows for the 10 Let (x 1,..., x n) be a sample of d draws wth IE(x) = µ, V ar(x) = σ 2, sample mean x, and sample varance ˆσ 2. For testng H 0 : µ 0 we use the test statstc T = n x, whch under the ˆσ 2 null-hypothess has a standard normal dstrbuton. In our case we get T = 4.45 and T = 30.60, respectvely. 22

23 use of the dstrbuton of the frst passage tme n the defnton of ex ante expected total surplus. In case the nformaton spllover outweghs the Stackelberg effect a war of attrton arses. To make a comparable welfare analyss for ths case one has to consder all possble paths for the arrval of sgnals before the preempton regon s ht. So, not only the dstrbuton for the frst passage tme, but the dstrbuton of second, thrd, etc. passage tmes for values k K have to be consdered, condtonal on the fact that the preempton value s not reached. Such an analyss s not analytcally tractable. However, one could estmate the ex ante expected total surplus by use of smulatons. Also n ths case ambguous results regardng the welfare effects of monopoly and duopoly can be expected, dependng on the poston of the crtcal nvestment level for a monopolst relatve to p L. An addtonal effect concernng the welfare comparson of monopoly and duopoly n case of a war of attrton s the free rder effect. In a duopoly both frms lke the other to nvest frst so that t does not need to take the rsk that the project has low value. Consequently frms nvest too late, leadng to a lower expected consumer surplus. 6 Conclusons Non-exclusvty s a man feature that dstngushes real optons from ther fnancal counterparts (Zngales (2000)). A frm havng a real nvestment opportunty often shares ths possblty wth one or more compettors and ths has a negatve effect on profts. The mplcaton s that, to come to a meanngful analyss of the value of a real opton, competton must be taken nto account. Ths paper consders a duopoly where both frms have the same possblty to nvest n a new market wth uncertan payoffs. As tme passes uncertanty s gradually resolved by the arrval of new nformaton regardng the qualty of the nvestment project n the form of sgnals. Generally speakng, each frm has the choce of beng the frst or second nvestor. A frm movng frst reaches a hgher market share by havng a Stackelberg advantage. However, beng the second nvestor mples that the nvestment can be undertaken knowng the payoff wth certanty, snce by observng the performance n the market of the frst nvestor t s possble to obtan full nformaton regardng the qualty of the nvestment project. The outcome manly depends on the speed at whch nformaton arrves over tme. If the qualty and quantty of the sgnals s suffcently hgh, the nformaton advantage of the second nvestor s low so that the Stackelberg advantage of the frst nvestor domnates, whch always results n a preempton game. In the other scenaro, ntally a war of attrton prevals where t s preferred to wat for the compettor to undertake the rsky nvestment. Durng the tme where ths war of 23