STRATEGIC EXERCISE OF REAL OPTIONS: INVESTMENT DECISIONS IN TECHNOLOGICAL SYSTEMS

Transcription

1 TRTEGC EXERCE OF REL OPTON: NVETENT ECON N TECHNOLOGCL YTE Kevn ZHU John WEYNT Graate chool of anagement Unversty of Calforna, rvne, C , U [email protected] epartment of anagement cence an Engneerng tanfor Unversty, tanfor, C , U bstract Vewng nvestment projects n new technologes as real optons, ths paper stes the effects of enogenos competton an asymmetrc nformaton on the strategc exercse of real optons. We frst evelop a mlt-pero, game-theoretc moel an show how competton leas to early exercse an aggressve nvestment behavors an how competton eroes opton vales. We then relax the typcal fll-nformaton assmpton fon n the lteratre an allow nformaton asymmetry to exst across frms. Or moel shows, n contrast to the lteratre that payoff s nepenent of the orerng of exercse, that the seqental exercse of real optons may generate both nformatonal an payoff externaltes. We also fn some srprsng bt nterestng reslts sch as havng more nformaton s not necessarly better. Keywors: Technology nvestment, competton, real optons, game theory, ynamc games, ncomplete nformaton, technologcal systems, an technology nnovaton 1. ntrocton nvestment opportntes n new technologes (so calle real assets) can be consere as collectons of real optons. t s well nerstoo that optons on real assets share smlartes wth call optons on fnancal secrtes (xt an Pnyck 1994). nalogos to fnancal optons on stocks an bons, real optons are optons on real or physcal assets sch as technologes, eqpment, procton facltes, ol eposts, an offce blngs. The term nvest means a frm exercses ts opton by nvokng an ntal cost to exchange for a real asset that may pay a stream of ftre cash flows. Ths allows fnancal opton prcng theory to be extene to vale real optons. gnfcant applcatons are fon n captal nvestments, technology management, new proct evelopment, R&, natral resorces, an real estate nvestment (rennan an chwartz 1985, conal an egel 1986, Paock, egel, an mth 1988, Wllams 1993, alwn an Clark 1994, N /3/13/57 JOURNL OF YTE CENCE N YTE ENGNEERNG CN11-983/N JE 3 Vol. 1, No. 3, pp57-78, eptember, 3

2 trategc Exercse of Real Optons: nvestment ecsons n Technologcal ystems Grenaer an Wess 1997, an erton 1997). On the other han, the analogy between fnancal optons an real optons s close bt not exact. The two ffer n terms of traablty, lqty, ownershp, an how the exercse of optons may mpact the nerlyng asset (Zh 1999b). n partclar, compettve nteracton becomes fnamentally mportant n the valaton an exercse of real optons, whle t may not be sch a sgnfcant concern for fnancal optons. ch compettve nteractons may have profon effects on opton exercse ecsons an the resltng eqlbrm, effects that have yet to be aresse n the real optons lteratre (Tallon, Kaffman, Lcas, Whnston, an Zh ). Unlke call optons on fnancal secrtes, real optons may be stngshe by whether the owner s rght to exercse the opton s exclsve. epenng on how exclsve ths rght s, real optons can be classfe as propretary or share. Propretary optons prove exclsve rghts to exercse, whch may reslt from patents on a technology or the frm s nqe ntellectal captal that compettors cannot plcate. n contrast, share real optons are non-propretary, collectve opportntes of the nstry, lke the opportnty to ntroce a new proct that may be sbject to close sbstttes, or the chance to bl a new plant to serve a partclar geographc market wthot barrers to compettve entry. n the real worl, the lxry of propretary optons s selom avalable. When the optons are non-propretary, one frm an ts compettors hol an opton on the same asset, an whoever exercses frst may get the nerlyng asset. The tmng of the exercse ecson col have a profon mpact on the realze vale of the opton, whch s frther complcate by the jont presence of ncertanty, competton, an prvate nformaton. Wth olgopolstc ownershp of the nvestment opportnty, the acton of any one owner can affect the vales of other assets n the portfolo, as well as the actons of other owners. Uner the threat of competton, the exercse of optons strategcally epens on the traeoff between the benefts an costs of gong ahea wth an nvestment aganst watng for more nformaton. Watng can have an nformatonal beneft (conal an egel 1986). However, f a frm chooses to efer exercsng ts opton ntl better nformaton s receve (ths resolvng ncertanty), t rns the rsk that another frm may preempt t by exercsng frst (Zh 1999a). ch an early exercse by a compettor can eroe the profts or even force the opton to expre prematrely. espte ts mportance, competton has been typcally gnore n most of the real optons lteratre. Only a few recent papers have starte to aress ths sse (see, e.g., Trgeorgs 1996, Grenaer 1996, mt an Trgeorgs 1998, an Joaqn an tler ). Ths brgeonng boy of lteratre has prove mportant nsght nto how competton mpacts the valaton an exercse of non-propretary optons on real assets. 1 However, a key assmpton n ths work s that 1 n aton to real optons, the lteratre of fnancal secrtes also has several papers that analyze the strategc exercse of warrants an convertble secrtes n a fll nformaton context (e.g., Emanel 1983, Constantnes 1984, an patt an terbenz 1988). 58 JOURNL OF YTE CENCE N YTE ENGNEERNG / Vol. 1, No. 3, eptember, 3

3 ZHU an WEYNT agents have symmetrc an complete nformaton. gents are assme to be perfectly nforme abot the parameters of the opton. No prvate an ncomplete nformaton s nvolve. symmetrc nformaton Real worl observaton has offere s many realstc statons n whch agents are mperfectly an fferentally nforme. Examples abon n both the fnancal an real optons omans, thogh the vast majorty of applcatons are lkely to occr n the real optons market. For example, ll Gates knows better abot the prospect an volatlty of crosoft s stock optons than an average market partcpant. mazon.com may have better nformaton on the cost (ths proftablty) of sellng books on-lne than the tratonal book retalers lke arnes & Nobel. ntel mght have better nformaton abot the cost to proce 64-bt mcroprocessors than ts compettors lke. n ol exploraton, frms obtan prvate nformaton abot the probablty of fnng an ol epost n a specfc area throgh sesmc srveys an n-hose geophyscs expertse. ore examples exst n hgh tech an R& that show how competton an asymmetrc nformaton manfests tself n technology markets. The nformaton asymmetry among frms may be e to factors sch as pror nvestment on R&, learnng crve n a new market, n-hose expertse, an actve nformaton gatherng actvtes lke market research. s frms often have asymmetrc prvate nformaton n technology or real asset nvestments, relaxng the fll-nformaton assmpton wll a sbstantal realsm to the state of knowlege. few recent stes ncle asymmetrc nformaton n ther opton valaton moels. ack (1993) proves an extenson of the Kyle (1985) moel of contnos nser trang that ncles asymmetrc nformaton on fnancal optons. Whle there s no strategc exercse featre n the moel, nformaton s conveye by trang n the optons. mt an Trgeorgs (1998) examne R& strateges sng a real optons moel that contans ncomplete nformaton an sgnalng strateges. ore recently, a octoral ssertaton at tanfor Unversty (Zh 1999b) evelops real optons an game-theoretc moels for nvestment ecsons n nformaton technologes, n whch nformaton asymmetry an enogenos competton are explctly moele. Grenaer (1999) evelops a contnos-tme moel for eqlbrm opton exercse wth prvate sgnals, n whch nformatonal cascaes an herng behavor n opton exercse are analyze. espte ths recent sgns of avancement n the fel, several problems stll exst wth the crrent lteratre. The most mportant lmtatons are: (1) The orerng/tmng of exercse s assme to be fxe rather than enogenosly etermne; () Payoffs are assme to be nepenent of the orer of exercse; (3) nformatonal externaltes an payoff externaltes are assme to be separate rather than combne. 3 Not every sty n the nformatonal herng occrs when agents gnore ther own prvate nformaton an nstea emlate the behavor of other agents. 3 Externalty occrs when one agent s acton affects another agent. JOURNL OF YTE CENCE N YTE ENGNEERNG / Vol.1, No. 3, eptember, 3 59

4 trategc Exercse of Real Optons: nvestment ecsons n Technologcal ystems lteratre has all of these problems, bt most of them have one or more of them. ressng these problems systematcally wol lkely brng the real optons theory closer to realty. mplcatons of symmetrc nformaton to Opton Prcng by rbtrage or Eqlbrm s mentone earler, real assets (especally new technologes) are often sbject to sbstantal transacton costs, nvsblty, an the nablty to be sol short. We assme that the nerlyng technology s nvsble so that the owner cannot sell (or exercse) a small part of t n orer to reveal ts vale. Ths makes the arbtrage prcng qestonable. n aton, asymmetrc nformaton can tself lea to the falre to prce optons by arbtrage. s emonstrate by etemple an elon (1991) an ack (1993), trang n the opton affects the flow of nformaton, makng a seemngly renant asset not capable of beng prce by arbtrage. 4 Even when an opton wol appear to be renant, ang t to the market can have real conseqences becase ts prce may reveal nformaton abot the fnamental vale of the asset. When the opton s trae, the volatlty of the nerlyng asset becomes stochastc as a reslt of the change n the nformaton flow. Ths elmnates the potental for ynamcally replcatng the opton. Therefore, an eqlbrm prcng approach 4 The opton can be prce by arbtrage f t s renant that s, t can be create synthetcally by trang the nerlyng asset an other assets. f the opton s not renant, then ts exercse may have an effect on the nerlyng asset prce (as well as ts volatlty), becase prces wll ajst to a new eqlbrm when a nonrenant asset s create. (nstea of non-arbtrage prcng) mst be se. The eqlbrm approach relaxes the traablty assmptons neee for arbtrage prcng. To avo frther complcaton, we assme rsk netralty, so that prces are etermne by sconte expecte vales, where the expectaton s contonal on the avalable nformaton. Uner ths rsk-netralty assmpton, all assets are prce so as to yel an expecte rate of retrn eqal to the rsk-free rate. Ths seemngly restrctve assmpton can easly be relaxe by ajstng the rft rate to accont for a rsk premm n the manner of Cox, ngersoll an Ross (1985). n moelng enogenos competton an asymmetrc nformaton, ths paper bls pon another lne of lteratre, namely ynamc games (Kreps & Wlson 198, Kreps, lgrom, Roberts, Wlson 198, an Cho & Kreps 1987), an asymmetrc nformaton (Henrcks & Kovenock 1989, anerjee 199, an Chamley & Gale 1994). The followng stnctons exst between or moel an those exstng moels n the lteratre: (1) Or moel recognzes the opton vale of watng to better resolve ncertanty--ths opton vale s not only conceptalze bt also qantfe n or moel; () We enogenze the tmng an the leaer-follower seqence of nvestment whle the lteratre typcally assmes an exogenos orer of who moves frst. The rest of the paper s organze as follows. ecton enogenzes competton n a complete bt possbly mperfect nformaton settng. ecton 3 moels asymmetrc nformaton n a mlt-pero game tree strctre. ecton 4 concles the paper. 6 JOURNL OF YTE CENCE N YTE ENGNEERNG / Vol. 1, No. 3, eptember, 3

5 ZHU an WEYNT. Competton n Opton Exercse The vale of a real opton can be flly captre only f t s exercse n an optmal way, whch s partly contngent on correct antcpaton of compettors' moves. Compettors o not exercse ther optons ranomly. Rather they o ths base on certan ratonal calclatons. t s ths necessary to enogenze compettors ecsons. n orer to o so, we assme (1) compettors make ratonal calclatons n etermnng when to exercse ther optons, ths exhbtng optmzng behavor; () each player makes ecsons by montorng an ongong ncertan state varable an antcpatng compettor s moves; an (3) the payoffs epen on the resltng eqlbrm. n ths secton, we assme that the frms have complete bt possbly mperfect nformaton. 5 We wll then move on to eal wth ncomplete nformaton n the next secton. ppose two rval frms face an nvestment opportnty for a new technology. oth frms can ece to nvest now or wat. The nvestment opportnty can be eferre, mplyng a eferral opton embee n the nvestment project, as shown n Fgre 1. The payoff of the nvestment project epens on 5 s efne n the game theory lteratre, perfect nformaton means that at each move n the game the player wth the move knows the fll hstory of the play of the game ths far. That s, every nformaton set n the game s a sngleton. mperfect nformaton, n contrast, means that there s at least one nonsngleton nformaton set. Complete nformaton means that the payoff fnctons are common knowlege,.e., there s no prvate nformaton on payoffs, costs, or feasble strateges. the tmng of the exercse ecsons of both frms. pecfcally, we efne the game as follows: Players: Frm an Frm. trateges: n each pero, each frm eces ether to nvest () or efer () n an nvsble technology that reqres a lmpy nvestment otlay,, t. 6 f a frm eces to nvest, t also nees to ece how mch to proce,.e., a qantty q [, ) (=, ) that maxmzes ts expecte payoff. Hence, each frm has a strategy space = (, ; q ), (=, ). Payoffs: The payoff to frm,.e., ts expecte proft π ( q, q j ), s a fncton of the strateges chosen by t an ts compettor. f both frms an nvest wthot observng each other s ecson, they wll splt the market accorng to a Nash-Cornot eqlbrm. f one frm nvests frst an the other oes later, ther payoffs wll be etermne throgh a tackelberg leaer-follower eqlbrm (Fenberg an Trole 1991). f one frm nvests frst, bt the other never oes, then t wll enjoy a monopoly poston. V t,s () - t, V t,s () - t V t,s () - t, C t,s () C t,s(), V t,s() - t C t,s (), C t,s () Fgre 1 mltaneos move an Nash eqlbrm n fgre 1, f both frms efer an keep the opton alve, the payoff wol be the vale of 6, t may be tme- an state-epenent. We also se a smplfe notaton to enote nvestment otlay that s only frm specfc. JOURNL OF YTE CENCE N YTE ENGNEERNG / Vol.1, No. 3, eptember, 3 61

6 trategc Exercse of Real Optons: nvestment ecsons n Technologcal ystems the opton (C) that they can ece whether or not to exercse later. The vales of V an C are frm-specfc an path-epenent, as ncate by the sperscrpts an sbscrpts..1 Qantty ecsons an Eqlbrm Otcomes We frst erve the eqlbrm qanttes an payoffs from an optmzaton process. These wll serve as blng blocks n or sbseqent analyss of a Nash eqlbrm ner enogenos competton n a mlt-pero game strctre. ppose P(Θ t, Q) s the nverse eman fncton,.e., P Θ, Q) = Θ b( q + q ) (1) ( t t where Θ t s the stochastc eman-shft parameter, representng the ncertanty n market eman. Θ t s assme to follow a log-normal ffson process n contnos tme, or a bnomal process n screte tme. 7 Parameter b measres the elastcty of eman, whch s nversely relate to the qalty of the proct. Q = q + q s the aggregate qantty on the market, where q an q are the qanttes proce by frms an, respectvely. enote C as frm s cost fncton,.e., C ( q ) = CF + cq, () where C F s the fxe cost, an c s the margnal cost. For smplcty, assme C =. 7 nce we assme manageral flexblty n otpt ecsons, Q wll be zero f eman becomes too low, ths avong negatve prce, a problem potentally assocate wth ths type of eman fnctons. F.1.1 Frms ove wth Perfect nformaton f frms an nvest seqentally, one frm wll be able to observe the other s move. ppose frm nvests frst an frm, pon observng s move, follows p. We se the backwar ncton metho to solve the game (Fenberg an Trole 1991). 8 ase on backwar ncton, the follower s ecson s max π ( q, q ) = max P( Θ,( q + q )) c q q q t The leaer s ecson s max π q, q q = q ( ( )) ( ( ( ))) max P Θ, q + q q c q q t olvng the optmzaton problem yels the eqlbrm profts: 1 ( ) π = Θt c + cj 8b (3) 1 ( 3 ) π j = Θt cj + c 16b where the sbscrpt represents the leaer, j the follower..1. Frms ove wth mperfect nformaton f frms an make ther ecsons wthot observng each other, each wol have mperfect nformaton abot the other s actal moves. Ths s eqvalent to the staton that they nvest smltaneosly. Then each frm etermnes ts optmal qantty by solvng the 8 ackwar ncton s a solton concept for ynamc games. t works n a smple manner: go to the en of the game an work backwar, one move at a tme. n the leaer-follower competton, backwar ncton analyzes the follower s ecson frst, assmng the leaer has alreay been n the market. 6 JOURNL OF YTE CENCE N YTE ENGNEERNG / Vol. 1, No. 3, eptember, 3

7 ZHU an WEYNT followng optmzaton problem: max π ( q, q ) = q max[ P( Θ,( q + q )) q C ( q )] q j t j where π (=, ) s frm s proft, q, q j are qanttes of frms an j respectvely. olvng ths optmzaton problem yels the eqlbrm qantty: q 1 = ( Θt c + cj ), j. (4) 3b Then the eqlbrm proft for each frm s 1 ( ) π = Θt c + cj (5) 9b t s straghtforwar to verfy the seconorer conton, π ( q, q q j ) <, ths the qantty choces maxmze the proft. Notce t s the nformaton strctre, rather than the tmng, that makes the games fferent. The players nee not act smltaneosly: t sffces that each choose a strategy wthot knowlege of the other s choce, as wol be the case n the Prsoner s lemma f the prsoners reache ecsons at arbtrary tmes whle n separate cells. seqental-move, nobserve-acton game has the same Nash eqlbrm as the smltaneos-move Cornot game. f operatng cash flows last n years, n [1, ), the net present vale, NPV, of the proft vales wll be: π NPV = V = + n t t=1 (1 k) (6) where k s the scont rate. For perpetal operatng cash flows, the NPV can be smplfe as NPV = V π =. (7) k. The lt-pero oel We se a mlt-pero game tree strctre as an extensve-form representaton of the opton-exercse game. s shown n Fgre, two frms an ece ether to nvest () or efer () n each pero. Then Natre (N) eces that the market eman wll be ether movng p to Θ or own to Θ accorng to a bnomal process, where 1 an 1 are the mltplcatve bnomal parameters. Upon observng the moves mae n the prevos pero an the evelopment of the market eman, each frm eces agan to nvest or efer n the next pero. The game can go on for as many peros as neee. We analyze the mlt-pero game base on backwar ncton. ppose the game has only one pero left, at the en noes of the game tree, the payoffs for both frms are etermne by the eqlbrm otcomes of the compettve nvestment sbgames n (3) an (5), epenng on what eqlbrm the game ens p--nash-cornot, tackelberg, or monopoly. We then se the backwar ncton process to fgre ot the sbgame perfect eqlbrm an then se the ynamc programmng metho to roll back the vales from the last pero to the secon last one, an so on (Lenberger 1998). Once havng these vales n place, both frms then fgre ot ther optmal strateges. Eqlbrm s fon by solvng the whole JOURNL OF YTE CENCE N YTE ENGNEERNG / Vol.1, No. 3, eptember, 3 63

8 trategc Exercse of Real Optons: nvestment ecsons n Technologcal ystems game. gan the game s solve by backwar ncton, bt ths tme the frst step n workng backwars from the en of the game nvolves solvng a real game (the smltaneos-move game between frms an n the fnal pero, gven the moves n the prevos pero) rather than solvng a sngle-agent optmzaton problem. t=1 t=... ( Θ c c t 1+ ) / 9 kb- ( Θt c + c ) 1 / 9kb ( pc + (1 p) C ) R ( pc t t / + t + (1 p) Ct ) / R?.. t=n L = ( Θ c c ) / 8kb - t + F = ( Θ 3c c ) / 16 kb - t j + j?.. N N Frms an ece ether to nvest () or efer () n each pero. Then Natre (N) eces that the market eman wll be ether movng p to Θ or own to Θ accorng to a bnomal process. Upon observng the moves mae n the prevos pero an the evelopment of the market eman, each frm eces or agan n the next pero. t the en noes of the game tree, the payoffs for both frms are etermne by the eqlbrm vales erve throgh the optmzaton process. bgame perfect eqlbrm s fon by backwar ncton an ynamc programmng approach..3 Competton Eroes Opton Vale Once we have the strctre of the mlt-pero moel n place, we are reay to examne how competton affects opton exercse n an mperfectly compettve market. s a benchmark, let s start wth a symmetrc opoly moel wth mperfect nformaton. Frms an are ex ante eqal players they have eqal margnal cost, an none enjoys an nformatonal avantage over the other. Fgre 3 shows sch an example nvolvng two compettors wth eqal margnal cost, c =. Usng the approach escrbe n the c Fgre Generc strctre of the mlt-pero moel prevos secton, we fn that the eqlbrm s (, ), 9 meanng both frms nvest an obtan a proft of (5, 5). Notce they col get a proft of (198, 198) f both wat an observe the market movement, then ece to nvest f the market moves p, or efer f the market moves own. bsent cooperaton, however, each frm rshes to exercse ts opton prematrely. 9 We se a strategy par, (frm s acton, frm s acton), to represent the combnaton of frms strateges. For example, (, ) means that frm nvests an frm efers. 64 JOURNL OF YTE CENCE N YTE ENGNEERNG / Vol. 1, No. 3, eptember, 3

9 ZHU an WEYNT C = 8 C = Usng the approach escrbe n. an the generc strctre n Fgre, the eqlbrm s fon to be (, ) as represente by the bol lne, meanng both frms nvest an obtan a proft of (5, 5). Parameter vales are: -4 N t c c = 8, Θ 3, =1.3, =.77, b=1, r=1%, 375, = (1 r). = = = Fgre 3 ymmetrc opoly Frm t + N , 5 5, 3 Frm 3, 5 198, 198 Fgre 4 boptmal eqlbrm s shown n Fgre 4, ths sboptmal early n an effort to preempt compettors or n rsh eqlbrm falls n the classc fear of beng preempte by compettors. ch Prsoner s lemma. 1 Frms ten to move fear of compettve preempton can lea to a smltaneos rsh to early exercse, a 1 We assme n ths moel that frms engage n non-cooperatve competton. Of corse, the nferor rsh eqlbrm may be mprove by cooperaton. f n a repeate game, cooperaton s possble, becase when frms nteract over tme threats an promses concernng ftre behavor may nflence crrent behavor. Kreps, lgrom, Roberts, an Wlson (198) prove a lanmark accont of the role of reptaton n achevng ratonal cooperaton n a fntely repeate Prsoners lemma. JOURNL OF YTE CENCE N YTE ENGNEERNG / Vol.1, No. 3, eptember, 3 65

10 trategc Exercse of Real Optons: nvestment ecsons n Technologcal ystems phenomenon we have often observe n real-worl technology markets. The real optons lteratre has nvestgate the opton vale of watng to a frm when payoffs are stochastc an nvestment rreversble (see, e.g., conal an egel 1986, aj an Pnyck 1987, xt an Pnyck 1994). t has been shown n these stes that frms wll typcally elay nvestng ntl well after the pont at whch expecte sconte benefts eqal ntal costs. n so ong, they explot the opton vale of watng. The opton vale of watng, however, may be overestmate when the rsk of compettve eroson or preempton s omtte. s we have shown above, f other frms nvest frst an n so ong enjoy an avantage, the fear of compettve preempton may rece or estroy the opton vale of watng. When sch strategc behavor s ntroce nto the stanar moel of opton exercse, frms wol exercse ther optons mch more aggressvely, a pattern that may be characterze as racng wth the competton. Ths may help explan some real worl observatons that companes exercse ther optons at a very early stage espte ther ablty to efer ther ecsons. Competton may change the nvestment behavors of a frm t may become more aggressve n makng nvestment ecsons. We have wtnesse waves of acqston an other aggressve nvestment behavors where nstry rvalry s ntense an barrers of entry are low (as typcal n the hgh-tech nstry). One sch example s the aggressve nvestment n nternet-base technologes (as cone as the "ot-com" banwagon) rng any frms, especally those n lcon Valley n the Unte tates, concerne abot fallng behn on the technology crve, engage n hge e-commerce spenng wthot ervng any tangble benefts (ara an khopahyay ). nother example s that semconctor manfactrers sometmes contne to bl capacty n the face of eclnng eman an ncreasng le rate of capacty. Ths reslts n excess capacty for the semconctor nstry as a whole. Whle ths kn of behavor s often regare as rratonal from a non-strategc perspectve, or moel proves a ratonal fonaton for sch excessve capacty blng patterns n the semconctor nstry. t s the competton that leas to the rsh eqlbrm whch n trn rves the aggressve capacty nvestment ecsons. 3. symmetrc nformaton fter examnng the effects of mperfect competton on opton exercse, we are reay to trn to nformaton strctres. s scsse n the ntrocton secton, nformaton asymmetry oes exst among competng frms n technology markets. ncorporatng asymmetrc, ncomplete nformaton wll a greater realsm to the moel. Recall that n an opton-exercse game wth complete nformaton the frms payoff fnctons are common knowlege. n a game wth ncomplete nformaton, n contrast, at least one frm s ncertan abot another frm s payoff or cost fnctons. 66 JOURNL OF YTE CENCE N YTE ENGNEERNG / Vol. 1, No. 3, eptember, 3

11 ZHU an WEYNT 3.1 oel of nformaton trctre nformaton s ncomplete an asymmetrc. Frm knows ts own cost fncton, C ( q ) = c q, bt has only ncomplete nformaton abot frm s cost fncton. The followng probablty strbton represents frm s belef abot frm s cost fncton: C ( q ch q ) = clq wth probablty θ wth probablty (1 θ ) (8) where c L < c < ch. Frm knows both frms cost fncton, ths has speror nformaton (Frm col have jst nvente a new technology). ll of ths s common knowlege: frm knows that frm has speror nformaton, frm knows that frm knows ths, an so on. The eman fncton s the same as efne n (1). n sch a game wth ncomplete nformaton, we say that frm has two possble types, c L an c H, or ts type space T = c, c. Frm s type space s s { L H } smply T = { c }. Frm knows ts own type as well as frm s type, whle frm s ncertan abot s type. Formally, P( t = ch t = c ) = θ P( t = cl t = c) = 1 θ (9) represent frm s belef abot frm s types, gven ts own type. t s a stnctve featre of the ayesan eqlbrm that belefs are elevate to the level of mportance of strateges n sch ncomplete-nformaton games bgame Eqlbrm ner symmetrc nformaton 3..1 mltaneos Exercses Frms an ece ether to nvest or efer wthot observng each other s moves. nce frm knows ts own cost fncton, t wll choose an optmal qantty base on ts tre cost. Natrally, frm may want to choose a lower qantty f ts margnal cost s hgh than f t s low. Frm, for ts part, shol antcpate that frm may talor ts qantty to ts cost n ths way. Let q ( c H ) an q ( c L ) enote frm s qantty choces as a fncton of ts cost, an let q enote frm s sngle qantty choce. f frm s cost s c H, t wll choose q ( ) to solve c H max π ( q, q ; c ) = q max[ P( Θ,( q + q )) c ] q q H mlarly, f s cost s q ( c ) to solve L t H max π ( q, q ; c ) = q c L, t wll choose max[ P( Θ,( q + q )) c ] q q L t L Frm, however, has only a probablty strbton on frm s cost fncton. t wol have to optmze ts proft ner ths ncomplete nformaton. ase on frm s crrent nformaton set, frm knows that frm s cost s hgh wth probablty θ an low 11 However, note that frms choose ther strateges, bt they o not choose ther belefs. Ther belefs are etermne by the nformaton avalable to them. JOURNL OF YTE CENCE N YTE ENGNEERNG / Vol.1, No. 3, eptember, 3 67

12 trategc Exercse of Real Optons: nvestment ecsons n Technologcal ystems wth probablty (1-θ). t ths shol antcpate that frm s qantty choce wll be q ( c H) wth probablty θ an q ( c L) wth probablty (1-θ), respectvely. athematcally, frm s ecson s to choose q to maxmze ts expecte proft sch that: max π ( q, q ) = q max{ θ [ P( Θ,( q + q ( c ))) c ] q q t H + (1 θ)[ P( Θ, ( q + q ( c ))) c ] q } t L olvng the frst-orer contons of these optmzaton problems yels the optmal qanttes: 1 q = 3b [ Θt c + θch + (1 θ) cl] 1 1 θ q ( ch) = ( Θ ) ( ) 3b t ch + c + c 6b H c (1) L 1 θ q( cl) = 3b( Θt cl + c) 6b( ch cl) The corresponng eqlbrm profts are: π = [ Θ c + θc + (1 θ) c ] π π 1 9b t H L 1 1 θ ( ch) = 9b [( Θt ch + c) + ( ch cl)] 1 θ ( cl) = 9b [( Θt cl + c) ( ch cl)] (11) The reslts above n (1) consttte a ayesan Nash eqlbrm, becase they meet the mtal-best-response crteron. That s, each frm s qantty choce s a best response to the other frm s choces, gven ts belef abot ts compettor s types. Compare the eqlbrm qanttes q, q ( c H ), an q ( c L ) n (1) to the Nash-Cornot eqlbrm ner complete nformaton wth costs c an c n (3). ssmng that the vales of margnal costs are sch that both frms eqlbrm qanttes are postve, 1 1 frm proces q = ( Θ 3b t c + cj) n the fll nformaton case. Uner ncomplete nformaton, n contrast, q ( c H ) 1 s greater than ( Θ ) 3 t c b H + c an q ( c L ) s less than 1 ( Θ ) 3 t c b L + c. Ths occrs becase frm not only talors ts qantty to ts own cost bt also respons to the fact that frm cannot o so. f frm s cost s low, for example, t proces more becase ts cost s low bt also proces less becase t knows that frm wll proce a qantty that maxmzes ts expecte proft an ths s larger than frm wol proce f t knew frm s cost to be low. 3.. eqental Exercses The orerng of seqental moves s crcal for an opton-exercse game ner asymmetrc nformaton, becase ecsons of exercse (an nonexercse) may reveal prvate nformaton. Frms can nfer nformaton by movng later than others. The orer of moves reflects each frm s calclate traeoff between the extra rewar from exercsng early an the nformatonal beneft from watng to learn compettors prvate nformaton throgh ther reveale actons. n the lteratre, the orerng of actons has been typcally assme to be pre-etermne. n contrast, we allow the orerng of exercse to be enogenosly etermne throgh agents optmzng ecsons. Two seqences are possble: 1 ppose c H s not so hgh that the hgh cost frm proces nothng. The sffcent conton to rle 1 ot ths problem s ch < 3 ( Θ t + c ). 68 JOURNL OF YTE CENCE N YTE ENGNEERNG / Vol. 1, No. 3, eptember, 3

13 ZHU an WEYNT eqence 1: The less-nforme frm () moves frst an the more-nforme frm () follows ccorng to backwar ncton, we frst solve the follower s ecson,.e., max π ( q, q, ch ) = max P( Θt, ( q( q) q( ch ) q( ch ) + q c c q c max π ( q, q, cl) = max P( Θt, ( q( q) q( cl) q( cl) + q cl cl q c L then the leaer s ecson, { ( ))) ] ( ) H H H ( ))) ] ( ) ( ( )) ( )) ] } ( q q ) = θ P Θ q + q ( c ) max π, max, q q t H ] ( 1 θ ) (, ( ) c q + P Θ q + q c c q t L The soltons to the above optmzaton problems are 1 q = b [ Θt c + θch + (1 θ) cl] 1 1 θ q ( ch) = 4b( Θt 3cH + c) + 4b ( ch cl) 1 θ q( cl) = 4b( Θt 3cL + c) 4b( ch cl) (1) Then the corresponng eqlbrm profts are 1 π = 8b [ Θt c+ θch + (1 θ) cl] 1 π( ch) = [( Θ 3 ) (1 )( )] 16b t ch + c + θ ch cl 1 π( cl) = 16b [( Θt 3cL + c) θ( ch cl)] (13) eqence : The more-nforme frm () moves frst an the less-nforme frm () follows f the frm wth prvate nformaton moves frst, the follower wol have an opportnty to nfer ts prvate nformaton throgh reveale actons. ore specfcally, frm wol c H observe s qantty choces, q ( ) or q ( c L ), an nfer frm s cost fncton, c H or c L, accorngly. Ths, the prvate nformaton of the more-nforme frm may become pblc va ts exercse ecsons. s a conseqence of ths nformaton revelaton, nformaton asymmetry may be mtgate. Upon learnng frm s prvate nformaton, frm chooses ts qantty to maxmze ts proft. Contonal on that frm learne c = c H, frm s ecson wol be: max π ( q, q( ch)) = q. max[ P( Θ,( q + q ( c ))) c ] q q t H mlarly, contonal on that frm learne c = cl, frm s ecson wol be: max π ( q, q( cl)) = q. max[ P( Θ,( q + q ( c ))) c ] q q t L ntcpatng frm s above response, frm solves for q ( c H ) when ts tre cost s c H,.e., max π ( q, q ( c )) = q( ch ) q( ch ) H t H H H max [ P( Θ,( q ( q ) + q ( c ))) c ] q ( c ) y the same reasonng, frm solves for q ( c L ) when ts tre cost s c L,.e., q( cl) q( cl) q q cl max π (, ( )) = t L L L max[ P( Θ,( q ( q ) + q ( c ))) c ] q ( c ) olvng these optmzaton problems yels the followng eqlbrm qanttes: Contonal on c = c, H JOURNL OF YTE CENCE N YTE ENGNEERNG / Vol.1, No. 3, eptember, 3 69

14 trategc Exercse of Real Optons: nvestment ecsons n Technologcal ystems 1 q( ch) = 4b ( Θt 3c + ch) 1 q( ch) = b ( Θt ch + c) Contonal on c = cl, 1 q( cl) = 4b ( Θt 3c + cl) 1 q( cl) = b ( Θt cl + c) (14) (15) The corresponng eqlbrm profts are: 1 π ( ch) = 16b ( Θt 3c + ch) (16) 1 π ( ch) = 8b ( Θt ch + c) π ( c ) = ( Θ 3c + c ) π 1 L 16b t L 1 ( cl) = 8b ( Θt cl + c) (17) where (16) s contonal on c = ch, whle (17) s contonal on c = cl. 3.3 The lt-pero oel ner symmetrc nformaton We se a mlt-pero game tree strctre, lke n ecton., as an extensve-form representaton of the opton-exercse game. t the en noes of the game tree, the payoffs for both frms are etermne by the eqlbrm vales erve n the prevos secton. epenng on what eqlbrm the game ens p, the vales are n (11), (13), (16) or (17). We then se the backwar ncton process to fn ot the ayesan sbgame perfect eqlbrm an then se the ynamc programmng approach to roll back the vales from pero t to pero (t-1). Once havng the vales of these varos possbltes, each frm eces ts best strategy. Notce that the game essentally regenerates tself f t reaches a (, ) branch. n other wor, the game begnnng n the (, ) path (shol t be reache) s jst lke the game as a whole (begnnng n the frst pero). The only fference s that Θ t may have evolve nto a new level, an the frms may have msse the cash flows n the prevos peros whle they were watng. Ths featre helps smplfy the eqlbrm analyss for a mlt-pero game. To see how asymmetrc nformaton manfests tself n opton-exercse games, conser the followng two scenaros When Frm Has Farly ccrate elef abot Frm s Cost n opton-exercse game wth asymmetrc nformaton s llstrate n Fgre 5. Frm s belef abot frm s cost s P( c = ch) = θ =., or eqvalently, P( c = cl) = 1 θ =.8. Ths means frm beleves that there s 8% chance frm s type s low cost, whle frm tself knows ts tre cost s c L. Ths frm s nformaton s farly accrate. Usng backwar ncton, the eqlbrm s fon to be (, ), meanng that the more nforme player () nvests whle the less nforme player () wats. Uner the parameter vales gven above, the profts are fon to be (, 63) for frms an respectvely When Frm Has Less ccrate bt ore Optmstc elef abot s Cost nother scenaro s shown n Fgre 6, where frm has less accrate bt more optmstc assessment on s tre cost,.e., P( c = ch) = θ =.8. Usng the same approach as above, the eqlbrm s fon to have change to (, ), meanng that both frms an nvest, resltng n a proft of (66, 19) for frms an respectvely. 7 JOURNL OF YTE CENCE N YTE ENGNEERNG / Vol. 1, No. 3, eptember, 3

15 ZHU an WEYNT θ =. C = 8 C H = 1 C L = N N Usng backwar ncton, the eqlbrm s fon to be (, ). The eqlbrm profts are fon to be (, 63) for frms an respectvely ner the followng parameter assmptons: θ =., c = 8, c H = 1, t c L = 6, Θ = 3, =1.3, =.77, b=1, r=1%, = 375, t = (1 + r). Fgre 5 symmetrc opoly scenaro 1: When frm has farly accrate belef abot s cost θ =.8 C = 8 C H = 1 C L = N N The only fference between Fgres 5 an 6 s that θ change from. to.8. Ths means that frm has less accrate bt more optmstc assessment on s tre cost. The eqlbrm s fon to have change to (, ), resltng n a proft of (66, 19) for frms an respectvely. Parameter vales are: θ =. 8, c = 8, t c H =1, c L = 6, Θ = 3, =1.3, =.77, b=1, r=1%, = 375, t = (1 + r). Fgre 6 symmetrc opoly scenaro : When frm has less accrate bt more optmstc belef abot s cost JOURNL OF YTE CENCE N YTE ENGNEERNG / Vol.1, No. 3, eptember, 3 71

16 trategc Exercse of Real Optons: nvestment ecsons n Technologcal ystems 3.4 Havng etter nformaton ay Hrt Yo! s shown n these two scenaros, f θ s low (e.g., θ =.), meanng frm has farly accrate belef abot frm s cost. The game ens p n the eqlbrm (, ), becase ths belef leas frm to behave conservatvely as t beleves ts compettor s a strong one (wth low cost). On the other han, f θ s hgh enogh (e.g., θ=.8), frm confently beleves that frm s a weak player (wth hgh cost). Ths optmstc (thogh naccrate) belef leas frm to behave aggressvely, resltng n the (, ) Nash eqlbrm. rprsngly, the more accrate assessment on compettor s cost fncton actally leas to lower eqlbrm profts for frm, as shown n Table 1. Table 1 elefs an eqlbrm profts π () π () θ =. 63 θ = Ths happens becase the belef leas the frm to behave more conservatvely an ts compettor knows ths an ths behaves more aggressvely. For ths reason, havng better nformaton may actally hrt a frm! The observaton that frm oes worse when t has better nformaton llstrates an mportant fference between sngle- an mlt-agent ecson problems. n sngle-agent ecson theory, havng more nformaton can never make the ecson maker worse off. n game theory, however, havng more nformaton (or more precsely, havng t known to the other players that one has more nformaton) can make a player worse off. 3.5 Opton Exercse Generates oth nformaton an Payoff Externaltes s scsse n the ntrocton secton, a key assmpton typcally se n the lteratre s that each agent s payoff s nepenent of the orerng of exercse. Everyone who chooses the rght ecson gets the same rewar regarless of how many others chose ths ecson before or after her (see, e.g., anerjee 199). Whle ths assmpton greatly smplfes the moel, t col lea to some nrealstc eqlbra (sch as the most nforme agent may en p the worst off.). There exst many statons n whch the orerng oes matter an may matter a great eal. Or moel relaxes ths assmpton. ong so allows s to enogenze both the payoff strctre an the orerng of exercse. Or moel shows that the opton exercse of one frm mpacts not only the nformaton set of the other frm bt also the actal payoffs from exercsng the opton. There s extra rewar for beng the frst to exercse the opton (so calle frst-mover avantage ), whle at the same tme prvate nformaton of the frst mover s reveale, enablng the followers to free re on the leaers prvate nformaton. We have ths combne two types of externaltes n or moel: the nformatonal externalty an the payoff externalty. The exstence of asymmetrc nformaton leas natrally to attempts by the nforme to commncate or mslea an to attempts by the 7 JOURNL OF YTE CENCE N YTE ENGNEERNG / Vol. 1, No. 3, eptember, 3

17 ZHU an WEYNT nnforme to learn or respon. Ths nformaton asymmetry may nce gamng behavors. 13 For example, a hgh-cost frm wol try to masqerae as a low-cost player. However, sch sgnals wol have to be creble f they were to change compettors belefs or behavors. One sch creble strategy mght be to make a strategc nvestment n a new technology by ncrrng an rreversble cost. ong so may nce the compettor nto belevng that the frm has nvente a low-cost technology an case t to behave more conservatvely. any other types of nformaton sgnalng exst, bt they are ot of the scope of ths paper. 3.6 Extensons The above moel an analyss can be extene to more peros than the above examples. We jst roll the eqlbrm payoffs of pero t back to the prevos pero (t-1) ntl we reach the begnnng pero of the game. ase on the NPV s of varos possbltes, each frm eces ts best strateges. Fgre 7 llstrates how the moel works n a mlt-pero settng. The nvestment opportnty remans avalable for 3 peros, nstea of as shown n Fgres 5 an 6 (n the case of more peros, same procere apples repeately). nce the opton s stll alve at the en of pero, ts nexercse vale s not zero. nstea, ths vale wol 13 We assme that only actons are creble n commncatng prvate nformaton. Cheap talks lke press release cannot be nformatve: all frms wth speror nformaton prefer to be perceve as low cost, regarless ther tre costs. o there cannot exst an eqlbrm n whch cheap talks affect compettors actons. have to be etermne throgh the opton-exercse eqlbrm n the remanng peros. Notce the path n bol lnes (, ) (, ), frm has alreay nveste n pero 1, bt frm remans ncommtte at the en of the secon pero becase the eman (ths the proft as a tackelberg follower) s stll not hgh enogh to jstfy the nvestment. Frm wats for another pero, an then eces to nvest when the eman s frther p, bt to let the opton expre f the eman s own. f frm nvests, two frms wol share the market n a tackelberg leaer-follower eqlbrm. f frm lets the opton expres wthot exercse, then frm wol enjoy monopoly proft. The payoff from the sbgame-perfect eqlbrm can be calclate by the formla we erve earler. The same procere apples to all other branches of the game tree. We then solve the whole game backwar an fn ot the eqlbrm s (, ), meanng that frm (the better-nform frm) exercse the opton frst whle frm wats. Consstent wth the case n Fgre 5, the opton-exercse eqlbrm s agan seqental, wth the better-nforme frm movng frst. Notce the present vales of the eqlbrm payoff are (, 63) n Fgre 5 an (8, 578) n Fgre 7. Ths, longer opton lfe gves hgher payoff to the less-nforme frm, whle the payoff for the better-nforme frm col be hgher f ts compettor oes not enter or lower f the compettor oes. The reason s that the longer opton lfe gves the nformatonally savantage frm more opportntes to nfer the leaer s prvate nformaton. JOURNL OF YTE CENCE N YTE ENGNEERNG / Vol.1, No. 3, eptember, 3 73

18 trategc Exercse of Real Optons: nvestment ecsons n Technologcal ystems ?..?..? The fgre llstrates how the moel works n a mlt-pero settng. The parameters are the same as n Fgre 5 except that the game s one more pero longer. Usng backwar ncton, the eqlbrm s fon to be (, ). Consstent wth the case n Fgre 5, the opton-exercse eqlbrm s agan seqental, wth the better-nforme frm movng frst. The eqlbrm profts are (8, 578) for frms an respectvely. Ths longer opton lfe gves hgher payoff to frm. Fgre 7 symmetrc nformaton: ore peros f there are more than two frms n the opton-exercse game, for any nval frm what matters s whether one of the (n-1) other frms nvests earler than t. To represent mltple players, we can se a mlt-player game tree. 14 key fference may arse as players are ae, however. s the nmber of frms ncreases, the lkelhoo of nformatonal herng or nvestment cascae may ncrease sbstantally The prpose of or moel s manly to analyze opoly or olgopoly statons, where the nmber of competng frms s lmte. f there are too many players, the fference that each of them col make may become neglgble. That wol be a fferent staton from what we try to moel. 15 ee anerjee (199) an Grenaer (1999) for frther scssons on nformatonal herng an nvestment cascae. 4. Conclsons ost of the real optons lteratre has focse on market envronments wthot strategc nteractons. On the other han, the nstral organzaton lteratre enogenzes market strctre, yet t typcally gnores ncertanty an the opton vale of watng. Conserng the jont effects of ncertanty an competton, ths paper ntegrates the game-theoretc moels of strategc market nteractons wth a real optons approach to nvestment ner ncertanty. Unlke the lteratre, we sppose that frms have ncomplete nformaton abot each other s cost (.e., type). Ths leas to ayesan 74 JOURNL OF YTE CENCE N YTE ENGNEERNG / Vol. 1, No. 3, eptember, 3

19 ZHU an WEYNT Nash eqlbra that we have analyze n etal. The man focs of or research, n contrast to others n the lteratre, s to moel asymmetrc nformaton an ts mpact on opton-exercse strateges an the resltng ayesan Nash eqlbrm. We have attempte to captre ths throgh evelopng a mlt-pero, game-theoretc moel. The ynamc eqlbrm natre of ths moel ffers sgnfcantly from that of the crrent lteratre on real optons. n the stanar moels of opton exercse, the orerng of agents moves s typcally assme to be exogenos an not etermne by any sort of optmzng behavor. n or moel, however, both tmng an orerng are the essence of the game; agents exercse strategcally an the seqence of exercse s enogenos. We have shown that the opton exercse strateges ner asymmetrc nformaton can be very fferent from those ner fll nformaton. Or reslts also show how competton eroes opton vale, an why havng better nformaton may actally hrt a frm. n aton, or reslts complement an exten the lteratre by showng that the orerng of seqental opton exercse reveals prvate nformaton. The frm that nvests frst captres more profts, whle the frm that nvests later gets an opportnty to learn the prvate nformaton of the leaer. Ths opton exercse generates both nformatonal an payoff externaltes n the sense that the exercse ecson of one frm may affect both the payoff an the nformaton set of ts compettors. The reslts obtane here serve to a greater realsm to the theory of technology nvestment ner asymmetrc nformaton. The economc nsghts gane throgh the moel may have certan mplcatons n real nvestment ecsons. For example, frms conserng nvestng n a new technology nee to strategcally conser how ther nvestment payoffs may be affecte by ther compettors moves. They also nee to balance the frst-mover avantage aganst the nformatonal benefts of movng later, as prvate nformaton may be reveale from the seqental exercse of sch real optons n technology markets. 5. cknowlegements We are gratefl to Wllam harpe, lake Johnson, teve Grenaer, Robert Wlson, Jm weeney, av Lenberger, an the semnar partcpants at tanfor Unversty for constrctve scssons on or research. The sal sclamer apples. References [1] ack, K., symmetrc nformaton an optons, Revew of Fnancal tes, Vol.6, pp435-47, [] alwn, C. an K. Clark, olartyn-esgn: n analyss base on the theory of real optons, workng paper, Harvar sness chool, Cambrge,, 1994 [3] anerjee,.v., smple moel of her behavor, Qarterly Jornal of Economcs, Vol.17, No.3, pp , 199 [4] ara,., an T. khopahyay, nformaton technology an bsness performance: Past, present an ftre, n Framng the omans of T anagement: JOURNL OF YTE CENCE N YTE ENGNEERNG / Vol.1, No. 3, eptember, 3 75

20 trategc Exercse of Real Optons: nvestment ecsons n Technologcal ystems Projectng the Ftre throgh the Past, R.W. Zm (e.), Pnnaflex Ecaton Resorces, nc.,. [5] rennan,. an E. chwartz, Evalatng natral resorce nvestments, Jornal of sness, Vol.58, No., pp135-57, [6] Chamley, C. an. Gale, nformaton revelaton an strategc elay n a moel of nvestment, Econometrca, Vol.6, No.5, pp165-85, [7] Cho,.-K., an. Kreps, gnalng games an stable eqlbra, Qarterly Jornal of Economcs Vol.1, No., pp179-1, [8] Constantnes, G.., Warrant exercse an bon converson n compettve market, Jornal of Fnancal Economcs, Vol.13, pp , [9] Cox, J.C., J.E. ngersoll, an.. Ross, n nter temporal general eqlbrm moel of asset prces, Econometrca, Vol.53, pp , [1] etemple, J., an L. elen, general eqlbrm analyss of opton an stock market nteractons, nternatonal Economc Revew, Vol.3, pp79-33, [11] xt,.k. an R.. Pnyck, nvestment ner Uncertanty, Prnceton Unversty Press, Prnceton, NJ, [1] Emanel,.C., Warrant valaton an exercse strategy, Jornal of Fnancal Economcs, Vol.1, pp11-35, [13] Fenberg,. an Trole, J., Game Theory, T Press, Cambrge,, [14] Grenaer,.R., The strategc exercse of optons: evelopment cascaes an overblng n real estate markets, Jornal of Fnance, Vol.51, No.5, pp , [15] Grenaer,.R. an. Wess, nvestment n technologcal nnovatons: n opton prcng approach, Jornal of Fnancal Economcs, Vol.44, pp , [16] Grenaer,.R., nformaton revelaton throgh opton exercse, Revew of Fnancal tes, Vol.1, No.1, pp95-19, [17] Henrcks, K. an. Kovenock, symmetrc nformaton, nformaton externaltes, an effcency: the case of ol exploraton, Ran Jornal of Economcs, Vol., No., pp164-18, [18] Joaqn,.C. an K.C. tler, Compettve nvestment ecsons: a synthess, n New evelopments n the Theory an pplcatons of Real Optons, by.j. rennan an L. Trgeorgs (es.), Oxfor Unversty Press,. [19] Kreps,., P. lgrom, J. Roberts, an R. Wlson, Ratonal cooperaton n the fntely repeate Prsoner s lemma, Jornal of Economc Theory, Vol.7, pp45-5, 198. [] Kreps,. an R. Wlson, eqental eqlbrm, Econometrca, Vol.5, No.4, pp863-94, 198. [1] Kyle,.., Contnos actons an nser trang, Econometrca, Vol.53, pp , [] Lenberger,. G., nvestment cence, Oxfor Unversty Press, New York, NY, [3] aj,. an R. Pnyck, Tme to bl, opton vale, an nvestment ecsons, Jornal of Fnancal Economcs, Vol.18, No.1, pp7-7, JOURNL OF YTE CENCE N YTE ENGNEERNG / Vol. 1, No. 3, eptember, 3

21 ZHU an WEYNT [4] conal, R. an. egel, The vale of watng to nvest, Qarterly Jornal of Economcs, Vol.14, No.1, pp77-7, [5] erton, Robert, C., Nobel Lectre, pplcatons of Opton-Prcng Theory: Twenty-Fve Years Later, ecember 9, The Nobel Fonaton, [6] Paock, J.L.,.R. egel, an J.L. mth, Opton valaton of clams on real assets: the case of offshore petrolem leases, The Qarterly Jornal of Economcs, Vol.13, pp479-58, [7] mt, H.T.J. an L. Trgeorgs, R& Opton trateges, workng paper, Erasms Unversty an Unversty of Chcago, [8] patt, C.. an F.T. terbenz, Warrant exercse, vens, an renvestment polcy, Jornal of Fnance, Vol.43, pp493-56, [9] Tallon, P., R. Kaffman, H. Lcas,. Whnston, an K. Zh, Usng real optons analyss for evalatng ncertan nvestments n nformaton technology, Commncatons of the ssocaton for nformaton ystems (C), Vol.8, pp ,. valable at c.e/kzh/pffles/c_jornalartcle. pf. [3] Trgeorgs, L., Real Optons, The T Press, Cambrge,, [31] Wllams, J.T., Eqlbrm an optons on real assets, Revew of Fnancal tes, Vol.6, pp85-85, [3] Zh, K., Evalatng nformaton technology nvestment: cash flows or growth optons? Workshop on nformaton ystems an Economcs (WE), Charlotte, NC, ec. 11-1, 1999a. [33] Zh, K., trategc nvestment n nformaton Technologes: Real-Optons an Game-Theoretc pproach, Unpblshe octoral ssertaton, tanfor Unversty, tanfor, C, 1999b. Kevn Zh receve hs Ph.. egree from tanfor Unversty an s crrently on the faclty of the Graate chool of anagement, Unversty of Calforna, rvne, U. Hs ssertaton was ttle trategc nvestment n nformaton Technologes: Real-Optons an Game-Theoretc pproach, n whch he poneere an nnovatve approach that ntegrate real optons an game theory for moelng nvestment strateges ner competton. Hs crrent research focses on strategc nvestment n nformaton technologes, economcs of nformaton systems an electronc markets, economc an organzatonal mpacts of nformaton technology, an nformaton transparency n spply chans. Hs research nvolves both economc moelng an emprcal nvestgaton. Hs work has been accepte for pblcaton n jornals sch as nformaton ystems Research, Eropean Jornal of nformaton ystems, Electronc arkets, an Commncatons of the C. One of hs papers has won the est Paper war of the nternatonal Conference on nformaton ystems (C),. He was the recpent of the caemc chevement war of tanfor Unversty, the Faclty Research war of the Unversty of Calforna, an the Charles an Twyla artn Excellence n Teachng war (vote by an exectve stents). ee more nformaton at JOURNL OF YTE CENCE N YTE ENGNEERNG / Vol.1, No. 3, eptember, 3 77

22 trategc Exercse of Real Optons: nvestment ecsons n Technologcal ystems John P. Weyant s Professor of anagement cence an Engneerng at tanfor Unversty, a enor Fellow n the nsttte for nternatonal tes, an rector of the Energy oelng Form (EF) at tanfor Unversty. Professor Weyant earne a../.. n eronatcal Engneerng an stronatcs,.. egrees n Engneerng anagement an n Operatons Research an tatstcs all from Rensselaer Polytechnc nsttte, an a Ph.. n anagement cence wth mnors n Economcs, Operatons Research, an Organzaton Theory from Unversty of Calforna at erkeley. Hs crrent research focses on economc moels for strategc plannng, competton an nvestment n hgh-tech nstres, an analyss of global clmate change polcy optons. He s on the etoral boars of ntegrate ssessment, Envronmental anagement an Polcy, an The Energy Jornal an a member of NFOR, the mercan Economcs ssocaton, an mercan Fnance ssocaton. 78 JOURNL OF YTE CENCE N YTE ENGNEERNG / Vol. 1, No. 3, eptember, 3