Research Article Collaborative Development Planning Model of Supporting Product in Platform Innovation Ecosystem

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1 Mathmatical Problms in Enginring, Articl ID , 7 pags Rsarch Articl Collaborativ Dvlopmnt Planning Modl of Supporting Product in Platform Innovation Ecosystm Wi Zhang, 1, Hamid Rza Karimi, 3 Qingpu Zhang, 1, and Shaobo Wu 4 1 School of Managmnt, Harbin Institut of Tchnology, Harbin , China HIT-UMKC Institut for Entrprnurship and Innovation, Harbin Institut of Tchnology, Harbin , China 3 Dpartmnt of Enginring, Faculty of Enginring and Scinc, Univrsity of Agdr, 4898 Grimstad, Norway 4 School of Businss Planning, Chongqing Tchnology and Businss Univrsity, Chongqing , China Corrspondnc should b addrssd to Shaobo Wu; wushaobo1979@163.com Rcivd 8 Fbruary 014; Accptd 17 March 014; Publishd 3 April 014 Acadmic Editor: Mohammd Chadli Copyright 014 Wi Zhang t al. This is an opn accss articl distributd undr th Crativ Commons Attribution Licns, which prmits unrstrictd us, distribution, and rproduction in any mdium, providd th original work is proprly citd. In ordr to improv th markt valu of th product, th platform ntrpris oftn participats in th dvlopmnt procss of supporting product of mrging industry s platform innovation cosystm. This papr puts forward a rvnu sharing contract btwn th platform company and th supporting company by crating a collaborativ dvlopmnt modl of th supporting product in th cosystm, and this papr studis th platform ntrpris invstmnt rsourc proprty s (complmntary or substitution) impact on th supporting ntrpris R&D fforts and th rvnu sharing factor and analyzs collaborativ dvlopmnt mchanism of supporting product of mrging industry platform innovation cosystm. Th rsarch indicats that whn platform ntrpris and supporting ntrpris s rsourcs ar complmntary, th supporting ntrpris R&D ffort lvl and rvnu sharing cofficint incras as th platform company s invstmnt incrass. Whn platform ntrpris and supporting ntrpris s rsourcs ar substitutiv, th supporting ntrpris s R&D ffort lvl and rvnu sharing cofficint dcras as th platform company s invstmnt incrass. 1. Introduction In today s incrasingly comptitiv markt, tchnological innovation basd on innovativ platform is incrasingly important for mrging industris (such as prsonal computrs, computr oprating systms, and th Intrnt industry). In ordr to mt th divrs nds of usrs and hav accss to xtrnal ntwork conomic ffcts, th platform ownrs usually us th stratgy opning platform tchnology intrfac and ncourag xtrnal innovation organizations (such as ntrpriss, univrsitis, and rsarch instituts) to conduct innovation of complmntary componnts basd on product platform [1. Tchnologis innovativ platform and a rang of complmntary xtrnal componnts togthr provid usrs with a complt st of product or srvic solution [. For xampl, in ordr to improv th product innovation spd and only focus on th rsarch and dvlopmnt of platform tchnology (microprocssor), th Intrnt companis sk th outsid innovation organizations to dvlop th softwar through frly opning th intrfac of platform tchnology and clos intgration btwn hardwar, middlwar, and application softwar that forms th ovrall solution and constituts a platform for innovation cosystms. Hnc, th platform innovation cosystm is an intrdpndnt partnrship stablishd by th cor innovation ntrpriss which opns innovation platform intrfac, and othr participants who hav th product tchnology supplid th disadvantags of cor ntrpris, such as companis, univrsitis, rsarch instituts, upstram supplirs, and downstram distributors, usrs, and vn comptitors [3 5. Each innovation organization forms group rlations which is similar with cosystms within th platform innovation; thy coxist, mutually parasitic, and work togthr to crat valu for consumrs. In platform innovation cosystms, th markt valu is dcidd not only by cor platform products but also by rlvant supporting complmntary componnts. For xampl, in th aircraft platform innovation cosystm in which Airbus is th cor ntrpris, th influnc for th

2 Mathmatical Problms in Enginring product valu is from not only th fuslag structur don by Airbus but also th aircraft ngins and othr supporting complmntary componnts. So th tchnology innovation of ancillary products is so important, and platform companis ar oftn also involvd in th dvlopmnt of complmntary products and cooprat with th supporting ntrpriss. In addition to focusing on th dvlopmnt of platform architctur, Airbus also is involvd in th dvlopmnt of aircraft ngins, thus incrasing th valu of systm products. Thr ar alrady a lot of rsarchs on platform innovation cosystm. Baldwin and Clark [6 andschilling[7 studid th mthods about nginring dsign, platform architctur, and modular innovation in platform cosystm. Suarz and Battls [8 and Murmann and Frnkn [9 analyzd volution of platform tchnology and th tchnical advantags of platform innovation. Prrons [10 studid th platform ntrpriss procss on trust and control mchanisms that maintaind th lading position in platform innovation cosystm. Adnr and Kapoor [11conductd th mpirical rsarch on th tchnology during 196 and 005 yars in th global smiconductor CD quipmnt industry and found that th xtrnal challngs of cor ntrpris innovation prformanc in innovation cosystm dpnds on not only th ntrpriss scal in cosystm but also thir rlativ cology position. Nambisan and Baron [1 studid th main functions of th cor ntrpris in platform innovation cosystm, th slction critria of coopration mmbrs as wll as coopration ruls. Cccagnoli t al. [13 studid th motivation of outsid supporting companis that addd into platform innovation cosystm, including quickly accssing to th stablishd markts, acquiring th corrsponding brand and rputation advantag, and gtting th chancs to larn tchnical knowldg and achiv IPO in thcapitalmarkt.s.scholtnandu.scholtn[14 studid th control mchanisms of platform innovation cosystm. From th xisting litratur, th study of multiplatform innovation cosystm focusd on architctur, ladrship mchanism, th mchanisms forming th advantags, and opration mchanism. Thr ar fwr studis on collaborativ dvlopmnt of complmntary products in platform innovation cosystm, spcially for th supporting product dvlopmnt of platform companis. W also cannot find th suitabl thoris to support th influncing rlationship btwn th natur (complmntary or altrnativ) of th platform ntrpris rsourcs and dvlopmnt fforts and rvnu sharing cofficint of supporting ntrpris. Hnc, our study has som practical and thortical valu. Th rsarch objct in this papr is th collaborativ dvlopmnt of supporting product in platform innovation cosystm undr asymmtric information. In this study, th platform ntrpriss look forward to rducing th costs of supporting ntrpris and improving invstmnt nthusiasm for supporting product dvlopmnt by th bhaviors of ancillary products dvlopmnt. As th fforts of supporting product dvlopmnt ar unobsrvabl by supporting ntrpriss, thy oftn us this information advantag to bring moral hazard. Prvious studis gnrally us th rvnu sharingcontractinprincipal-agntthorytosolvsuchmoral hazard problm, but thr is rarly litratur involvd in principal participation in agnt s production and dvlopmnt activitis. In this papr, w stablishd th principalagnt modl undr platform ntrpriss participating in innovation, proposd rvnu-sharing contract btwn th supporting ntrpriss and platform ntrpriss, studid thinfluncofnatur(complmntaryoraltrnativ)of platform ntrpriss rsourc inputs on rsarch and dvlopmnt ffort and rvnu sharing cofficint of supporting businss, and finally analyzd collaborativ dvlopmnt mchanisms of supporting products in mrging industry platform innovation cosystm.. Modl Assumptions of Supporting Product Collaborativ Dvlopmnt W assumd that a platform innovation cosystm consists of a platform ntrpris which is involvd in dvloping platform product tchnology and a supporting ntrpris which is involvd in dvloping supporting product [ Ths two typs of ntrpriss combin th platform product andsupportingproductandthnprovidthconsumrs with a complt st of product solutions. Th collaboration of platform ntrpris and supporting ntrpris can b shown from th following procsss. (1) Contract Signing. Platform ntrpris first proposs coopration contract to supporting ntrpris; th principal trmsshouldbincluddinrvnusharingmchanisms and th participation commitmnts of platform ntrpris. Supporting ntrpris computs its xpctd rvnu undr th contract; if th xpctd bnfits outwigh th rtaind arnings, it chooss th coopration or rfuss to accpt th contract. () Supporting Product Production. Whn th platform ntrpris achivs its commitmnt to th invstmnt on supporting product, th supporting ntrpris bgins to choos its ffort on dvloping supporting product and implmnt th coopration agrmnt. (3) Incom Paymnts. Aftr th platform ntrpris and supporting ntrpris collaborativly finish th dvlopmnt of complmntary products, th platform ntrpris should pay th supporting ntrpris. In ordr to facilitat conducting our rsarch, w mak th following assumptions. (1) Output of supporting products ar affctd by th fforts of rsarch and dvlopmnt (R&D) th supporting ntrpris paid and xtrnal random factors; output function is π=μ+ε,whrin is th ffort of supporting ntrpris R&D; platform ntrpris cannotobsrvthffortofsupportingntrpris. μ is th influncing of supporting ntrpris ffort on supporting product and ε is th influncing of xtrnal random on production, ε N(0,1). W hav E(π) = E(μ + ε) = μ,var(π) = σ. () Th production cost of supporting ntrpris is affctd by its own ffort of R&D and th influncing

3 Mathmatical Problms in Enginring 3 of platform ntrpris on supporting ntrpris; its production cost function is a quadratic function C(, T), T is th quantity of th rsourc, such as th human and matrial rsourcs invstd to dvlop supporting product by platform ntrpris, and its invstmnt cost is (1/)κT (κ is a constant which is gratr than 0). Th production cost function of supporting ntrpris should mt th conditions C(, T)/ > 0, C(, T)/ >0, which prsnts thatincasofthinvstmntofplatformntrpris not changing, with th ffort of supporting ntrpris invstmnt incrasd, its production cost would b incrasd but th spd of th addition will b fastr; it mts th condition 3 C(, T)/ 3 = 0 undr th quadratic function. Furthrmor, th production cost of supporting ntrpris should mt th condition C(, T)/ T < 0, which prsnts that in cas of th ffort of supporting ntrpris R&D staying constant, with th invstmnt of platform ntrpris incrasd, thcostofsupportingntrpriswillbrducd. (3) Th contract signd by platform ntrpris and supporting ntrpris is includd in th contnts fixd paymnt and distribution of bnfits, assuming th form of contract is R(π) = a + bπ (a > 0, b > 0); a isthfixdpaymntthplatformntrprispaysto supporting ntrpris and b is th distribution ratio of bnfits gaind by supporting ntrpris. 3. Modl Establishmnt of Supporting Product Collaborativ Dvlopmnt According to th prvious assumptions, if th platform ntrpris is risk-nutral, whil th supporting ntrpris is riskavrs, th utility function is with risk-avrs charactristics u(r) = ρr ; ρ is th amount of risk avrsion and th risk costs of supporting ntrpris ar (1/)ρb σ.thrvnu function of platform ntrpris can b xprssd as V 1 =π R(π) 1 κt = (1 b) μ a 1 κt. (1) Th rvnu function of supporting ntrpris can b xprssd as V =E[R (π) C(, T) 1 ρb σ =a+bμ C(, T) 1 ρb σ. In th dcision procss of invsting th month into dvloping th supporting product by platform ntrpris, according to rational conomic man hypothsis, it should maximizitsownintrstsasadcisionobjctiv.thrfor, thproblmofthplatformntrprisistochoos(a, b, T, ) maximizing thir crtainty quivalnt incom: () max (a,b,t,) (1 b) μ a 1 κt, (3) assuming that crtainty incom corrsponding to rsrvation utility of supporting ntrpris is w 0 (w 0 >0). Supporting ntrpris accpts th conditions of th contract providd by ntrpris companis; th conditions it involvd in th dvlopmnt of supporting products ar that its bnfits ar gratr that crtainty incom corrsponding to th rsrvation utility, so th participation constraint condition (IR) is a+bμ C(, T) 1 ρb σ w 0. (4) Asthplatformntrpriscannotobsrvsupporting ntrpris s ffort of invstmnt and natural status ε,for any givn incntiv contract in advanc, th supporting ntrpris always chooss th ffort maximizing thir xpctd utility function; thrfor, th dsirabl ffort of platform ntrpris can only b achivd through inspiring utilitymaximizing bhavior of supporting ntrpris, which must b mt with incntiv compatibility constraints condition (IC): arg max [a + bμ C (, T) 1 ρb σ. (5) Basdonthabov(3) (5), w can transform th problm that platform ntrpris maximizs its own crtainty quivalnt incom into a planning problm H1: max (a,b,t,) (1 b) μ a 1 κt s.t. (IR) a+bμ C(, T) 1 ρb σ w 0 (IC) arg max [a + bμ C (, T) 1 ρb σ. (6) 4. Modl Solution and Analysis In th planning problm H1, only whn th platform ntrpris pays th lowst lvl w 0,thsupportingntrpriswill tak part in th dvlopmnt of supporting products, so formula (4) is with quality; it can b rwrittn as a+bμ C(, T) 1 ρb σ =w 0. (7) Transforming th form of formula (4): a=w 0 bμ+c(, T) + 1 ρb σ. (8) Substituting formula (8) into th objctiv function of formula (3), liminating a, w hav V 1 =μ 1 ρb σ C(, T) 1 κt. (9) Solving th incntiv compatibility constraints conditions of (5) and a drivation of,whav μb C (, T) =0. (10)

4 4 Mathmatical Problms in Enginring According to formula (10), w can gt b = C(, T)/μ, and substituting formula (8) into it and liminating b,w hav a nw optimization problm H: max (T,) μ ρσ μ (, T) [ C C(, T) 1 κt w 0. (11) In formula (11), by giving th spcific xprssion of C(, T), it is asy to obtain th optimal invstmnt T and th ffort of supporting ntrpris. And thn by substituting into (10), w can obtain th rvnu sharing cofficint inthcontract.howvr,ourconcrnisthinfluncof natur (complmntary or altrnativ) of platform ntrpriss rsourc inputs on rsarch and dvlopmnt ffort and rvnu sharing cofficint of supporting businss, so w nd to stablish th rlationship btwn inputs T for supporting product by platform ntrpris and R&D ffort paid by supporting ntrpris. In th formula (11), gt a drivation for and st it to zro; th optimal first-ordr conditions can b obtaind as follows: μ ρσ C (, T) C (, T) C (, T) μ =0. (1) Formula (11) prsnts inputs T of platformntrpris;w can obtain th ffort of supporting ntrpris by mploying formula (1), in which w can s as th function of T.Using a drivation for T, w can obtain th influnc of platform ntrpris inputs T on th lvl of ffort of supporting ntrpris: { ρσ C (, T) μ [ + C (, T) } T +[ ρσ μ C (, T) C (, T) T 3 C (, T) T + ρσ C (, T) 3 C (, T) μ 3 + C (, T) T =0. + ρσ C (, T) μ (13) As th cost function C(, T) is a quadratic function, obtain 3 C(, T)/ 3 =0,sousingformula(13), w hav T = (ρσ μ C (, T) C (, T) T + ρσ μ C (, T) ( ρσ C (, T) μ [ 3 C (, T) T + C (, T) T ) 1 + C (, T) ). (14) Considring th abov analyss, w will analyz th influnc of natur (complmntary or altrnativ) of platform ntrpriss rsourc inputs on R&D ffort of supporting businss basd on formula (14). In prvious assumptions, C(, T)/ > 0, C(, T)/ > 0,sothpositivand ngativ of formula (14) dpnd on th positiv and ngativ of C(, T)/ T and 3 C(, T)/ T.Inthcost function of supporting ntrpris C(, T), C(, T)/ is thmarginalcostofffortpaidbysupportingntrpris, and C(, T)/ T is th influnc of platform ntrpris rsourc inputs on th marginal cost of ffort paid by supporting ntrpris. If C(, T)/ T < 0, itprsnts that th marginal cost of ffort paid by supporting ntrpris will rduc with th inputs of platform ntrpris; that is, th inputs of platform ntrpris and supporting ntrpris ar complmntary; if C(, T)/ T > 0, itprsntsthat th marginal cost of ffort paid by supporting ntrpris will incras with th inputs of platform ntrpris; that is, th inputs of platform ntrpris and supporting ntrpris ar substitutiv. C(, T)/ is th scond drivativ of supporting ntrpris s R&D inputs ffort, that is, th chang rat of th first drivativ C(, T)/ ;th gomtric maning of th first drivativ is th slop of th cost curv, whil th gomtric maning of th scond drivativ is th curvatur of th cost curv. In th complmntary situation, that is, C(, T)/ T < 0, th mor inputs th platform ntrpris invsts for supporting product dvlopmnt, th smallr th slop of C(, T) is.inordrtoguarantthatthslopofthcostcurv C(, T) ofthsupportingntrprisffortundrthsituation of high inputs of platform ntrpris is always smallr than th low inputs of platform ntrpris, it has to mak th curvatur of th cost curv C(, T) undr th situation of high inputs of platform ntrpris smallr than th curvatur of th cost curv C(, T) of th supporting ntrpris ffort undr th situation of low inputs of platform ntrpris, as shown in Figur 1. Wcansthatthcostcurvofsupporting ntrpris in th situation of platform ntrpris low inputs is obviously stpr than th situation of high inputs of platform ntrpris. That is, in th complmntary situation, thinfluncofplatformntrprisinputsonthchang rat of marginal cost C(, T) can mt 3 C(, T)/ T < 0 [18.Hnc,basdonthprviousanalyss,wcanknow that whn th inputs of platform ntrpris and supporting ntrpris ar complmntary, thr ar th conditions that C(, T)/ T < 0 and 3 C(, T)/ T < 0.Incontrast, in th substitutiv situation, th cost curv of supporting ntrpris in th situation of platform ntrpris high inputs is obviously stpr than th situation of low inputs of platform ntrpris, as shown in Figur ; thr ar th conditions that C(, T)/ T > 0 and 3 C(, T)/ T > 0. Considringprviousassumptionsandthabovanalyss about influnc of natur (complmntary or altrnativ) of platform ntrpriss rsourc inputs on R&D ffort of supporting ntrpris, undr th complmntary situation, as C(, T)/ T < 0, 3 C(, T)/ T < 0,and C(, T)/ > 0, C(, T)/ >0,whav ρσ μ C (, T) [ + C (, T) >0. (15)

5 Mathmatical Problms in Enginring 5 C(, T) Y axis X axis C(, T l ) C(, T h ) Figur 1: Th cost curv of supporting ntrpris undr th complmntary situation. C(, T) Y axis X axis C(, T l ) C(, T h ) Figur : Th cost curv of supporting ntrpris undr th substitutiv situation. (ρσ /μ ) ( C(, T)/ ) ( C(, T)/ T) + (ρσ /μ ) ( C(, T)/ ) ( 3 C(, T)/ T)+( C(, T)/ T) > 0. It is asy to find that / T < 0 in formula (14). So w can gt conclusion : in th nw industry platform innovation cosystm, whn th inputs of platform ntrpris andsupportingntrprisarsubstitutiv,thlvlofffort paid by supporting ntrpris will rduc if platform ntrpris incrass its inputs. From conclusion 1 and conclusion, w can know that in th nw industry platform innovation cosystm, if th rsourc inputs of platform ntrpris and supporting ntrpris ar complmntary in collaborativ dvlopmnt supporting products, th participant of platform ntrpris has th incntivs for tchnology innovation inputs of supporting ntrpris; th possibl rason is that th incras of platform ntrpris complmntary inputs would incras th possibility of th succss dvloping th supporting product.ifthrsourcinputsofplatformntrprisandsupporting ntrpris ar substitutiv in collaborativ dvlopmnt supporting products, th inputs of platform ntrpris will rduc th motivation of supporting ntrpris incrasing tchnology innovation inputs; th possibl rason is that thsupportingntrprisgivsmorhoptothplatform ntrpris to incras its inputs and it has a lazy motivation and thus is mor willing to lt th platform ntrpris tak risk arising from inputs in product dvlopmnt. Th following is to analyz th impact of rvnu sharing cofficint b on th inputs of platform ntrpris; by th formula (10), w can obtain b = C(, T)/μ. Establishing th rlationship btwn b and th inputs T of platform ntrpris, a drivation for T, w hav b T = 1 C (, T) μ [ T + C (, T). (17) T Substituting formula (14)intoformula(17), w can obtain As (ρσ /μ ) ( C(, T)/ ) ( C(, T)/ T) < 0, (ρσ /μ ) ( C(, T)/ ) ( 3 C(, T)/ T) < 0,whav (ρσ /μ ) ( C(, T)/ ) ( C(, T)/ T) + (ρσ /μ ) ( C(, T)/ ) ( 3 C(, T)/ T)+( C(, T)/ T) < 0. It is asy to find that / T > 0 in formula (14). So w can gt conclusion 1: in th nw industry platform innovation cosystm, whn th inputs of platform ntrpris and supporting ntrpris ar complmntary, th lvl of ffort paid by supporting ntrpris will incras if platform ntrpris incrass its inputs. Considring prvious assumptions and th abov analyss about influnc of natur (complmntary or altrnativ) of platform ntrpriss rsourc inputs on cost function of supporting ntrpris, undr th substitutiv situation, as C(, T)/ T > 0, 3 C(, T)/ T > 0,and C(, T)/ > 0, C(, T)/ >0,whav ρσ μ C (, T) [ + C (, T) >0. (16) As (ρσ /μ ) ( C(, T)/ ) ( C(, T)/ T) > 0, (ρσ /μ ) ( C(, T)/ ) ( 3 C(, T)/ T) > 0,whav b T = C (, T) (ρσ μ 3 C (, T) T (μ{ ρσ C (, T) μ [ C (, T) ) 1 + C (, T) }). (18) Analyzing formula (18), considring prvious assumptions and th abov analyss about influnc of natur (complmntary or altrnativ) of platform ntrpriss rsourc inputs on cost function of supporting ntrpris, undr th complmntary situation, as C(, T)/ T < 0, 3 C(, T)/ T < 0,and C(, T)/ > 0, C(, T)/ >0,w hav μ{ ρσ C (, T) μ [ + C (, T) }>0, ρσ μ C (, T) 3 C (, T) T C (, T) <0, so b T >0. (19)

6 6 Mathmatical Problms in Enginring So w can gt conclusion 3: in th nw industry platform innovation cosystm, whn th inputs of platform ntrpris and supporting ntrpris ar complmntary, th rvnu sharing cofficint of supporting ntrpris will incras if platform ntrpris incrass its inputs. Analyzing formula (18), considring prvious assumptionsandthabovanalyssaboutinfluncofnatur(complmntary or altrnativ) of platform ntrpriss rsourc inputs on cost function of supporting ntrpris, undr th substitutiv situation, as C(, T)/ T > 0, 3 C(, T)/ T > 0, C(, T)/ > 0, and C(, T)/ >0,w hav μ{ ρσ C (, T) μ [ + C (, T) }>0, ρσ C (, T) 3 C (, T) μ T C (, T) >0, so b T <0. (0) So w can gt conclusion 4: in th nw industry platform innovation cosystm, whn th inputs of platform ntrpris andsupportingntrprisarsubstitutiv,thrvnusharing cofficint of supporting ntrpris will rduc if platform ntrpris incrass its inputs. From conclusion 3 and conclusion 4 w can know that in th nw industry platform innovation cosystm, whn th rsourc inputs of platform ntrpris and supporting ntrpris ar complmntary in collaborativ dvlopmnt supporting products, if th platform ntrpris incrass its inputs for dvloping th supporting product, it should incras th rvnu sharing cofficint of supporting ntrpris ltting it tak mor risks. Th possibl rason is that thinputsofplatformntrprisrducthmarginalcost of supporting ntrpris for tchnology innovation and, in contrast, incras its marginal rvnu, so th supporting ntrpris will mak its marginal cost qual to marginal rvnu, and platform ntrpris would lik to incras rvnu sharing cofficint to incras th inputs of supporting ntrpris. In contrast, whn th rsourc inputs of platform ntrpris and supporting ntrpris ar substitutiv in collaborativ dvlopmnt supporting products, if th platform ntrpris incrass its inputs for dvloping th supporting product, it should rduc th rvnu sharing cofficint of supporting ntrpris ltting it tak fwr risks. Th possibl rason is that th inputs of platform ntrpris may incras th marginal cost of supporting ntrpris for tchnology innovation and, in contrast, rduc its marginal rvnu. It is difficult for platform ntrpris to incras th inputs of supporting ntrpris by incrasing rvnu sharing cofficint. 5. Conclusion Th valu of nw industry platform innovation cosystm dpnds on not only th ffct of platform ntrpris on platform product but also th valu of supporting product, so platform ntrpris always participats in th dvlopmnt of supporting product. From th prvious analyss, w can find supporting ntrpris R&D ffort and rvnu sharing cofficint in collaborativ procss dpnding on th natur of platform ntrpris inputs on supporting product. (1) Whn th inputs of platform ntrpris and supporting ntrpris ar complmntary, incrasing platform ntrpris inputs will gnrat th positiv incntivs for supporting ntrpris. In contrast, whn th inputs of platform ntrpris and supporting ntrpris ar substitutiv, incrasing platform ntrpris inputs will gnrat th ngativ incntivs for supporting ntrpris. Th conclusions for constructing co-innovation platform hav two inspirations: firstly, for th platform ntrpriss in mrging industry innovation cosystm, thy should choos partnrs with complmntary rsourcs in building innovation cosystm procss. For xampl, whn IBM built innovation cosystm, itonlyfocusdonhardwardvlopmntplatform;thgnral partnrs it chos ar with middlwar and application softwar dvlopmnt capabilitis which ar complmntary for it. Scondly, if in th platform innovation cosystm th platform ntrpris and supporting ntrpris hav sparat rsourc substitution, platform ntrpris should b lss involvd in th dvlopmnt of supporting product, bcaus whn th rsourcs ar substitutiv, incrasing th inputs of platform ntrpris will rduc th nthusiasm of supporting ntrpriss, an incras of supporting ntrpris lazy motivation; if th platform ntrpris and supporting ntrpris ar th complmntary rsourcs, th formr should incras its inputs for dvloping supporting product; this is bcaus incrasing inputs of platform ntrpris incras th liklihood of succssful product dvlopmnt, which also has a good incntiv for supporting ntrpris. () Whn th inputs of platform ntrpris and supporting ntrpris ar complmntary, th rvnu sharing cofficint of supporting ntrpris will incras if platform ntrpris incrass its inputs. Whn th inputs of platform ntrprisandsupportingntrprisarsubstitutiv,th rvnu sharing cofficint of supporting ntrpris will rduc if platform ntrpris incrass its inputs. Hnc, in th contract dsign procss, platform ntrpris should tak full account of th natur of dvlopmnt inputs for supporting product. Undr th complmntary situation, th contract should incras th proportion of variabl incom of supporting ntrpris, rducing fixd pay part, so that th supporting ntrpris should tak mor dvlopmnt risks; undr th substitutiv situation, th contract should rduc thproportionofvariablincomofsupportingntrpris and incras th portion of th fixd paymnt, so th supporting ntrpris taks lss dvlopmnt risks. This conclusion has som thortical rfrnc valu for th contract dsign of supporting product s collaborativ dvlopmnt in nw industry platform innovation cosystm. Conflict of Intrsts Th authors dclar that thr is no conflict of intrsts rgarding th publication of this papr.

7 Mathmatical Problms in Enginring 7 Acknowldgmnt This work was supportd by National Natural Scinc Funds of China (Grant nos , , and ), Humanitis and Social Scincs Youth Foundation of Chins Ministry of Education (Grant no. 3YJC630166), and th National Social Scinc Foundation of China (Grant no. 1CTQ09). Rfrncs [1 W. Zhang and Q. Zhang, Multi-stag valuation and slction in th formation procss of complx crativ solution, Quality &Quantity,013. [ A. Gawr and M. Cusumano, How companis bcom platform ladrs, MIT Sloan Managmnt Rviw, vol. 49, no., pp.8 35,008. [3 S. Yin, H. Luo, and S. Ding, Ral-tim implmntation of faulttolrant control systms with prformanc optimization, IEEE Transactions on Industrial Elctronics, vol.64,no.5,pp , 014. [4 S. Yin, G. Wang, and H. Karimi, Data-drivn dsign of robust fault dtction systm for wind turbins, Mchatronics,013. [5W.Zhang,Q.Zhang,andH.Karimi, Skingthimportant nods of complx ntworks in product R&D tam basd on fuzzy AHP and TOPSIS, Mathmatical Problms in Enginring,vol.013,ArticlID3759,9pags,013. [6C.Y.BaldwinandK.B.Clark,Dsign Ruls: Th Powr of Modularity, MIT Prss, Cambridg, Mass, USA, 000. [7 M. A. Schilling, Toward a gnral modular systms thory and its application to intrfirm product modularity, Acadmy of Managmnt Rviw,vol.5,no.,pp ,000. [8 F. Suarz and F. Battls, For tchnological dominanc: an intgratd framwork, Rsarch Policy, vol.33,no.,pp.71 86, 004. [9 J.P.MurmannandK.Frnkn, Towardasystmaticframwork for rsarch on dominant dsigns, tchnological innovations, and industrial chang, Rsarch Policy, vol. 35, no. 7, pp , 006. [10 R. K. Prrons, Th opn kimono: how Intl balancs trust and powr to maintain platform ladrship, Rsarch Policy,vol.38, no. 8, pp , 009. [11 R. Adnr and R. Kapoor, Valu cration in innovation cosystms: how th structur of tchnological intrdpndnc affcts firm prformanc in nw tchnology gnrations, Stratgic Managmnt Journal,vol.31,no.3,pp ,010. [1 S. Nambisan and R. A. Baron, Entrprnurship in innovation cosystms: ntrprnurs slf-rgulatory procsss and thir implications for nw vntur succss, Entrprnurship Thory and Practic,vol.37,no.5,pp ,01. [13 M.Cccagnoli,C.Forman,P.Huang,andD.J.Wu, Cocration of valuina platform cosystm: th cas of ntrpris softwar, MIS Quartrly,vol.36,no.1,pp.63 90,01. [14 S. Scholtn and U. Scholtn, Platform-basd innovation managmnt: dircting xtrnal innovational fforts in platform cosystms, th Knowldg Economy,vol.,no.3,pp , 01. [15 S. Yin, S. Ding, A. Haghani, and H. Hao, Data-drivn monitoring for stochastic systms and its application on batch procss, Intrnational Systms Scinc,vol.44,no.7,pp , 013. [16 S. Yin, S. Ding, A. Haghani, H. Hao, and P. Zhang, A comparison study of basic data drivn fault diagnosis and procss monitoring mthods on th bnchmark Tnnss Eastman procss, Procss Control, vol., no. 9, pp , 01. [17 S. Yin, X. Yang, and H. R. Karimi, Data-drivn adaptiv obsrvr for fault diagnosis, Mathmatical Problms in Enginring,vol.01,ArticlID83836,1pags,01. [18 A. V. Iyr, L. B. Schwarz, and S. A. Znios, A principal-agnt modl for product spcification and production, Managmnt Scinc,vol.51,no.1,pp ,005.

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