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Research Article Collaborative Development Planning Model of Supporting Product in Platform Innovation Ecosystem Wei Zhang, 1,2 Hamid Reza Karimi, 3 Qingpu Zhang, 1,2 and Shaobo Wu 4 1 School of Management, Harbin Institute of Technology, Harbin 150001, China 2 HIT-UMKC Institute for Entrepreneurship and Innovation, Harbin Institute of Technology, Harbin 150030, China 3 Department of Engineering, Faculty of Engineering and Science, University of Agder, 4898 Grimstad, Norway 4 School of Business Planning, Chongqing Technology and Business University, Chongqing 400067, China Correspondence should be addressed to Shaobo Wu; [email protected] Received 28 February 2014; Accepted 17 March 2014; Published 3 April 2014 Academic Editor: Mohammed Chadli Copyright © 2014 Wei Zhang et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In order to improve the market value of the product, the platform enterprise oſten participates in the development process of supporting product of emerging industry’s platform innovation ecosystem. is paper puts forward a revenue sharing contract between the platform company and the supporting company by creating a collaborative development model of the supporting product in the ecosystem, and this paper studies the platform enterprise investment resource property’s (complementary or substitution) impact on the supporting enterprise R&D efforts and the revenue sharing factor and analyzes collaborative development mechanism of supporting product of emerging industry platform innovation ecosystem. e research indicates that when platform enterprise and supporting enterprise’s resources are complementary, the supporting enterprise R&D effort level and revenue sharing coefficient increase as the platform company’s investment increases. When platform enterprise and supporting enterprise’s resources are substitutive, the supporting enterprise’s R&D effort level and revenue sharing coefficient decrease as the platform company’s investment increases. 1. Introduction In today’s increasingly competitive market, technological innovation based on innovative platform is increasingly important for emerging industries (such as personal comput- ers, computer operating systems, and the Internet industry). In order to meet the diverse needs of users and have access to external network economic effects, the platform owners usu- ally use the strategy opening platform technology interface and encourage external innovation organizations (such as enterprises, universities, and research institutes) to conduct innovation of complementary components based on product platform [1]. Technologies innovative platform and a range of complementary external components together provide users with a complete set of product or service solution [2]. For example, in order to improve the product innovation speed and only focus on the research and development of platform technology (microprocessor), the Internet companies seek the outside innovation organizations to develop the soſtware through freely opening the interface of platform technology and close integration between hardware, middleware, and application soſtware that forms the overall solution and constitutes a platform for innovation ecosystems. Hence, the platform innovation ecosystem is an inter- dependent partnership established by the core innovation enterprises which opens innovation platform interface, and other participants who have the product technology supplied the disadvantages of core enterprise, such as companies, universities, research institutes, upstream suppliers, and downstream distributors, users, and even competitors [35]. Each innovation organization forms group relations which is similar with ecosystems within the platform innovation; they coexist, mutually parasitic, and work together to create value for consumers. In platform innovation ecosystems, the market value is decided not only by core platform products but also by relevant supporting complementary components. For example, in the aircraſt platform innovation ecosystem in which Airbus is the core enterprise, the influence for the Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2014, Article ID 690589, 7 pages http://dx.doi.org/10.1155/2014/690589

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Page 1: Research Article Collaborative Development Planning Model ...downloads.hindawi.com/journals/mpe/2014/690589.pdf · Research Article Collaborative Development Planning Model of Supporting

Research ArticleCollaborative Development Planning Model ofSupporting Product in Platform Innovation Ecosystem

Wei Zhang,1,2 Hamid Reza Karimi,3 Qingpu Zhang,1,2 and Shaobo Wu4

1 School of Management, Harbin Institute of Technology, Harbin 150001, China2HIT-UMKC Institute for Entrepreneurship and Innovation, Harbin Institute of Technology, Harbin 150030, China3Department of Engineering, Faculty of Engineering and Science, University of Agder, 4898 Grimstad, Norway4 School of Business Planning, Chongqing Technology and Business University, Chongqing 400067, China

Correspondence should be addressed to Shaobo Wu; [email protected]

Received 28 February 2014; Accepted 17 March 2014; Published 3 April 2014

Academic Editor: Mohammed Chadli

Copyright © 2014 Wei Zhang et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

In order to improve the market value of the product, the platform enterprise often participates in the development process ofsupporting product of emerging industry’s platform innovation ecosystem. This paper puts forward a revenue sharing contractbetween the platform company and the supporting company by creating a collaborative development model of the supportingproduct in the ecosystem, and this paper studies the platform enterprise investment resource property’s (complementary orsubstitution) impact on the supporting enterprise R&D efforts and the revenue sharing factor and analyzes collaborativedevelopment mechanism of supporting product of emerging industry platform innovation ecosystem. The research indicates thatwhen platform enterprise and supporting enterprise’s resources are complementary, the supporting enterprise R&D effort level andrevenue sharing coefficient increase as the platform company’s investment increases. When platform enterprise and supportingenterprise’s resources are substitutive, the supporting enterprise’s R&D effort level and revenue sharing coefficient decrease as theplatform company’s investment increases.

1. Introduction

In today’s increasingly competitive market, technologicalinnovation based on innovative platform is increasinglyimportant for emerging industries (such as personal comput-ers, computer operating systems, and the Internet industry).In order to meet the diverse needs of users and have access toexternal network economic effects, the platform owners usu-ally use the strategy opening platform technology interfaceand encourage external innovation organizations (such asenterprises, universities, and research institutes) to conductinnovation of complementary components based on productplatform [1]. Technologies innovative platform and a range ofcomplementary external components together provide userswith a complete set of product or service solution [2]. Forexample, in order to improve the product innovation speedand only focus on the research and development of platformtechnology (microprocessor), the Internet companies seekthe outside innovation organizations to develop the software

through freely opening the interface of platform technologyand close integration between hardware, middleware, andapplication software that forms the overall solution andconstitutes a platform for innovation ecosystems.

Hence, the platform innovation ecosystem is an inter-dependent partnership established by the core innovationenterprises which opens innovation platform interface, andother participants who have the product technology suppliedthe disadvantages of core enterprise, such as companies,universities, research institutes, upstream suppliers, anddownstream distributors, users, and even competitors [3–5].Each innovation organization forms group relations whichis similar with ecosystems within the platform innovation;they coexist, mutually parasitic, and work together to createvalue for consumers. In platform innovation ecosystems, themarket value is decided not only by core platform productsbut also by relevant supporting complementary components.For example, in the aircraft platform innovation ecosystemin which Airbus is the core enterprise, the influence for the

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2014, Article ID 690589, 7 pageshttp://dx.doi.org/10.1155/2014/690589

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2 Mathematical Problems in Engineering

product value is from not only the fuselage structure doneby Airbus but also the aircraft engines and other supportingcomplementary components. So the technology innovationof ancillary products is so important, and platformcompaniesare often also involved in the development of complementaryproducts and cooperate with the supporting enterprises.In addition to focusing on the development of platformarchitecture, Airbus also is involved in the development ofaircraft engines, thus increasing the value of system products.

There are already a lot of researches on platform inno-vation ecosystem. Baldwin and Clark [6] and Schilling [7]studied the methods about engineering design, platformarchitecture, and modular innovation in platform ecosystem.Suarez and Battles [8] and Murmann and Frenken [9]analyzed evolution of platform technology and the technicaladvantages of platform innovation. Perrons [10] studied theplatform enterprises’ process on trust and control mech-anisms that maintained the leading position in platforminnovation ecosystem. Adner and Kapoor [11] conducted theempirical research on the technology during 1962 and 2005years in the global semiconductor CD equipment industryand found that the external challenges of core enterpriseinnovation performance in innovation ecosystem dependson not only the enterprises scale in ecosystem but alsotheir relative ecology position. Nambisan and Baron [12]studied the main functions of the core enterprise in platforminnovation ecosystem, the selection criteria of cooperationmembers as well as cooperation rules. Ceccagnoli et al.[13] studied the motivation of outside supporting companiesthat added into platform innovation ecosystem, includingquickly accessing to the established markets, acquiring thecorresponding brand and reputation advantage, and gettingthe chances to learn technical knowledge and achieve IPO inthe capital market. S. Scholten and U. Scholten [14] studiedthe control mechanisms of platform innovation ecosystem.

From the existing literature, the study of multiplatforminnovation ecosystem focused on architecture, leadershipmechanism, the mechanisms forming the advantages, andoperation mechanism. There are fewer studies on collabo-rative development of complementary products in platforminnovation ecosystem, especially for the supporting productdevelopment of platform companies. We also cannot findthe suitable theories to support the influencing relationshipbetween the nature (complementary or alternative) of theplatform enterprise resources and development efforts andrevenue sharing coefficient of supporting enterprise. Hence,our study has some practical and theoretical value.

The research object in this paper is the collaborativedevelopment of supporting product in platform innovationecosystem under asymmetric information. In this study, theplatform enterprises look forward to reducing the costs ofsupporting enterprise and improving investment enthusiasmfor supporting product development by the behaviors ofancillary products development. As the efforts of supportingproduct development are unobservable by supporting enter-prises, they often use this information advantage to bringmoral hazard. Previous studies generally use the revenuesharing contract in principal-agent theory to solve suchmoralhazard problem, but there is rarely literature involved in

principal participation in agent’s production and develop-ment activities. In this paper, we established the principal-agent model under platform enterprises participating ininnovation, proposed revenue-sharing contract between thesupporting enterprises and platform enterprises, studiedthe influence of nature (complementary or alternative) ofplatform enterprises’ resource inputs on research and devel-opment effort and revenue sharing coefficient of supportingbusiness, and finally analyzed collaborative developmentmechanisms of supporting products in emerging industryplatform innovation ecosystem.

2. Model Assumptions of Supporting ProductCollaborative Development

We assumed that a platform innovation ecosystem consistsof a platform enterprise which is involved in developingplatform product technology and a supporting enterprisewhich is involved in developing supporting product [15–17].These two types of enterprises combine the platform productand supporting product and then provide the consumerswith a complete set of product solutions.The collaboration ofplatform enterprise and supporting enterprise can be shownfrom the following processes.

(1) Contract Signing. Platform enterprise first proposescooperation contract to supporting enterprise; the principalterms should be included in revenue sharing mechanismsand the participation commitments of platform enterprise.Supporting enterprise computes its expected revenue underthe contract; if the expected benefits outweigh the retainedearnings, it chooses the cooperation or refuses to accept thecontract.

(2) Supporting Product Production. When the platformenterprise achieves its commitment to the investment onsupporting product, the supporting enterprise begins tochoose its effort on developing supporting product andimplement the cooperation agreement.

(3) Income Payments. After the platform enterprise and sup-porting enterprise collaboratively finish the development ofcomplementary products, the platform enterprise should paythe supporting enterprise.

In order to facilitate conducting our research, we makethe following assumptions.

(1) Output of supporting products are affected by theefforts of research and development (R&D) the sup-porting enterprise paid and external random factors;output function is 𝜋 = 𝜇𝑒 + 𝜀, wherein 𝑒 is the effortof supporting enterprise R&D; platform enterprisecannot observe the effort of supporting enterprise.𝜇 is the influencing of supporting enterprise efforton supporting product and 𝜀 is the influencing ofexternal random on production, 𝜀 ∼ 𝑁(0, 1). We have𝐸(𝜋) = 𝐸(𝜇𝑒 + 𝜀) = 𝜇𝑒, var(𝜋) = 𝜎2.

(2) The production cost of supporting enterprise isaffected by its own effort of R&D and the influencing

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Mathematical Problems in Engineering 3

of platform enterprise on supporting enterprise; itsproduction cost function is a quadratic function𝐶(𝑒, 𝑇), 𝑇 is the quantity of the resource, such as thehuman and material resources invested to developsupporting product by platform enterprise, and itsinvestment cost is (1/2)𝜅𝑇2 (𝜅 is a constant whichis greater than 0). The production cost function ofsupporting enterprise should meet the conditions𝜕𝐶(𝑒, 𝑇)/𝜕𝑒 > 0, 𝜕2𝐶(𝑒, 𝑇)/𝜕2𝑒 > 0, which presentsthat in case of the investment of platform enterprisenot changing, with the effort of supporting enterpriseinvestment increased, its production cost would beincreased but the speed of the addition will be faster;it meets the condition 𝜕3𝐶(𝑒, 𝑇)/𝜕3𝑒 = 0 under thequadratic function. Furthermore, the production costof supporting enterprise should meet the condition𝜕𝐶(𝑒, 𝑇)/𝜕𝑇 < 0, which presents that in case of theeffort of supporting enterprise R&D staying constant,with the investment of platform enterprise increased,the cost of supporting enterprise will be reduced.

(3) The contract signed by platform enterprise and sup-porting enterprise is included in the contents fixedpayment and distribution of benefits, assuming theform of contract is 𝑅(𝜋) = 𝑎 + 𝑏𝜋 (𝑎 > 0, 𝑏 > 0);𝑎 is the fixed payment the platform enterprise pays tosupporting enterprise and 𝑏 is the distribution ratio ofbenefits gained by supporting enterprise.

3. Model Establishment of Supporting ProductCollaborative Development

According to the previous assumptions, if the platform enter-prise is risk-neutral, while the supporting enterprise is risk-averse, the utility function is with risk-averse characteristics𝑢(𝑅) = −𝑒

𝜌𝑅; 𝜌 is the amount of risk aversion and the riskcosts of supporting enterprise are (1/2)𝜌𝑏2𝜎2. The revenuefunction of platform enterprise can be expressed as

𝑉1= 𝜋 − 𝑅 (𝜋) −

1

2

𝜅𝑇2= (1 − 𝑏) 𝜇𝑒 − 𝑎 −

1

2

𝜅𝑇2. (1)

The revenue function of supporting enterprise can beexpressed as

𝑉2= 𝐸 [𝑅 (𝜋) − 𝐶 (𝑒, 𝑇)] −

1

2

𝜌𝑏2𝜎2

= 𝑎 + 𝑏𝜇𝑒 − 𝐶 (𝑒, 𝑇) −

1

2

𝜌𝑏2𝜎2.

(2)

In the decision process of investing the month intodeveloping the supporting product by platform enterprise,according to rational economic man hypothesis, it shouldmaximize its own interests as a decision objective. Therefore,the problem of the platform enterprise is to choose (𝑎, 𝑏, 𝑇, 𝑒)maximizing their certainty equivalent income:

max(𝑎,𝑏,𝑇,𝑒)

(1 − 𝑏) 𝜇𝑒 − 𝑎 −

1

2

𝜅𝑇2, (3)

assuming that certainty income corresponding to reservationutility of supporting enterprise is 𝑤

0(𝑤0> 0).

Supporting enterprise accepts the conditions of the con-tract provided by enterprise companies; the conditions itinvolved in the development of supporting products are thatits benefits are greater that certainty income correspondingto the reservation utility, so the participation constraintcondition (IR) is

𝑎 + 𝑏𝜇𝑒 − 𝐶 (𝑒, 𝑇) −

1

2

𝜌𝑏2𝜎2≥ 𝑤0. (4)

As the platform enterprise cannot observe supportingenterprise’s effort of investment 𝑒 and natural status 𝜀, for anygiven incentive contract in advance, the supporting enter-prise always chooses the effort 𝑒 maximizing their expectedutility function; therefore, the desirable effort 𝑒 of platformenterprise can only be achieved through inspiring utility-maximizing behavior of supporting enterprise, which mustbe met with incentive compatibility constraints condition(IC):

𝑒 ∈ arg max [𝑎 + 𝑏𝜇𝑒 − 𝐶 (𝑒, 𝑇) − 12

𝜌𝑏2𝜎2] . (5)

Based on the above (3)∼(5), we can transform the prob-lem that platform enterprise maximizes its own certaintyequivalent income into a planning problem H1:

max(𝑎,𝑏,𝑇,𝑒)

(1 − 𝑏) 𝜇𝑒 − 𝑎 −

1

2

𝜅𝑇2

s.t. (IR) 𝑎 + 𝑏𝜇𝑒 − 𝐶 (𝑒, 𝑇) − 12

𝜌𝑏2𝜎2≥ 𝑤0

(IC) 𝑒 ∈ arg max [𝑎 + 𝑏𝜇𝑒 − 𝐶 (𝑒, 𝑇) − 12

𝜌𝑏2𝜎] .

(6)

4. Model Solution and Analysis

In the planning problem H1, only when the platform enter-prise pays the lowest level 𝑤

0, the supporting enterprise will

take part in the development of supporting products, soformula (4) is with equality; it can be rewritten as

𝑎 + 𝑏𝜇𝑒 − 𝐶 (𝑒, 𝑇) −

1

2

𝜌𝑏2𝜎2= 𝑤0. (7)

Transforming the form of formula (4):

𝑎 = 𝑤0− 𝑏𝜇𝑒 + 𝐶 (𝑒, 𝑇) +

1

2

𝜌𝑏2𝜎2. (8)

Substituting formula (8) into the objective function offormula (3), eliminating 𝑎, we have

𝑉1= 𝜇𝑒 −

1

2

𝜌𝑏2𝜎2− 𝐶 (𝑒, 𝑇) −

1

2

𝜅𝑇2. (9)

Solving the incentive compatibility constraints conditionsof (5) and a derivation of 𝑒, we have

𝜇𝑏 −

𝜕𝐶 (𝑒, 𝑇)

𝜕𝑒

= 0. (10)

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4 Mathematical Problems in Engineering

According to formula (10), we can get 𝑏 = 𝜕𝐶(𝑒, 𝑇)/𝜇𝜕𝑒,and substituting formula (8) into it and eliminating 𝑏, we havea new optimization problem H2:

max(𝑇,𝑒)

𝜇𝑒 −

𝜌𝜎2

2𝜇2[

𝜕𝐶 (𝑒, 𝑇)

𝜕𝑒

]

2

− 𝐶 (𝑒, 𝑇) −

1

2

𝜅𝑇2− 𝑤0. (11)

In formula (11), by giving the specific expression of𝐶(𝑒, 𝑇), it is easy to obtain the optimal investment 𝑇 and theeffort 𝑒 of supporting enterprise. And then by substitutinginto (10), we can obtain the revenue sharing coefficientin the contract. However, our concern is the influence ofnature (complementary or alternative) of platform enter-prises’ resource inputs on research and development effortand revenue sharing coefficient of supporting business, sowe need to establish the relationship between inputs 𝑇 forsupporting product by platform enterprise and R&D effort 𝑒paid by supporting enterprise.

In the formula (11), get a derivation for 𝑒 and set it to zero;the optimal first-order conditions can be obtained as follows:

𝜇 −

𝜌𝜎2

2𝜇2⋅

𝜕𝐶 (𝑒, 𝑇)

𝜕𝑒

𝜕2𝐶 (𝑒, 𝑇)

𝜕2𝑒

𝜕𝐶 (𝑒, 𝑇)

𝜕𝑒

= 0. (12)

Formula (11) presents inputs 𝑇 of platform enterprise; wecan obtain the effort 𝑒 of supporting enterprise by employingformula (12), in which we can see 𝑒 as the function of𝑇. Usinga derivation for 𝑇, we can obtain the influence of platformenterprise inputs 𝑇 on the level of effort 𝑒 of supportingenterprise:

{

𝜌𝜎2

2𝜇2⋅ [

𝜕2𝐶 (𝑒, 𝑇)

𝜕2𝑒

]

2

+

𝜌𝜎2

2𝜇2⋅

𝜕𝐶 (𝑒, 𝑇)

𝜕𝑒

𝜕3𝐶 (𝑒, 𝑇)

𝜕3𝑒

+

𝜕2𝐶 (𝑒, 𝑇)

𝜕2𝑒

}

𝜕𝑒

𝜕𝑇

+ [

𝜌𝜎2

2𝜇2⋅

𝜕2𝐶 (𝑒, 𝑇)

𝜕2𝑒

𝜕2𝐶 (𝑒, 𝑇)

𝜕𝑒 𝜕𝑇

+

𝜌𝜎2

2𝜇2⋅

𝜕𝐶 (𝑒, 𝑇)

𝜕𝑒

𝜕3𝐶 (𝑒, 𝑇)

𝜕2𝑒 𝜕𝑇

+

𝜕2𝐶 (𝑒, 𝑇)

𝜕𝑒 𝜕𝑇

] = 0.

(13)

As the cost function𝐶(𝑒, 𝑇) is a quadratic function, obtain𝜕3𝐶(𝑒, 𝑇)/𝜕

3𝑒 = 0, so using formula (13), we have

𝜕𝑒

𝜕𝑇

= − (

𝜌𝜎2

2𝜇2⋅

𝜕2𝐶 (𝑒, 𝑇)

𝜕2𝑒

𝜕2𝐶 (𝑒, 𝑇)

𝜕𝑒 𝜕𝑇

+

𝜌𝜎2

2𝜇2

𝜕𝐶 (𝑒, 𝑇)

𝜕𝑒

𝜕3𝐶 (𝑒, 𝑇)

𝜕2𝑒 𝜕𝑇

+

𝜕2𝐶 (𝑒, 𝑇)

𝜕𝑒 𝜕𝑇

)

× (

𝜌𝜎2

2𝜇2⋅ [

𝜕2𝐶 (𝑒, 𝑇)

𝜕2𝑒

]

2

+

𝜕2𝐶 (𝑒, 𝑇)

𝜕2𝑒

)

−1

.

(14)

Considering the above analyses, we will analyze the influ-ence of nature (complementary or alternative) of platformenterprises’ resource inputs on R&D effort of supporting

business based on formula (14). In previous assumptions,𝜕𝐶(𝑒, 𝑇)/𝜕𝑒 > 0, 𝜕2𝐶(𝑒, 𝑇)/𝜕2𝑒 > 0, so the positive andnegative of formula (14) depend on the positive and neg-ative of 𝜕2𝐶(𝑒, 𝑇)/𝜕𝑒 𝜕𝑇 and 𝜕3𝐶(𝑒, 𝑇)/𝜕2𝑒 𝜕𝑇. In the costfunction of supporting enterprise 𝐶(𝑒, 𝑇), 𝜕𝐶(𝑒, 𝑇)/𝜕𝑒 isthe marginal cost of effort paid by supporting enterprise,and 𝜕2𝐶(𝑒, 𝑇)/𝜕𝑒 𝜕𝑇 is the influence of platform enterpriseresource inputs on the marginal cost of effort paid bysupporting enterprise. If 𝜕2𝐶(𝑒, 𝑇)/𝜕𝑒 𝜕𝑇 < 0, it presentsthat the marginal cost of effort paid by supporting enterprisewill reduce with the inputs of platform enterprise; that is,the inputs of platform enterprise and supporting enterpriseare complementary; if 𝜕2𝐶(𝑒, 𝑇)/𝜕𝑒 𝜕𝑇 > 0, it presents thatthe marginal cost of effort paid by supporting enterprisewill increase with the inputs of platform enterprise; that is,the inputs of platform enterprise and supporting enterpriseare substitutive. 𝜕2𝐶(𝑒, 𝑇)/𝜕2𝑒 is the second derivative ofsupporting enterprise’s R&D inputs effort, that is, the changerate of the first derivative 𝜕𝐶(𝑒, 𝑇)/𝜕𝑒; the geometricmeaningof the first derivative is the slope of the cost curve, while thegeometric meaning of the second derivative is the curvatureof the cost curve.

In the complementary situation, that is, 𝜕2𝐶(𝑒, 𝑇)/𝜕𝑒 𝜕𝑇 < 0, the more inputs the platform enterprise investsfor supporting product development, the smaller the slope of𝐶(𝑒, 𝑇) is. In order to guarantee that the slope of the cost curve𝐶(𝑒, 𝑇) of the supporting enterprise effort under the situationof high inputs of platform enterprise is always smaller thanthe low inputs of platform enterprise, it has to make thecurvature of the cost curve𝐶(𝑒, 𝑇) under the situation of highinputs of platformenterprise smaller than the curvature of thecost curve 𝐶(𝑒, 𝑇) of the supporting enterprise effort underthe situation of low inputs of platform enterprise, as shownin Figure 1. We can see that the cost curve of supportingenterprise in the situation of platform enterprise low inputsis obviously steeper than the situation of high inputs ofplatform enterprise. That is, in the complementary situation,the influence of platform enterprise inputs on the changerate of marginal cost 𝐶(𝑒, 𝑇) can meet 𝜕3𝐶(𝑒, 𝑇)/𝜕2𝑒 𝜕𝑇 < 0

[18]. Hence, based on the previous analyses, we can knowthat when the inputs of platform enterprise and supportingenterprise are complementary, there are the conditions that𝜕2𝐶(𝑒, 𝑇)/𝜕𝑒 𝜕𝑇 < 0 and 𝜕3𝐶(𝑒, 𝑇)/𝜕2𝑒 𝜕𝑇 < 0. In contrast,

in the substitutive situation, the cost curve of supportingenterprise in the situation of platform enterprise high inputsis obviously steeper than the situation of low inputs ofplatform enterprise, as shown in Figure 2; there are theconditions that 𝜕2𝐶(𝑒, 𝑇)/𝜕𝑒 𝜕𝑇 > 0 and 𝜕3𝐶(𝑒, 𝑇)/𝜕2𝑒 𝜕𝑇 >0.

Considering previous assumptions and the above analy-ses about influence of nature (complementary or alternative)of platform enterprises resource inputs on R&D effort ofsupporting enterprise, under the complementary situation,as 𝜕2𝐶(𝑒, 𝑇)/𝜕𝑒 𝜕𝑇 < 0, 𝜕3𝐶(𝑒, 𝑇)/𝜕2𝑒 𝜕𝑇 < 0, and 𝜕𝐶(𝑒, 𝑇)/𝜕𝑒 > 0, 𝜕2𝐶(𝑒, 𝑇)/𝜕2𝑒 > 0, we have

𝜌𝜎2

2𝜇2⋅ [

𝜕2𝐶 (𝑒, 𝑇)

𝜕2𝑒

]

2

+

𝜕2𝐶 (𝑒, 𝑇)

𝜕2𝑒

> 0. (15)

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Mathematical Problems in Engineering 5

Yaxis

X axis e

C(e,T)

C(e, Tl)

C(e, Th)

Figure 1: The cost curve of supporting enterprise under the com-plementary situation.

Yaxis

X axis e

C(e,T)

C(e, Tl)

C(e, Th)

Figure 2: The cost curve of supporting enterprise under thesubstitutive situation.

As (𝜌𝜎2/2𝜇2) ⋅ (𝜕2𝐶(𝑒, 𝑇)/𝜕2𝑒) ⋅ (𝜕2𝐶(𝑒, 𝑇)/𝜕𝑒 𝜕𝑇) < 0,(𝜌𝜎2/2𝜇2) ⋅ (𝜕𝐶(𝑒, 𝑇)/𝜕𝑒) ⋅ (𝜕

3𝐶(𝑒, 𝑇)/𝜕

2𝑒 𝜕𝑇) < 0, we have

(𝜌𝜎2/2𝜇2) ⋅ (𝜕2𝐶(𝑒, 𝑇)/𝜕

2𝑒) ⋅ (𝜕

2𝐶(𝑒, 𝑇)/𝜕𝑒 𝜕𝑇) + (𝜌𝜎

2/2𝜇2) ⋅

(𝜕𝐶(𝑒, 𝑇)/𝜕𝑒) ⋅ (𝜕3𝐶(𝑒, 𝑇)/𝜕

2𝑒 𝜕𝑇) + (𝜕

2𝐶(𝑒, 𝑇)/𝜕𝑒 𝜕𝑇) < 0.

It is easy to find that 𝜕𝑒/𝜕𝑇 > 0 in formula (14).So we can get conclusion 1: in the new industry platform

innovation ecosystem, when the inputs of platform enterpriseand supporting enterprise are complementary, the level ofeffort paid by supporting enterprise will increase if platformenterprise increases its inputs.

Considering previous assumptions and the above analy-ses about influence of nature (complementary or alternative)of platform enterprises resource inputs on cost function ofsupporting enterprise, under the substitutive situation, as𝜕2𝐶(𝑒, 𝑇)/𝜕𝑒 𝜕𝑇 > 0, 𝜕3𝐶(𝑒, 𝑇)/𝜕2𝑒 𝜕𝑇 > 0, and 𝜕𝐶(𝑒, 𝑇)/

𝜕𝑒 > 0, 𝜕2𝐶(𝑒, 𝑇)/𝜕2𝑒 > 0, we have

𝜌𝜎2

2𝜇2⋅ [

𝜕2𝐶 (𝑒, 𝑇)

𝜕2𝑒

]

2

+

𝜕2𝐶 (𝑒, 𝑇)

𝜕2𝑒

> 0. (16)

As (𝜌𝜎2/2𝜇2) ⋅ (𝜕2𝐶(𝑒, 𝑇)/𝜕2𝑒) ⋅ (𝜕2𝐶(𝑒, 𝑇)/𝜕𝑒 𝜕𝑇) > 0,(𝜌𝜎2/2𝜇2) ⋅ (𝜕𝐶(𝑒, 𝑇)/𝜕𝑒) ⋅ (𝜕

3𝐶(𝑒, 𝑇)/𝜕

2𝑒 𝜕𝑇) > 0, we have

(𝜌𝜎2/2𝜇2) ⋅ (𝜕2𝐶(𝑒, 𝑇)/𝜕

2𝑒) ⋅ (𝜕

2𝐶(𝑒, 𝑇)/𝜕𝑒 𝜕𝑇) + (𝜌𝜎

2/2𝜇2) ⋅

(𝜕𝐶(𝑒, 𝑇)/𝜕𝑒) ⋅ (𝜕3𝐶(𝑒, 𝑇)/𝜕

2𝑒 𝜕𝑇) + (𝜕

2𝐶(𝑒, 𝑇)/𝜕𝑒 𝜕𝑇) > 0.

It is easy to find that 𝜕𝑒/𝜕𝑇 < 0 in formula (14).So we can get conclusion 2: in the new industry platform

innovation ecosystem, when the inputs of platform enterpriseand supporting enterprise are substitutive, the level of effortpaid by supporting enterprise will reduce if platform enter-prise increases its inputs.

From conclusion 1 and conclusion 2, we can knowthat in the new industry platform innovation ecosystem, ifthe resource inputs of platform enterprise and supportingenterprise are complementary in collaborative developmentsupporting products, the participant of platform enterprisehas the incentives for technology innovation inputs of sup-porting enterprise; the possible reason is that the increaseof platform enterprise complementary inputs would increasethe possibility of the success developing the supporting prod-uct. If the resource inputs of platform enterprise and support-ing enterprise are substitutive in collaborative developmentsupporting products, the inputs of platform enterprise willreduce the motivation of supporting enterprise increasingtechnology innovation inputs; the possible reason is thatthe supporting enterprise gives more hope to the platformenterprise to increase its inputs and it has a “lazy” motivationand thus is more willing to let the platform enterprise takerisk arising from inputs in product development.

The following is to analyze the impact of revenue sharingcoefficient 𝑏 on the inputs of platform enterprise; by theformula (10), we can obtain 𝑏 = 𝜕𝐶(𝑒, 𝑇)/𝜇𝜕𝑒. Establishingthe relationship between 𝑏 and the inputs 𝑇 of platformenterprise, a derivation for 𝑇, we have

𝜕𝑏

𝜕𝑇

=

1

𝜇

[

𝜕2𝐶 (𝑒, 𝑇)

𝜕2𝑒

𝜕𝑒

𝜕𝑇

+

𝜕2𝐶 (𝑒, 𝑇)

𝜕𝑒𝜕𝑇

] . (17)

Substituting formula (14) into formula (17), we can obtain

𝜕𝑏

𝜕𝑇

= − (

𝜌𝜎2

2𝜇2⋅

𝜕𝐶 (𝑒, 𝑇)

𝜕𝑒

𝜕3𝐶 (𝑒, 𝑇)

𝜕2𝑒𝜕𝑇

𝜕2𝐶 (𝑒, 𝑇)

𝜕2𝑒

)

× (𝜇{

𝜌𝜎2

2𝜇2⋅ [

𝜕2𝐶 (𝑒, 𝑇)

𝜕2𝑒

]

2

+

𝜕2𝐶 (𝑒, 𝑇)

𝜕2𝑒

})

−1

.

(18)

Analyzing formula (18), considering previous assump-tions and the above analyses about influence of nature (com-plementary or alternative) of platform enterprises resourceinputs on cost function of supporting enterprise, under thecomplementary situation, as 𝜕2𝐶(𝑒, 𝑇)/𝜕𝑒 𝜕𝑇 < 0, 𝜕3𝐶(𝑒,𝑇)/𝜕2𝑒 𝜕𝑇 < 0, and 𝜕𝐶(𝑒, 𝑇)/𝜕𝑒 > 0, 𝜕2𝐶(𝑒, 𝑇)/𝜕2𝑒 > 0, we

have

𝜇{

𝜌𝜎2

2𝜇2⋅ [

𝜕2𝐶 (𝑒, 𝑇)

𝜕2𝑒

]

2

+

𝜕2𝐶 (𝑒, 𝑇)

𝜕2𝑒

} > 0,

𝜌𝜎2

2𝜇2⋅

𝜕𝐶 (𝑒, 𝑇)

𝜕𝑒

𝜕3𝐶 (𝑒, 𝑇)

𝜕2𝑒 𝜕𝑇

𝜕2𝐶 (𝑒, 𝑇)

𝜕2𝑒

< 0, so 𝜕𝑏

𝜕𝑇

> 0.

(19)

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6 Mathematical Problems in Engineering

So we can get conclusion 3: in the new industry platforminnovation ecosystem, when the inputs of platform enterpriseand supporting enterprise are complementary, the revenuesharing coefficient of supporting enterprise will increase ifplatform enterprise increases its inputs.

Analyzing formula (18), considering previous assump-tions and the above analyses about influence of nature (com-plementary or alternative) of platform enterprises resourceinputs on cost function of supporting enterprise, underthe substitutive situation, as 𝜕2𝐶(𝑒, 𝑇)/𝜕𝑒 𝜕𝑇 > 0, 𝜕3𝐶(𝑒,𝑇)/𝜕2𝑒 𝜕𝑇 > 0, 𝜕𝐶(𝑒, 𝑇)/𝜕𝑒 > 0, and 𝜕2𝐶(𝑒, 𝑇)/𝜕2𝑒 > 0, we

have

𝜇{

𝜌𝜎2

2𝜇2⋅ [

𝜕2𝐶 (𝑒, 𝑇)

𝜕2𝑒

]

2

+

𝜕2𝐶 (𝑒, 𝑇)

𝜕2𝑒

} > 0,

𝜌𝜎2

2𝜇2⋅

𝜕𝐶 (𝑒, 𝑇)

𝜕𝑒

𝜕3𝐶 (𝑒, 𝑇)

𝜕2𝑒 𝜕𝑇

𝜕2𝐶 (𝑒, 𝑇)

𝜕2𝑒

> 0, so 𝜕𝑏

𝜕𝑇

< 0.

(20)

So we can get conclusion 4: in the new industry platforminnovation ecosystem, when the inputs of platform enterpriseand supporting enterprise are substitutive, the revenue shar-ing coefficient of supporting enterprise will reduce if platformenterprise increases its inputs.

From conclusion 3 and conclusion 4 we can know thatin the new industry platform innovation ecosystem, whenthe resource inputs of platform enterprise and supportingenterprise are complementary in collaborative developmentsupporting products, if the platform enterprise increasesits inputs for developing the supporting product, it shouldincrease the revenue sharing coefficient of supporting enter-prise letting it take more risks. The possible reason is thatthe inputs of platform enterprise reduce the marginal costof supporting enterprise for technology innovation and, incontrast, increase its marginal revenue, so the supportingenterprise will make its marginal cost equal to marginalrevenue, and platform enterprise would like to increase rev-enue sharing coefficient to increase the inputs of supportingenterprise. In contrast, when the resource inputs of plat-form enterprise and supporting enterprise are substitutivein collaborative development supporting products, if theplatform enterprise increases its inputs for developing thesupporting product, it should reduce the revenue sharingcoefficient of supporting enterprise letting it take fewer risks.The possible reason is that the inputs of platform enterprisemay increase the marginal cost of supporting enterprise fortechnology innovation and, in contrast, reduce its marginalrevenue. It is difficult for platform enterprise to increase theinputs of supporting enterprise by increasing revenue sharingcoefficient.

5. Conclusion

The value of new industry platform innovation ecosystemdepends on not only the effect of platform enterprise onplatform product but also the value of supporting product,

so platform enterprise always participates in the developmentof supporting product. From the previous analyses, we canfind supporting enterprise R&D effort and revenue sharingcoefficient in collaborative process depending on the natureof platform enterprise inputs on supporting product.

(1) When the inputs of platform enterprise and sup-porting enterprise are complementary, increasing platformenterprise inputs will generate the positive incentives forsupporting enterprise. In contrast, when the inputs of plat-form enterprise and supporting enterprise are substitutive,increasing platform enterprise inputs will generate the nega-tive incentives for supporting enterprise. The conclusions forconstructing eco-innovation platform have two inspirations:firstly, for the platform enterprises in emerging industryinnovation ecosystem, they should choose partners withcomplementary resources in building innovation ecosystemprocess. For example, when IBM built innovation ecosystem,it only focused on hardware development platform; the gen-eral partners it chose are with middleware and applicationsoftware development capabilities which are complementaryfor it.

Secondly, if in the platform innovation ecosystem theplatform enterprise and supporting enterprise have separateresource substitution, platform enterprise should be lessinvolved in the development of supporting product, becausewhen the resources are substitutive, increasing the inputs ofplatform enterprise will reduce the enthusiasm of supportingenterprises, an increase of supporting enterprise “lazy” moti-vation; if the platform enterprise and supporting enterpriseare the complementary resources, the former should increaseits inputs for developing supporting product; this is becauseincreasing inputs of platform enterprise increase the likeli-hood of successful product development, which also has agood incentive for supporting enterprise.

(2) When the inputs of platform enterprise and sup-porting enterprise are complementary, the revenue sharingcoefficient of supporting enterprise will increase if platformenterprise increases its inputs. When the inputs of platformenterprise and supporting enterprise are substitutive, therevenue sharing coefficient of supporting enterprise willreduce if platform enterprise increases its inputs. Hence,in the contract design process, platform enterprise shouldtake full account of the nature of development inputs forsupporting product. Under the complementary situation, thecontract should increase the proportion of variable incomeof supporting enterprise, reducing fixed pay part, so that thesupporting enterprise should take more development risks;under the substitutive situation, the contract should reducethe proportion of variable income of supporting enterpriseand increase the portion of the fixed payment, so the support-ing enterprise takes less development risks. This conclusionhas some theoretical reference value for the contract designof supporting product’s collaborative development in newindustry platform innovation ecosystem.

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper.

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Mathematical Problems in Engineering 7

Acknowledgment

This work was supported by National Natural Science Fundsof China (Grant nos. 71273076, 71301065, and 71303271),Humanities and Social Sciences Youth Foundation ofChineseMinistry of Education (Grant no. 3YJC630166), and theNational Social Science Foundation of China (Grant no.12CTQ029).

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