D Outsourcing Contract for the Unverified Value of Tacit Knowledge Sharing

Purpose: The purpose of this paper is to provide a R&D outsourcing contract design framework to incent R&D outsourcing service providers sharing tacit knowledge. Design/methodology/approach: The author uses the principal-agent theory to builds multitask principal-agent model which focuses on two cases. One case is that the effort costs of explicit and tacit knowledge sharing are complementary, while another is the effort costs are substitutable. Findings: When the costs of explicit and tacit knowledge sharing are complementary, the buyer can increase the incentive coefficient of explicit knowledge sharing to stimulate tacit knowledge sharing. This motive method not only stimulates tacit knowledge sharing, but also will further stimulate the effort levels of explicit knowledge sharing. Moreover, the multitask R&D outsourcing contract can motivate the effort of explicit knowledge sharing to achieve system optimization, but it fails to motivate the effort of tacit knowledge sharing to achieve system optimization. Research limitations/implications: In this paper we only consider that the outsourcing relationship is short-term, so the multitask R&D outsourcing contract is formal. In fact, the outsourcing relationship may be long-term, and the multitask R&D outsourcing contract will be informal.


Introduction
For acquiring external knowledge quickly, the enterprises may outsource R&D business to professional service providers (SP) (Han & Bae, 2014).Knowledge can be divided into explicit knowledge and tacit knowledge (Mulkay, 2014).Most of explicit knowledge in R&D outsourcing is expressed in the form of reports, patents software and so on.Its value can be verified by third-party organizations, such as review panel, Patent Office and Software Testing Center.In contrast, tacit knowledge can be transmitted and shared between SP and enterprises through communication, but its value cannot be verified like explicit knowledge (Suppiah & Sandhu, 2011).Zhou, Qu and Joyce (2012) thought that R&D outsourcing should be discussed within the context of risk management theory.Based on the British Petroleum (BP) neural network, they built a risk-warning model which can examine and manage R&D outsourcing risks.Bals, Kneis, Lemke and Pedersen (2013) emphasized that managers must understand, which R&D activities can be outsourced and which need to stay in-house in order to ensure competitiveness.R&D outsourcing may result in intellectual property infringement.Buss and Peukert (2015) discussed how the intellectual property infringement caused by R&D outsourcing fosters technology diffusion and affects R&D Outsourcing decision.
The outsourcing contract stipulates the rights and obligations of the buyer and contractors (Qi & Chau, 2012).At present, there are much literature which concern outsourcing contract.For example, Aksin, De Véricourt and Karaesmen (2008) studied a call center outsourcing contract analysis and choice problem, which faced by a contractor and a service provider, who receives an uncertain call volume over multiple periods and is considering outsourcing all or part of these calls to a contractor.Yao, Jiang, Young and Talluri (2010) studied three common outsourcing contracts (fixed-price, cost-plus, and gain-sharing) and address issues, when to outsource and which contracts to select.Based on analyzing risk factors of producer services outsourcing, Cai, Kai and Zou (2011) built the producer services outsourcing contract by designing the incentive and monitoring mechanism.Zhu, Li and Zheng (2014) built a game theoretic model, which is used to design the optimal contracts between the buyer and the supplier under two types of information scenario.Gershman and Kuznetsova (2013) thought that efficient contracts should guarantee not only fair rewards but also competitive selection in order to prevent an excessive inflow of the workforce from other sectors of the economy.
The existing outsourcing contracts may focus on the transmission and sharing of explicit knowledge whose value can be verified, and ignore the unverified value of tacit knowledge.It leads to the insufficient sharing of tacit knowledge in R&D outsourcing.However, a lot of tacit knowledge is the key for employers to make technological breakthrough (Martínez-Noya & García-Canal, 2011;Kloyer & Scholderer, 2012).Therefore, how to design an effective contract to share the tacit knowledge whose value is unverified and to acquire explicit knowledge is an issue that must be considered when the buyer formulates the R&D outsourcing contracts (Quinn & Strategy, 2013).
The existing R&D outsourcing contract researches concern the choice of R&D outsourcing contracts, the design and optimization of contracts parameters and so on.For example, Jain, Hasija and Popescu (2013) analysed and compared the effectiveness of fixed-price contracts and cost-plus contracts in terms of the choice of R&D outsourcing contracts from many aspects, such as ex ante information asymmetry and ex post information asymmetry, friction in renegotiation and project uncertainty.Aiming at parameter selection in R&D outsourcing contract, Ulset (1996) researched the outsourcing cases of 80 enterprises.It has achieved the effective mechanism of managing the R&D outsourcing contracts and puts forward the method to choose the parameters in R&D outsourcing contract.Aiming at researching the behavior that service providers disclose customers' knowledge in outsourcing, Lai, Riezman and Wang (2009) built the multi-period game model and optimizes the excitation parameters of R&D outsourcing contract.It has helped control the possible disclosure of service providers.Suppiah and Sandhu (2011) designed a structural questionnaire and carried out a field survey on the willingness of tacit knowledge sharing among 216 knowledge employees.The results showed that different types of psychological contracts have different influences on employees' willingness of tacit knowledge sharing.
All the literature above introduce the consequence of knowledge sharing, namely the value of knowledge, into contract when choosing R&D outsourcing contracts, designing and optimizing parameters, thereby linking the income of service providers with the value of knowledge to stimulate service providers to share knowledge (Pashupatimath & Ramakrishna, 2015).Explicit knowledge can be verified by the third-party organizations and be regarded as an object of contracts.Therefore, the knowledge-sharing of service providers above, which is stimulated by the connection between the income of service providers and the value of knowledge in R&D outsourcing contract, has some effects in stimulating explicit knowledge-sharing.Nevertheless, the value of tacit knowledge cannot be verified by the third-party organizations, thus the R&D outsourcing contract seems so feeble in stimulating tacit knowledge sharing (Kultti & Takalo, 2000).There are a lot of researches on inter-organizational tacit knowledge sharing (Cheng, 2011;Soekijad & Andriessen, 2003), which research strategic alliances, virtual team and supply chain separately, but there are few researches about tacit knowledge sharing in R&D outsourcing contracts.However, they focus on the problem of tacit knowledge sharing and ignore the fact that explicit knowledge sharing and tacit knowledge sharing should complement each other.For this problem, Song, Zhang and Li (2012) built a multitask principal-agent model for explicit knowledge sharing and tacit knowledge sharing.It emphatically analyzes whether the stimulation of explicit knowledge sharing will influence the stimulation of tacit knowledge sharing or not, and in what manner.But it is regrettable that the author does not provide further analysis about how to realize the stimulation of explicit and tacit knowledge sharing when the value of tacit knowledge cannot be verified.
Given this, this paper builds a multitask principal-agent model for explicit and tacit knowledge sharing stimulation in the case of unverified value of tacit knowledge, and analyzes the effect of formal contract and informal contract on the incentive of explicit and tacit knowledge sharing in R&D outsourcing contract in short-term as well as in long-term, so as to provide a theoretical model for formulating an effective R&D outsourcing contract and promoting the transfer of explicit and tacit knowledge sharing.

The Model
Consider a risk neutral buyer outsourcing R&D project to a risk neutral SP.Generally speaking, service providers create and innovate knowledge technology by investing knowledge, technology and human capital in R&D, most researches use the degree of service provider's hardworking to describe the R&D's investment of service providers quantitatively.For that reason, this paper follows this method, but it divides effort into two types according to the characteristics of knowledge, which includes explicit and tacit knowledge.One is e 1 , the level of efforts made in sharing explicit knowledge, which can be expressed by coding and whose value can be verified by the third-party organizations; the other is e 2 , the level of efforts made in sharing tacit knowledge, which cannot be expressed by coding and whose value cannot be verified by the third-party organizations, wherein 0 ≤ e 1 ≤ 1, 0 ≤ e 2 ≤ 1. Suppose further that the cost function of these two efforts is , wherein k 1 and k 2 are independent quadratic cost coefficients for the two efforts respectively, s is the cost correlation coefficient of the two efforts.The cost function above has the general features of convex function, which cost and marginal cost increase progressively.If s < 0, it means that the increase of one effort can lead to the decrease of the marginal cost of the other effort.In the same way, if s > 0, it means that the increase of one effort can lead to the increase of the marginal cost of the other effort.
Where e 1 is the input (efforts level) of service providers in sharing explicit knowledge, e 2 is the efforts level of service providers in sharing tacit knowledge, k 1 and k 2 are independent cost coefficient for the two efforts respectively, s is the cost correlation coefficient of the two efforts.
The cost function above has the general features of convex function, which cost and marginal cost increase progressively.On the other hand, the cross partial derivative of two efforts' cost function is .if s < 0, it means that the increase of one effort can lead to the decrease of the marginal cost of the other effort.In the same way, if s > 0, it means that the increase of one effort can lead to the increase of the marginal cost of the other effort.
Consequently, the cost correlation coefficient of two efforts s shows the complementary or substitutional relationship between explicit and tacit knowledge.The value which the buyer can earn from explicit and tacit knowledge sharing is π 1 (e 1 ) = λ 1 e 1 , π 2 = λ 2 e 2 , where λ 1 , λ 2 are the output coefficient.The value π 1 can be verified, but the value π 2 can be verified.As employers cannot observe the efforts of service providers, there is a moral hazard.The conventional method to solve this problem is offering incentive wage.This paper uses revenue sharing contract to stimulate service providers to work hard, and continues to use the linear revenuesharing contract.We assumes that the payment paid by buyer is W = F + β 1 π 1 + β 2 π 2 , wherein F is the fixed-price of R&D outsourcing, β 1 and β 2 are the incentive coefficients of revenue sharing, which are produced by sharing explicit and tacit knowledge.The component β 2 is not enforced by the third parties such as courts since the outcome π 2 is unverifiable.Formal contract is a kind of promise, which is used for ex ante definition and ex post verification.
Besides, it can be enforced by the third-party organizations (e.g.court).Under the formal R&D outsourcing contracts, the buyer and service providers are playing a single-cycle game.The time series of the game is shown in Figure 1.Conclusion 2 shows, when s > 0, namely the effort costs of explicit and tacit knowledge sharing can substitute each other, formal R&D outsourcing contracts cannot stimulate explicit and tacit knowledge sharing to be optimal.When s < 0, namely the effort costs of explicit and tacit knowledge sharing are complementary, formal R&D outsourcing contract can only stimulate explicit knowledge sharing to be optimal but fails to stimulate tacit knowledge sharing.That is to say, formal R&D outsourcing contract has not realized optimal system and has room for Pareto improvement.For tacit knowledge sharing especially, there is considerable room for Pareto improvement.

Conclusions
R&D outsourcing has become one of the most effective ways for enterprises to acquire external knowledge rapidly.The existing researches focus on transferring and sharing explicit knowledge whose value can be verified, but ignore the transmission and sharing of tacit knowledge whose value cannot be unverified .Thus leading to the lack of tacit knowledge sharing in R&D outsourcing.In order to stimulate tacit knowledge sharing as well as explicit knowledge sharing, a multitask principal-agent model of simultaneous stimulation of explicit and tacit knowledge is established and the incentive effects of formal and informal relational contracts on knowledge sharing are analyzed.Researches show that when the relationship between the costs of explicit and tacit knowledge sharing are mutually substitutable, formal contract can only stimulate the effort of sharing explicit knowledge but fails to stimulate the effort of sharing tacit knowledge.When the two are complementary, formal contract can stimulate the efforts of sharing explicit and tacit knowledge at the same time.However, it can only stimulate the effort of explicit knowledge sharing to the optimal level, not tacit knowledge sharing.

Figure 1 .
Figure 1.Time Series of the Game of Formal R&D Outsourcing Contract