Fund Project: the National Natural Science Foundation of China (70,601,009)

Study on Multi-levels Incentive Mechanism Model for Tacit Knowledge Sharing in Enterprise

CUI Guang-bin1， DONG Liang2, LI Yi-Jun1, GUAN Tao1 （1. School of Management, Harbin Institute of Technology, Harbin, China cgb717@hit.edu.cn） (2. Aircraft Design and Research Institute, Harbin Aircraft Industry Group co., LTD, Harbin, China)

Abstract—Tacit knowledge exists in knowledge main-bodies of different hierarchy in enterprise. To enable full sharing and improve core competitiveness, incentive models of knowledge sharing for knowledge main-bodies of different hierarchy should be established; According to principal- agency theory, and taking into account incomplete information of knowledge sharing, multi-stages incentive model of knowledge sharing for knowledge worker, incentive model of knowledge sharing for knowledge team based on team sharing interests, and incentive model of knowledge sharing for supplier, are proposed. The results indicate that, in order to acquire maximum rewards in enterprise, special incentive contracts are to be made for different knowledge main-bodies, optimal incentive decisions to meet enterprise own objective are to be made, and knowledge body’s knowledge sharing effort is to be improved.

Keywords- tacit knowledge sharing; principal-agent; incentive model

I. INTRODUCTION Nowadays, knowledge has been enterprises' strategic

source for survival and development, which simultaneously promotes their knowledge level and ability of technical innovation at the core of enterprises' competition. To win an advantage over the opponent in this competition, enterprises should manage and utilize all kinds of knowledge effectively and thus given birth to new managerial concepts and methods-Knowledge Management. Knowledge can be classified into explicit knowledge and tacit knowledge [1]. The definition of explicit knowledge and tacit knowledge was broadened [2]. Knowledge sharing gives the convenience in knowledge acquisition, and lows the cost of knowledge acquisition in order to increase the productivity of knowledge and make knowledge application easy [3]. Tacit knowledge sharing is not easy, not only because of the nature of tacit knowledge that is difficult in coding, but also because of shortage of the sharing and exchanging motivation. While information technology can make knowledge sharing easier, it can not motivate enterprises’ knowledge workers to share. Thus, non-technical factors of knowledge sharing have been focused on; incentive mechanism will play an important role in knowledge sharing [4-6]. Knowledge owners will be given the incentive mechanism to share. The incentive mechanism of knowledge sharing emphasizes persons’ rational behavior, and will help to stimulate knowledge workers’ enthusiasm to reach the goal of knowledge sharing in enterprises [7].

Some scholars gave qualitative analysis on incentive mechanism of knowledge sharing from the perspective of psychology and organizational behavior [8-9], but there is no quantitative discussion. The modeling and quantitative study on individual reward system and groups of reward system are proposed for intra-organizational knowledge sharing [10]. According to knowledge main-bodies’ hierarchy in an enterprise, tacit knowledge is distributed in individuals, teams, departments, and enterprise. Therefore, multi-level incentive mechanism models of knowledge sharing for knowledge workers, knowledge teams, and knowledge suppliers should be established in an enterprise.

II. MULTI-LEVEL INCENTIVE MECHANISM MODEL OF TACIT KNOWLEDGE SHARING

Tacit knowledge not only exists in knowledge workers and departments at different hierarchy in enterprises, which is difficult to be standardized and represented, and is not easy to be exchanged, shared, copied and coded, but also it can be acquired effectively by means of transferring and sharing from the outside enterprises [11].

There are complex processes of tacit knowledge flowing and transferring among knowledge main-bodies (individuals, teams, enterprise, etc.) of different hierarchy in enterprises. The processes of tacit knowledge transferring and flowing are illustrated as follows. 1. There are the activities of tacit knowledge flowing and transferring among the relevant knowledge workers. 2. There are the activities of tacit knowledge flowing and transferring from the knowledge workers to the teams through the socialization and externalization, or from the teams to the knowledge workers. 3. There are the activities of tacit knowledge flowing and transferring through the socialization and externalization from the knowledge workers to the enterprise, or from the enterprise to the knowledge workers. 4. There are the activities of tacit knowledge flowing and transferring among the teams. There are the activities of tacit knowledge flowing and transferring from the teams to the enterprise, or from the enterprise to the teams. 5. There are the activities of tacit knowledge flowing and transferring from the outside supplier to the enterprise. As is discussed above, the incentive mechanism models of multi-level knowledge sharing should be established for the enterprise.

2010 International Conference on E-Business and E-Government

978-0-7695-3997-3/10 $26.00 © 2010 IEEE

DOI 10.1109/ICEE.2010.492

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Knowledge sharing is at the core of knowledge management. The necessary hardware platforms not only are to be built, but also effective incentive mechanism should be given to the individuals, teams and supplier in enterprises. Because of incomplete information, knowledge workers’ efforts can not be observed directly and fully. The output of knowledge-sharing can be observed only, which is determined by both he random factors and knowledge workers’ knowledge sharing efforts. Non-technical factors are more important than technical factors in enterprises’ knowledge sharing.

III. INCENTIVE MECHANISM MODEL FOR TEAM

A. Assumptions and variable definitions Hypothesis 1: Enterprise is risk-neutral, and staffs are risk-

averse. All incentives for staffs, such as material, welfare, job promotion, as well as challenging work, based on economics, have the same effect as the monetary incentives.

Hypothesis 2: The team is composed of the member i and the member j, and both are the maximizers of rational and expected utility. ia represents the member i’ s efforts for its own work. ip represents the member i’ s efforts of knowledge sharing for the member j. ja represents the member j’ s efforts

for its own work. jp represents the member j’ s efforts of knowledge sharing for the member i. Suppose the production function with iπ = ia +k jp + iε , where k represents the knowledge sharing marginal cost, and iε represents the

external random invariable, subjecting to N(0， 2iσ )，with

E( iε )=0 and D( iε )= 2iσ ; Similarly, assuming

jπ = ja +k ip + jε ， jε subjects to N(0， 2jσ ).

Hypothesis 3: In order to make the analysis and description easier, assuming that the optimal incentive contract has a linear form. Witzman make linear contract reasonable [12], Holmstrom and Migrom proved that the linear contract is optimal and can be achieved [13]. Therefore, the incentive contract is represented with s(π )= βπα + .

Hypothesis 4: The cost function of the efforts is represented with ic = ib （ 2

ia + 2ip ）/2, where ib is the member i’s cost for

both for its own work and knowledge sharing; similarly, jc = jb （ 2

ja + 2jp ）/2.

Hypothesis 5: Team members are risk averse, utility function is represented with u(s) =- Exp （- ρ s ）, where ρ is the risk aversion coefficient.

B. Analysis of team members’ knowledge sharing In this paper, the incentive mechanism of sharing team’s

interests is made to promote knowledge sharing between team members, and the team’s benefit-sharing is schemed in the linear incentive contract that made by the principal. Members’ rewards are associated with the team’s benefits. The principal affords linear incentive contract represented with is = iα + iβ （

iπ + jπ ）, where iα is the member i’s fixed reward, and iβ is benefit-sharing incentive coefficient, for iβ ∈ （ 0 ， 1]. Similarly, js = jα + jβ （ iπ + jπ ）， jβ ∈（0，1]. Team members regard utility maximization as their goals. Expected utility maximization is equivalent to the maximization of certainty equivalent income, so expected utility can be replaced with the certainty equivalent income. The expected income minus the certainty equivalent income equals to the risk cost represented with ρ )(sD /2, where ρ denotes the risk aversion

coefficient. Set iρ )( isD /2= iρ 2iβ （ 2

iσ + 2jσ ）/2, where iw

denotes the member i’s income. Set E( iw )=E（ is - ic ）, and

iU =E （ is - ic ） - iρ 2iβ （ 2

iσ + 2jσ ） /2= iα + iβ （

ia +k jp + ja +k ip ）- ib （ 2ia + 2

ip ）/2- iρ 2iβ （ 2

iσ + 2jσ ）

/2, where iU denotes the member i’s certainty equivalent

income. Set jU =E （ js - jc ） - jρ 2jβ （ 2

iσ + 2jσ ）

/2= jα + jβ （ ia +k jp + ja +k ip ） - jb （ 2ja + 2

jp ） /2-

jρ 2jβ （ 2

iσ + 2jσ ） /2, where jU denotes the member j’s

certainty equivalent income. Under the incentive contract, team members choose their own optimal strategy represented with

*ia ， *

ip ∈ max iU . Set iU∂ / ia∂ = iU∂ / ip∂ =0, so the

corresponding optimal strategy *ia and ib then can be

computed as *ia = iβ / ib and *

ip =k iβ / ib , Similarly, *ja = jβ / jb ， *

jp =k jβ / jb .

C. Incentive Model

iα ， jα ， iβ ， jβ ∈ arg max E（ iπ + jπ - is - js ）

s.t. ( 1IR ) E（ is - ic ）- iρ 2iβ （ 2

iσ + 2jσ ）/2 ≥ is

( 2IR ) E（ js - jc ）- jρ 2jβ （ 2

iσ + 2jσ ）/2 ≥ js

( 1IC ) ia , ip ∈ arg max E（ is - ic ）- iρ 2iβ （ 2

iσ + 2jσ ）/2

( 2IC ) ja , jp ∈ arg max E（ js - jc ）- jρ 2jβ （ 2

iσ + 2jσ ）/2

Where is and js denote the reservation income. If the reservation income is less than the expected utility, the agent will not accept the incentive contract. Under the maximum expected utility, the principal pays no more for the agents, so the equation of participation constraint can be obtained. Thus, through the participation constraint, the following results are available:

iα = is - iβ （ ia +k jp + ja +k ip ）+ ib （ 2ia + 2

ip ）/2+

iρ 2iβ （ 2

iσ + 2jσ ）/2

jα = js - jβ （ ia +k jp + ja +k ip ）+ jb （ 2ja + 2

jp ）/2+

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jρ 2jβ （ 2

iσ + 2jσ ）/2

Based on iα , jα , *ia , *

ip , *ja and *

jp , the objective function can be computed by using first-order condition (partial derivatives). The results are as follows:

)(1

1222

2

jiiii

bkk

σσρβ

+++

+= ,

)(1

1222

2

jijjj

bk

k

σσρβ

+++

+=

D. Factors of affecting the optimal incentive contract

Because of ii b∂∂ /β <0， ii ρβ ∂∂ / <0， 2/ ii σβ ∂∂ <0，

jj b∂∂ /β <0， jj ρβ ∂∂ / <0，and 2/ jj σβ ∂∂ <0，If the cost factor, risk aversion and random factors are increased, incentive effect can be reduced; Because of ki ∂∂ /β >0，

kj ∂∂ /β >0, increasing the marginal cost of knowledge sharing is able to improve the incentive mechanism. Reducing the knowledge sharing coefficients and increasing the marginal cost of knowledge sharing are able to lead the knowledge sharing effort to be improved.

IV. INCENTIVE MECHANISM MODEL FOR INDIVIDUAL

A. Incentive Model Considering the multi-stage processes of knowledge

sharing in a enterprise, suppose the production function represented with π = ta +k tp + ε , where tp denotes the staff’s knowledge sharing effort at the t stage for (t = 1,2, ..., n), ta denotes the staff’s efforts for its own work, k denotes the knowledge sharing marginal cost, and ε denotes the external random invariable, subjecting to N(0， 2σ )，with E( ε )=0 and D(ε )= 2σ . Effort cost function is represented with c = b

（ 2ta + 2

tp ）/2, where b is the cost of knowledge sharing and work for its own. The optimal incentive contract is represented with s =α + β π , where β is the knowledge sharing incentive coefficient, for β ∈（0，1]; Enterprise is the risk-neutral, and staff is the risk-averse. Knowledge sharing incentive model is as follows:

α ， β ∈arg max （1- β ） αnkpan

ttt −+∑

=1

)(

s.t. )(IR α + β （ ta +k tp ）- b （ 2ta + 2

tp ）/2- ρ 2β 2σ /2 s≥

)(IC ∈pa, arg max α + β （ ta +k tp ）- b （ 2ta + 2

tp ）/2-ρ 2β 2σ /2

α = s - β （ ta +k tp ）+ b （ 2ta + 2

tp ）/2+ ρ 2β 2σ /2 is available from the participation constraint.

*a = β / b and *p =k β / b are available from the incentive constraint;

Based on *a , *p and α ,the objective function can be computed by using first-order condition (partial derivatives). The result is as follows:

β =22

2

1

1

ρσbk

k

++

+

B. Factors of affecting optimal incentive contract

(1) *a and *p are irrelevant with the stage t(for t = 1,2, ..., n). Enterprise is the ultimate beneficiaries of knowledge sharing, so knowledge sharing should be maintained persistently.

(2) Because of k∂∂ /β >0， b∂∂ /β <0， ρβ ∂∂ / <0， and 2/ σβ ∂∂ <0, increasing the marginal cost of knowledge

sharing and reducing the cost coefficient, the risk aversion coefficient and random factors are able to improve knowledge sharing.

V. INCENTIVE MECHANISM MODEL FOR SUPPLIER

A. Incentive Model Supplier i's efforts belong to private information, and can

not be observed. Manufacturer j can not provide rewards or punishment for supplier i through no confirmed information. Supplier i’s production function can be represented with iπ =

ia + iε , where ia denotes supplier i's efforts for its own work. It is supposed that manufacturer j’s production function is represented with jπ = ja + k ip + jε , where ip represents the supplier i’s knowledge sharing efforts for the manufacturer j, and k represents the knowledge sharing marginal cost. iε and

jε represent the external random invariables, and subjecting to

N(0， 2iσ )and N(0， 2

jσ ). The manufacturer makes a linear incentive contract for the supplier with is =α + β （k ip + iε ）, where α is the fixed reward, and β is the incentive coefficient of knowledge sharing, for β ∈ （ 0 ， 1]. The

supplier’s cost function is represented with ic = ib （ 2ia + 2

ip ）

/2, where ib is the supplier’s cost for both its own work and knowledge sharing; Similarly, the manufacturer’s cost function is represented with jc = jb （ 2

ja + 2ip ） /2, where jb is the

manufacturer’s cost for both its own work and knowledge sharing. The basic incentive model is as follows:

α , β , ja ∈arg max ja + k ip （1- β ）- α - jb （ 2ja + 2

ip ）/2

s.t. )(IR ia +α + β k ip - ib （ 2ia + 2

ip ）/2- iρ 2β 2iσ /2 ≥ is

)(IC ia , ip ∈ arg max ia + α + β k ip - ib （ 2ia + 2

ip ）/2-

iρ 2β 2iσ /2

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Where is denotes the reservation income. If the reservation income is less than the expected utility, the supplier will not accept the contract. Incentive constraint aims to motivate the supplier to make the greatest efforts to obtain expected utility.

α = is - ia - β k ip + ib （ 2ia + 2

ip ） /2+ iρ 2β 2iσ /2 is

available from the participation constraint. *ia =1/ ib and *

ip = β k/ ib are available from the incentive constraint;

Making use of α , *ia and *

ip , the objective function is able to be computed by using first-order condition (partial derivatives). The result is as follows:

*ja =1/ jb ， β = 2

ii2i

2j

2i

2i

bkbkbkb

σρ++

B. Factors of affecting optimal incentive contract

1) Because of *ip = /3k ( 2222

iiiji bkbkb σρ++ ) ，

kpi ∂∂ /* >0， ii bp ∂∂ /* <0， ji bp ∂∂ /* <0， ip ρ∂∂ /* <0，and 2* / ip σ∂∂ <0, increasing supplier’s marginal cost of knowledge

sharing and reducing the cost coefficient, the risk aversion coefficient and random factors are able to improve knowledge sharing efforts.

2) Because of k∂∂ /β >0， j/ b∂∂β <0， i/ ρβ ∂∂ <0，and 2i/ σβ ∂∂ <0, increasing the supplier's marginal cost of

knowledge sharing and reducing the manufacturer’s cost coefficient, the supplier’s risk aversion coefficient and random factors, can improve the incentive mechanism. If

ib > iji

/bk ρσ

, then i/ b∂∂β <0, increasing the supplier's

cost coefficient can offset the incentive mechanism; If

ib < iji

/bk ρσ

, then i/ b∂∂β >0, increasing the supplier’s

cost coefficient can improve the incentive mechanism; When

ib = iji

/bk ρσ

, β has the maximum.

VI. CONCLUSIONS 1) The greater knowledge main-body’s marginal cost of

knowledge sharing is, and the higher knowledge sharing efforts are. Though enterprise pay more agency cost, better effect and more earnings of knowledge sharing can be obtained.

2) The greater the knowledge sharing effort cost coefficient is, the more knowledge main-body’s knowledge sharing losses are, the lower the knowledge sharing efforts are, and the worse enterprise’s knowledge sharing effect is. Therefore, time, manpower, material and financial and other resources should

be provided for the knowledge main-body in order to reduce knowledge sharing losses.

3) The larger knowledge sharing incentive coefficient is, the higher knowledge main-body’s efforts are, and more earnings can be obtained consequently by enterprise. Therefore, when knowledge main-bodies are demanded to share knowledge, enterprise should explicitly inform them the incentive mechanism for implementation.

4) When knowledge main-body’s risk aversion is increased, knowledge sharing incentive coefficient is reduced, and incentive mechanism is able to be offset accordingly. Therefore, enterprise should relieve the staffs’ work risk in order to reduce the risk cost on account of knowledge sharing.

5) The greater uncertainty is in the processes of knowledge sharing, the smaller knowledge sharing incentive coefficient is, as a result, and the knowledge sharing efforts are reduced. The desired results of knowledge-sharing incentive mechanism can not be achieved. As far as possible, uncertain factors should be excluded from the knowledge sharing, thus enterprise’s final income may be a true reflection of knowledge main-body’s efforts.

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