An Incentive Mechanism for Knowledge Sharing in Research Team
Huo-di Zhu, Yan Liu, Bu-yu Xu
ChongQing University of Technology, ChongQing, China
(zhuhuodi@sohu.com)
Abstract - This paper focuses on the incentive
mechanism for knowledge sharing in Research team. The
team is assumed to be constituted by two members (the first
member and the second member），The team's output is
affected not only by the efforts of the first member (S1) and
the second member(S2), but also by the core competitive
knowledge of the second member（K2）. Making use of
game theory, we construct a multitasking model for team
members’ inputs that analyzes three decision variables that
influence team members’ knowledge sharing. And make a
series of profound conclusions that related to team
cooperation. These conclusions are important and
instructive to research team building and team performance
improvement。
Keywords - Game theory, Knowledge sharing,
Mechanism design, Research team, Team performance
I. INTRODUCTION
be more active to share noncritical knowledge of the
performance than critical knowledge of its core
competitiveness of the performance. Chen feiqiong and
[2]
Fan liangcong pointed out that the instability of the
Union will rise with the expansion of the difference in
degree of cooperation and competition between the forces
within the Union. Taking into account the potential longterm cost, knowledge sharing of the League members is a
very important decision. But because Union may be
dissolved at any time, if the know-how was easily learned
and mastered by other members of the Union, the
members presently possessed it would face the danger of
losing their competitive advantage.
In the research on factor affecting knowledge
sharing, there are "hard" aspects, such as technology and
[3]
[4]
[5]
tools (Albino , Cabrera 、Kwan and Cheung ）；
and also "Soft" aspects of cooperative motive, （
[6]
The team is the alliance of groups that composed of
members of the heterogeneity of complementary skills
who committed to a common purpose and performance
goals, and to assume certain responsibilities. Modern
management thinking are all pointed out and stressed that
the future organization form must be a dynamic team with
energy. The key is team members should be multiskilled
"generalist", enjoy a high degree of autonomy and
decision-making flexibility, and share their unique
knowledge for the research team building and team work
performance.
Most of the literature on team research focuses on
the formation of research teams, on the team building and
the importance that. However, the reality is the teams’
operating are not satisfactory, there is a problem of high
failure rate among them. A large number of failed cases
show that the there are still some gap between theoretical
research on the team and team management. The reason
why the team is existed lies in its ability to gain advantage
from cooperative members in achieving growth and
manage risk. In essence, team through collaborative create
value or mutual benefit income, that partners alone can
not achieve. So part of the reason to form the team is due
to the formation of the value of the partnership.
Thus, the expected synergies can not be achieved is a
major cause of team failure.
[1]
Empirical studies of Chan and Kensiger have shown
that, When the transfer of technical knowledge or
technical knowledge exchange is involved, the Union can
gain more value. Therefore, the Union's success depends
on member’s willing to share its proprietary knowledge
with the others in it. In an alliance, alliance members may
Ardichvili ）mutual trust between alliance members（
[7]
[8]
Levin and Cross ）、Corporate culture （Hlupic ），
and technology absorptive capacity and other factors. （
[9]
Cohen and Levinthal ） Research in knowledge-sharing
[10]
mechanism, Gupa and Govindarajan
studied the
knowledge sharing in multinational corporations;
[11]
Simonin
studied the knowledge sharing process
[12]
between the strategic partners; Lyles and the Salk
focused on how the international joint ventures access to
[13]
knowledge from their foreign partners; Griffith
got
used of the central unit and absorptive capacity of the
network to discuss knowledge sharing within the
[14]
organization; Zhuang
yaming and Li jinsheng
submitted a general pattern, the formation mechanism and
income distribution program of quantitative knowledge
share.
Recent research of knowledge-sharing focused on
how the agent decides whether to transfer knowledge to
[15]
[16]
team members. Lazear , Itch
studied the production
of every member of the group need to make a choice
between complete their own tasks and assist partners.
[17][18]
[19]
Holmstrom and Milgrom
, Baker
approach to the
extensions for each agent can perform a any number of
[18]
[16]
tasks. Holmstrom and Milgrom , Itch
showed how
job design and task allocation will change the choice of
[16]
agents in multitasking environment. As the Itch studied
that, relatively monotonous tasks may reduce the cost of
agents to help others, for example, to impart knowledge
may simply break up the monotony. By the same token,
engaged in more complex tasks may make agents feel
cumbrous in the transfer of knowledge.
This article will use a multitasking principal-agent
framework to induce team members to fully share
proprietary knowledge with core competitiveness by
setting incentive targets.
II. MODEL CONSTRCT
Assume that the team is made up of two members
The team's output is affected not only by the efforts
of the second member ( k2 ). Therefore, the team's
production function model is:
F  f  s1 , s2 , k2 
（1）
Assume the output of a special form team can be
expressed as:
F  1  k2  s1  s2 
（2）
Among them,  is the sensitivity of k2 to the
influence on the team output. 0    1
Equation (2) depicts the team output model by the
s1 ）, and the
member’s contribution knowledge,   0 ；Quadratic part
is the same efforts’ cost of the second member as that of
the first member.
Therefore, the expected utility of the second member
can be expressed as:
CE2  E  Q   s22 2   k2  rI 2 2 2
（6）
 M  I 1   k2  s1  s2   s22 2   k2  rI 2 2 2
Where, r represents the members’ value of risk
aversion. The first member hope he could control
its value was 0 or 1. Marginal productivity of
s1
and s2 is
increased by the effort of k2 , When the second member
contributes k2 （ k2  1 ）, take   1 , the team's output
doubled. It is worthwhile to pay attention that the team
still has a positive output when k2  0 . Next, we could get
team production signal (Such as team production):
P  1  k2  s1  s2   
（3）
 
And
When considering the other factors of the
environment that affect the level of team output, we
assume that the team output follow a normal distribution:
  N 0,  2
s1 、
s2 and k2 through choosing M or I, in order to maximize
its expected utility, i.e. a maximization of the difference
 s 2
2
between the expected revenue and negative utility 1
& the compensation for the second member . Assume that
the second member’s reservation utility was zero (U  0) ,
the first member can be expressed as follows:
s.t.
Maxmize E ( F  s 2 2  Q)
M ,I
1
2
2 2
E  Q   s2 2   k2  rI  2  0
s2 , k2  arg max  M  I 1   k2  s1  s2   s22 2   k2 
multiple efforts of the second member（ s2 、 k2 ）.For
convenience of analysis, as
suming that k2 was a duality decision variable, and
（5）
In equation (5),  is the cost of the second
s
s
of the first member ( 1 ) and the second member ( 2 ), but
also by the impact of the core competitiveness knowledge
individual efforts of the first member （
C  s2   s22 2   k2
s1  arg max 1   k2  s1  s2   s12 2   M  I 1   k2  s1  s2  
In the optimization model, the first member need not
pay the second member more than the second member’s
reservation utility. Therefore, the model sets participation
constraints, and brings out the total receipts of the second
member from the angle of the risk premium and the cost.
Therefore, the first member problem can be simply
expressed as:
2
2
2 2
（7）
Maxmize F  s1 2  s2 2   k2  rI  2
M ,I
s.t.
s2 , k2  arg max  M  I 1   k2  s1  s2   s22 2   k2 
s1  arg max 1   k2  s1  s2   s12 2   M  I 1   k2  s1  s2  
（8）
（9）
N  0,  2 
。
Assume that the revenue of the second member after
it joins in the team (Based on linear incentive model) may
be expressed as:
III. THE INFORMATION SOLUTION WHEN TEAM
MEMBERS’ EFFORT LEVEL CAN BE OBSERVED
Where Q is the total receipts of the the second
member; M is the fixed income of the second member; I
is the incentive level, 0  I  1 ; P is the team output
performance indicator (such as output, output value, etc.)
Assume that a cost of effort of the first member is:
Assume that the efforts of two members were
observed, (For example, in the absence of bilateral moral
hazard problem) the first member’s optimal result could
be achieved through paying the second member that equal
to the rewards reservation utility plus the cost of effort.
With these assumptions, the first member can be stated as:
2
2
（10）
Maxmize 1  k2  s1  s2   s1 2  s2 2   k2
Q  M  IP
C  s1   s12 2
（4）
For the second member’s multiple inputs, we assume
that the cost function as follows:
s1 , s2 , k2
A. The optimal level when k2  1
When the second member contributes its knowledge,
we could yield the optimal solution to the efforts of two
members and the receipts of the first member according to
equation (10):
s1*  1  
s  1 
*
2
H k*2 1  (1   )2  
B. The optimal level when k2  0
Meanwhile, according to equation (10), we can yield
the optimal solution to the efforts of two members and
receipts of the first member when the second member
does not contribute its knowledge:
s1*  1
s2*  1
H k*2 0  1
The first member in order to make k2  1 , If and only
if
H k*2 1  H k*2 0
 1       1
2
 I    1   
k  0 , then
If 2
I   s1  s2   
 I     s1  s2 
 I    1   k2 
（15）
From equation (14) and (15), there will be three
possible scenarios of stimulation to induce the second
I    1   
member to contribute knowledge. When
,
obviously the second member does not want to contribute
its knowledge. When I    , The second member will
  1     I   
contribute its knowledge. When
，it
will not be sure that the second member contributes its
knowledge. Figure 1 describes the possible scenarios
whether the second member contributes its knowledge.
A. Region Ⅰ
I    1   
In this region,
and k2  0 . Hereby, the
incentive level is too low to induce the second member to
contribute knowledge.( k2  0 ) According to formula (11)
and (12) we can obtain:
       2
Therefore, we define the upper limit of  as
    2
IV. THE INFORMATION SOLUTION WHEN TEAM
MEMBERS’ EFFORT LEVEL CAN NOT BE
OBSERVED
Further, to examine the more realistic situation, that
is, team members’ efforts level can not be directly
observed, but the team's output P can be observed.
From the constraints (8), obtaining the first-order
condition is:
s2  I 1   k2 
（11）
From the constraints (9), obtaining the first-order
condition is:
s1  1  I 1  k2 
（12）
Therefore,
s1  s2  1   k2
（13）
According to the conditions (8), considering
marginal revenue and cost of the second member
contribution variable k2 , we can obtain the following
relationship:
If k2  1 , then
I   s1  s2   
 I     s1  s2 
 I    1   k2 
（14）
s1  1  I
and s2  I
intervalⅠ
I    1   
k2  0
IntervalⅡ
intervalⅢ
  1     I   
k2  0
or
k2  1
  1   
I  
k2  1
 
I
Fig.1 Situation of motivating the second member to contribute
knowledge
Take these values into formula (7):
Maxmize 1  1  I 2 2  I 2 2  rI 2 2 2
I
The first order condition is:
I1  1
2  r 2
（16a）
Using the formula (16a), (11) and (12) we can obtain
directly the efforts of two members and the second
member’s compensation, the first member’s expected
revenue:
s11  1
1 1
1  r 2
1
s2  1
2  r 2
  3  r 2 
M1 
2
2  2  r 2 
（16b）
（16c）
（16d）
Q1  1  r
（16e）
2
H 1  3  r
2  2  r 2 
2
2
（16f）
2  2  r 2 
B. Region III
In this region, I    ， k2  1 . Hereby, the level of
stimulation is high enough to induce the second member
to contribute its knowledge ( k2  1 ), According to formula
(11) and (12), we can obtain:
s1  1  I 1   
和 s2  I 1   
Take these values into formula (7)
Maxmize 1   2  1  I 2 1   2 2  I 2 1   2 2  rI 2 2 2
I
The first order condition is:
I3 
1
（17a）
2
2  r
1   
make k2  1 , you need a higher incentive level. From
equation (11) (12) and (l7a), you can directly gain the
efforts of two members, the remuneration of the second
member, and expected income of the first member:
 1   2  r 2 
（17b）
s13  
 1   
 2 1   2  r 2 


1   
2
2 1     r 2
4
2
1     1     r 2 
3
Q 
3
H3 
 2 1   2  r 2 


1   
2
3 1   
2
2
（17c）

 r 2
2  2 1     r 2 


2
（17d）
2
 
（17e）
As long as   0 , based on comparison of members’
contributions between in the regional Ⅰand in the region
Ⅲ we could obtain:
s3  s 1
1 , the first member’s effort in the region Ⅲ is
① 1
more than that in the regionⅠ.
s3  s 1
2 ，the second member’s effort in the region Ⅲ
② 2
is more than that in the regionⅠ.
We can get a conclusion hereafter(1): high level of
stimulation in the region Ⅲnot only can induce the second
member
because of the higher s2 and k2 of the second member, for
the first member, a free-riding motivation come into
[18]
being. However, contrary to the Holmstrom’s
conclusions of free-riding in a team production, our study
show that the increase of the contribution of the second
member at the same time, the first member will increase
its own contribution too. Benefit directly from a high
contribution of the second member, the first member
would increase its marginal productivity itself.
In this case, because the first member has the
residual claim, and thus encourage it to increase its own
contribution, rather than to shirk its responsibility.
C. Region II
  1     I   
In this region,
，it is possible or
not for the second member to contribute its knowledge（
k2  0 or k2  1 ）.From the angle of  , this region may be
2
Obviously, for any value  was taken, it is certain
3
1
that I  I . This is not surprising, because in order to
s23 
This consequence may be somewhat surprising,
to contribute
k2
, but also cause the second
member to make a higher level of effort(
the first member accordingly(
s1
).
s2
), and so can
also shown in Figure 2 for three intervals:
intervalⅰ
intervalⅱ
  I
I     I  1   
k2  1
k2  0 or k2  1
  I  1   
k2  0
I  1   
I
Fig. 2
interval ⅲ

Influence of contribution cost on knowledge sharing
We can conclude from Figure 2, the separation of the
intervals is very intuitive. When the second member’s
cost ( k2 ) of contribution knowledge is very high (i.e.  is
very high), the second member will not choose to share its
knowledge. On the other hand, when the second
member’s cost ( k2 ) of contribution knowledge is very
low, the second member will choose to share its
knowledge. However, the situation of contribution
knowledge in interval ⅱ is not clear. Whether the first
member encourages the second member to make
contribution its knowledge in interval ⅱ , depends on
weather the revenue of the first member can be increased
in the case of contribution knowledge from the second
member ( k2  1 )rather than not( k2  0 ). Then, in interval
ⅱ , the necessary condition of the first member’s
encouragement the second member to contribution
knowledge can be expressed as:
H k2 1  H k2 0
（18）
From the previous derivation,
H 1  H k2 0  3  r
2
2  2  r 2 
H  H k2 1 
3
1   
2
3 1   
2
 r 2
2  2 1     r 2 


2
2
 
REFERENCES
Therefore, the necessary condition of encouragement
the second member to contribute knowledge in the
interval ⅱ may be obtained by the following calculation:
H k2 1  H k2 0


1   
2
3 1     r    
2
2  2 1     r 2 


2
1   
2
2
2
3 1     r    
2
2  2 1     r 2 


2
2
2
3  r 2
2  2  r 2 
3  r 2
2  2  r 2 
2
2
4
2
6 1    1     1  3r 2 1     1   r 2  1     1






 
2
2 
2
2  2  r  2 1     r


(19)
The conclusions (2) from the above: whether to
motivate the second member to share its knowledge in the
2
interval ⅱ depends on the risk factors ( r ), the
2
sensitivity
   of the influence of k

cost(
2
on the team output,
as well as the
) of the second member
contribute its knowledge.
to
V. CONCLUSION
This paper studies the effectiveness of the dynamic
mechanism of knowledge sharing in the research team.
Studies have shown that:
1st. There are three decision variables which are able
to influence knowledge sharing among research team,
they
are
sensitivity

cost( )
risk
 
factors,
risk
factors
( r
2
),the
of the influence on the team output, the
of member
2 to contribute its knowledge.
When the second member’s cost of contribution
knowledge is relatively lower, the first member is easier
to induce the second member to share its knowledge
through the incentive mechanism. However, the first
member’s benefits from encouragement other members to
share their knowledge, depends on the sensitivity of the
impact of the knowledge-sharing team output. In addition,
if the risk factor was very high, the first member should
have to pay the second member a very high risk premium.
2nd. When the first member induces the second
member to share its knowledge in use of incentive
mechanism, the first member will increase its own
investment in team production, which is different from the
phenomenon of free-riding in team production.
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